Case Study on Milkfish Production of Illera Fish Farm

7/27/2019 Case Study on Milkfish Production of Illera Fish Farm

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LIEZL GRACE M. JARDO

PHOEBE T. PECHON

JOHN PAUL S. SUABERON

(Researchers)

Presented to

DR. JOY C LIZADA

Case Study on Milkfish

Production of Illera Fish Farm


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Acknowledgement

We greatly acknlowledge the contributions of the following individuals whom without their

help and support, this forecasting paper would not have been possible:

to Marguerite Marie Illera and her family for providing us with the data set and other

information about their farm which we greatly needed;

to Jardos Residence for welcoming and accommodating us during the drafting of this paper;

to Tita Guia Martin for allowing us to stay overnight in her boarding house as we make

this paper;

to our families and friends for their moral support;

to Dr. Joy C. Lizada for her guidance and mentoring;

and to the God Almighty, for the wisdom and perseverance that he has bestowed upon us;

and to those who in one way or another has helped in the success of this paper.

The Researchers


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Table of Contents

Acknowledgement .................................................................................................................................................... 1

Table of Contents ...................................................................................................................................................... 2

List of Tables ............................................................................................................................................................... 3List of Figures ............................................................................................................................................................. 3

List of Appendices .................................................................................................................................................... 3

Introduction ................................................................................................................................................................ 4

Objectives of the Study ........................................................................................................................................... 6

Scope and Limitations............................................................................................................................................. 6

Methodology ............................................................................................................................................................... 6

i. Data Preparation ........................................................................................................................................ 7

ii. Sequence Chart Creation ......................................................................................................................... 7

iii. Benchmark Setting .................................................................................................................................... 7

iv. Data Pocessing ............................................................................................................................................. 7

v. Summary and Implication ................................................................................................................... 10

vi. Creation of Figures ................................................................................................................................. 11

Presentation of Data ............................................................................................................................................. 11

Forecasts and Accuracy Testing ...................................................................................................................... 15

Naive Forecasting Model .................................................................................................................................. 8

Moving Average .................................................................................................................................................... 8

Simple Exponential Smoothing ...................................................................................................................... 8

Time Series Regression ..................................................................................................................................... 9

Linear Trend Exponential Smoothing ......................................................................................................... 9

Non Linear Exponential Smoothing .......................................................................................................... 10

Summary/Implications ....................................................................................................................................... 20

Appendices ............................................................................................................................................................... 22

Bibliography ............................................................................................................................................................ 55


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List of Tables

Table 1. Production of milkfish (kg) by Illera Fish Farm. ................................................................... 11

Table 2. Calendar of milkfish farmer's in Dumangas. ................ Error! Bookmark not defined.

Table 3. Summary of Forecasting Models .................................................................................................... 21

Table 4. Nave Forecasting Model ................................................................................................................... 23

Table 5. Moving Average, N=3 ............................................................. Error! Bookmark not defined.

Table 6. Identification of , =0.1 ................................................................................................................... 28

Table 7. Simple Exponential Smoothing, =0.9 ........................................................................................ 34

Table 8. Linear regression calculations. .......................................... Error! Bookmark not defined.

Table 9.Time Series Regression ....................................................................................................................... 35

Table 10. Exponential smoothing with a linear trend, 1= .90, 2=.01.......................................... 45

Table 11. Non- Linear Smoothing, 1= .90, 2=.0, =.7 .......... Error! Bookmark not defined.

List of Figures

Figure 1.Data Analysis Process ................................................................................................... 11

Figure 2. Annual production of milkfish Chanos chanosin kilograms (Kg)............................. 13

Figure 3.Production of milkfish Chanos chanosin kilograms (Kg) per quarter...................... 14

Figure 4. Moving averages vs data..................................................Error! Bookmark not defined.

Figure 5. Forecast vs data with simple exponential smoothing...Error! Bookmark not defined.

Figure 6. Forecast using the time regression vs the data.............Error! Bookmark not defined.

Figure 7. Comparison of exponential smoothing with a linear trend data vs forecast.....Error!

Bookmark not defined.Figure 8. Comparison of exponential smoothing with a non-linear trend data vs forecast.

...........................................................................................................Error! Bookmark not defined.

List of Appendices

Appendix 1. Nave Forecasting Model ........................................................................................... 23

Appendix 2. Moving Average ...................................................................................................... 24

Appendix 3. Simple Exponential Smoothing.............................................................................. 28

Appendix 4. Time Series Regression .......................................................................................... 35

Appendix 5. Linear Exponential Smoothing .............................................................................. 37

Appendix 6. Non Linear Smoothing ............................................................................................ 47

Appendix 7. Milkfish production report by Illera fish pond as of September 15, 2013 ............... 54


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Introduction

In a country where fish is one of the main sources of animal protein, aquaculture

or fish culture can be expected to play a comparatively big role in supplying fish.

Milkfish aquaculture in the Philippines dates back to the 14thcentury. In 2004 and

2005 Philippines ranked first among the top milkfish producers in the world with a

total production of 273,456 MT and 289,000 metric tons. Today the country

produces about 391,983 metric tons, valued at Php 35.5 million. (Bureau of

Agricultural Statistics, 2012) and almost 99% of the harvest is consumed

domestically.

Milkfish is a mainstay in the Philippine diet and traditionally considered the

national fish. It is farmed under conditions ranging from freshwater ponds to

marine pens, but mostly in brackish ponds. The province of Iloilo is one of the top

milkfish producing provinces in the country, with production reaching 24,744 tons.

The towns of Barotac Nuevo and Dumangas, in particular, have extensive fishpond

areas leased from the government (FLAs) dedicated to milkfish farming.

Illeras fish farm is one of the aquaculture businesses found in Dumangas Iloilo.

It started last 2003, as a partnership between a bachelor and his brother in law. The

farm was approximately 8 hectares when it started and it operated quite some years

before the bachelor bought out his brother in laws shares. The brother in law

ventured to other businesses causing him to agree and sell his shares on the fish

farm. The farm cultures milkfish since it is the most profitable and most efficient fish

to culture in the said place. It is the most popular seafood dish among Filipinos and

is mostly used for Iloilos best cuisine. It is a tough and sturdy fish that could easily

adapt to its environment making it suitable for aquaculture and cultivation.


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Through the years the farm experienced circumstances that caused some

hindrances to its operation. Just like the climate change, the unexpected typhoons

(Frank 2008) that caused flash floods in various places in Iloilo, fish kill (2011) and

a lot more. Yet, because of good business operations, with the help of some fish

technologies, Illeras farm was able to overcome these hindrances and sustained its

operations causing its high production.

Today, the fish farm is approximately 15 hectares with 2 underdeveloped areas.

For 10 years it continued to culture milkfish. It plans to culture more aquatic

animals in the future like shrimps, tilapia and others. But in the mean time, it

focuses on milkfish and how to culture it best using some fish technologies to

increase production. The owner wanted to maximize its profit first using the

resources it has and expects to someday expand more and culture its desired

aquatic animals.

The purpose of this study is to forecast the last quarter of the year 2013 in

Illeras farm. Through this, the owner will be able to predict possible future

production, whether it may be profitable or not. It will also help the owner know if

the current factors of production contribute to future profitability or loss of the fish

farm. If there will be loss, it may help the owner analyze where the cause of the

inefficiency and may be able to plan out future course of action applicable in order

to eradicate the loss make it profitable instead.


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Objectives of the Study

To be able to analyze the data gathered using different models of forecasting andapply it to predict the future production of milkfish at Illeras fish farm.

To be able to identify the effect of technology, climate change and supply shocks onthe production of milkfish at Illeras fish farm

To be able to relate the analysis of the case to the future state of the milkfishindustry in Iloilo Province.

Scope and Limitations

The study limits its scope to the data which was strictly gathered from Illera Fish

Farm located at Dumangas, Iloilo. Further, it is only limited to Milkfish Chanos Chanos

cultured in brackish water fish ponds of the said fish farm. It merely focuses on the volume

of production in kilogram (kg) and excludes its monetary value inpeso () from the

first quarter of 2006 to the second quarter of 2013, which is used to forecast the

production of milkfish for the third period.

Methodology

The study utilizes both quantitative and qualitative data collection tools but still

rooted in a qualitative epistemological position that recognizes the importance of locating

the research within an economic, technological and environmental context. It also takes

seriously the social construction of these contexts and the identities the participants

construct within them.

The study used a milkfish production in kilograms (kg) data set from Illera Fish

Farm located at Dumangas, Iloilo to be examined using different forecasting and accuracy

tests (Nave Forecasting Model, Moving Average, Simple Exponential Smoothing, Time

Series Regression, Linear Trend Exponential Smoothing, Non linear Exponential Smoothing).


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The data set was collected on a quarterly basis from the first quarter 2006 to the second

quarter of 2013.

This study focused on milkfish production forecasting. The data analysis process

involved six procedures, as shown in Fig. 1 and described below.

i. Data PreparationTime series data from the first quarter of 2006 to the second quarter of 2013 was

used to prepare a data set for 30 quarters from the last quarter of 2013 to the last quarter

of 2015 forecasting.

ii. Sequence Chart CreationA sequence chart to consider milkfish production trends from the first quarter of

2006 to the second quarter of 2013 was plotted before the forecasts were created. This

chart displayed milkfish production trends to examine a seasonality factor within the trends,

so that suitable forecasting techniques were selected and utilized.

iii. Benchmark SettingThe Nave Forecasting Model was the first to be made to seve as the bench mark

model in order to check the accuracy of each models used (Moving Average, Simple

Exponential Smoothing, Time Series Regression, Linear Trend Exponential Smoothing, Non

linear Exponential Smoothing).

The study uses the Mean Square Error (MSE) to measure the accuracy of the

forecast over Mean Absolute Forecast Error or MAD (Mean Absolute Deviation) and the

Mean Percentage Error (MAPE) which are the other possible accuracy evaluation because

MSE gives more weight to large errors because they are squared and large forecast errors

can be extremely disruptive.

iv. Data PocessingMoving Average, Simple Exponential Smoothing, Time Series Regression, Linear

Trend Exponential Smoothing and Non linear Exponential Smoothing were used for


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forecast and was immediately compared to the Nave Model for deciding whether the Model

is appropriate.

The models MSE must beat that of the benchmark model in order to be an

appropriate model forecast to be considered.

Naive Forecasting Model

The formula for the Nave Forecasting Model which is the bench mark model

is:

Ft+1= Xt

where F is the forecast and X is the observed value. The subscript t is the index for the time

period as used in Appendix 1.

The formula for the forecast error in each period is :

et= Xt- Ft

where et is the error, Xt is the Data and Ft is the forecast as used in Appendix 1.

The data set (30 quarters) was divided in half and the forecasting samples were

used to compute the mean error measures.

Moving Average

Unweighted moving average, N is assigned with a value of 3. The forecasting

equation is:

Ft+1= (Xt+ Xt-1+Xi-2)/3

Simple Exponential Smoothing

The formula for Simple Exponential Smoothing is:

Ft+1= Ft+e1

where Ft+1 is the forecast for t+1, Ft is the forecast for t and e1is x Error in t.

For the model, F1 is equivalent to 727.00, the average of the warm- up sample. The

choice of has a considerable impact on the forecast. The best fitting value of is the one


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with the minimum MSE in the warm- up sample and 0.9 was then identified as the best to

be used as shown in Appendix 3.

Time Series Regression

The time-series regression is an analysis used to compare the bulk of production

versus the quarter when it was produced.

The best fitting line is the one which minimizes the sum of the squares of the errors

between the estimated points on the line and the actual production using the least- squares

method with the formula: Ft= a + b where Ft= forecast for t, a= the point at which the trend

line intercepts the x (production) axis, b= slope of the trend line, t= time, in this case, the

quarter of the year.

The slope was computed using the formula:

b=(tX-n )/ (t2-n 2),

where b= slope, t= time, X= dependent variable (production), = mean of the values of t and

= mean of the values of X.

Intercepts are calculated by the formula:

A= - b

Linear Trend Exponential Smoothing

The errors are used to continually adjust the intercept and the slope of the trend

line where adjustments are made with a sequence of equations repeated each period:

Smoothed level at the end of t = forecast of t + 1 error in t,

Smoothed trend at the end of t= smoothed trend at the end of t- 1 + 2 error in t,

And forecast for t +1= smoothed level at the end of t + smoothed trend at the end of t.


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In symbols, St= Ft+ 1et,, Tt=Tt-1 + 2et, Ft+1= St+Ttwhere Stis the smoothed level and Tt

is the smoothed trend. Smoothing parameters are 1 and2. The computations are shown in

shown in Appendix 5.

Since the intercept and slope of the regression are always used as the initial values

of S and T, a time series regression was first made on the warm- up sample.

S0= a, and T0=b where a= 109.1 and b= 56.1. 1= 0.9 and 2= 0.01 where the best

fitting 1 and 2 determined by finding the pair with the Minimum MSE computations as

shown in Appendix 5.

The formula for solving the error is: et= Xt-Ft.

Non Linear Exponential Smoothing

The formula for exponential smoothing model for nnon- linear trend is:

Smoothed level at the end of t= forecast for t + 1 error in t,

Smoothed trend at the end of t= smoothed trend at the end oft- 1 + 2error in t,

and Forecast for t + 1 = smoothed level at the end of t + smoothed trend at the

end of t.

In symbols, St= F1+ 1, , Tt= t-1+ 2et Ft+1=St+Tt.

Since the data set exhibits an exponential trend, >1 and is equal to 0.9. 1= 0.9 and

2= 0.01 were the best fitting 1 and 2.

v. Summary and ImplicationForecasting results from Moving Average, Simple Exponential Smoothing, Time

Series Regression, Linear Trend Exponential Smoothing, Non linear Exponential Smoothing

were analysed in order provide the figures for the forecast and to come up with the answers

to the objectives of this study and to conclude the implications of the findings.


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vi. Creation of FiguresFigures were created to present forecasting results, comparisons and errors so that

the manager or the decision maker may have a better understanding or vision before

planning and/or making decisions.

Figure 1.Data Analysis Process

Presentation of Data

In order to forecast production of milkfish in kilogram (kg) by the Illera Fish Farm

for the last quarter of 2013, data set from the second quarter of 2006 to the second quarter

of 2013 were used for the forecasting models, totalling into 30 quarters.

The data set collected from the said farm is presented in the following table.

Table 1. Production of milkfish (kg) by Illera Fish Farm.

Year Quarter t Production in Kgs

2006 2006-1 1 750

DataPreparation

Sequence ChartCreation

BenchmarkSetting

Data ProcessingSummary and

ImplicationCreation of

Figures

Start Process

Process Finish


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2006-2 2 685

2006-3 3 715

2006-4 4 775

2007 2007-1 5 795

2007-2 6 695

2007-3 7 705

2007-4 8 790

2008 2008-1 9 815

2008-2 10 685

2008-3 11 525

2008-4 12 635

2009 2009-1 13 825

2009-2 14 735

2009-3 15 895

2009-4 16 965

2010 2010-1 17 995

2010-2 18 865

2010-3 19 915

2010-4 20 995

2011 2011-1 21 1125

2011-2 22 905

2011-3 23 965

2011-4 24 1185

2012 2012-1 25 1245

2012-2 26 955


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2012-3 27 1005

2012-4 28 1210

2013 2013-1 29 1285

2013-2 30 1065

TOTAL 26705

Figure 2. Annual production of milkfish Chanos chanosin kilograms (Kg).

The graph shows an increasing production in Illeras fish farm through the years,except on the third quarter of year 2008. It was because of the Typhoon Frank (2008), the

most devastating typhoon in the history of province. It occurred midway between the

second and third quarter of the year.

The aftermath of Typhoon Frank is very evident, as such that it can be seen in the

sudden drop in production from 685 kg on the second quarter to 525 kg on the third

0

200

400

600

800

1000

1200

1400

P

r

o

d

i

n

k

g

t-Quarter

Illera's Fish Farm Production (2006-2013)

Production in Kgs


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quarter of the year 2008. As shown in figure 2, comparing the data from 2007 to 2008, a

decrease in fish production can be seen thus, a total loss of 325 kg.

After the typhoon, the farm started to recover its resources. During the year 2010,

an overall expansion was done by the management, which caused a slight increase of only

30 kg in the production for the first and second quarter. The expansion brought more fish to

breed at the farm, resulting to a dramatic increase in production of 155 kg from the second

to third quarter.

Figure 3.A Comparison of Illeras Fish Production per Quarter from 2006-2013

The fluctuations seen in figure 3 are caused different externalities such as weather

conditions, calamities, drought, tides and etc.

Extreme fluctuations as seen in figure 3 are due to an externality that happened in

Illeras farm. There is a dramatic decline in 2008 third and fourth production because of

Typhoon Frank. Dikes were destroyed which caused a big loss in the farms total fishproduction. Other externalities that affect fish production are changing weather conditions

and natural calamities such as flash flood, droughts and tides.

0

200

400

600

800

1000

1200

1400

2006 2007 2008 2009 2010 2011 2012 2013

p

ro

d

i

n

k

g

time- quarter

Q2

Q3

Q1

Q4


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Forecasts and Accuracy Testing

Results and discussions for the different forecasting models that were tested using

the raw and the deseasonalized data are presented below.

Naive Forecasting Model

Using the Nave Forecasting model, the following figure shows the forecasted production of

milkfish in kilogram over time t, per quarter. Both the raw and deseasonalized data were

presented.

Figure 4. Graph of naive forecasting model for production of milkfish.

The forecasted production of milkfish for the third quarter of 2013 using the Nave

Model is 1,065.00 and when deaseasonalized is equal to979.22.

The Mean Square Error (MSE) was then computed by dividing the sum of the

squared error by the number of forecasting samples (15 forecasting samples). The MSE forthe Nave Forecasting model is 22,343.33 and the deseasonalized MSE is 75,437.27,

computations shown in Appendix 1 Table 4.

Moving Average

0.00

200.00

400.00

600.00

800.00

1,000.00

1,200.00

1,400.00

1,600.00

2006-1

2006-3

2007-1

2007-3

2008-1

2008-3

2009-1

2009-3

2010-1

2010-3

2011-1

2011-3

2012-1

2012-3

2013-1

2013-3

P

r

o

d

i

n

K

g

t- Quarter

Raw Xt

Deseasoned Xt

Nave

Deseasoned Nave


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Results for the moving average model is ___________________________, the forecast for the third

quarter of 2013 is 1,141.25 and when deaseasonalized is 1,149.87. The forecast using the

moving averages versus the data is shown in Figure 2 above.

Figure 5. Moving average versus data.

MSE of both the undeseasonalized and the deseasonalized data were computed and was

found out to be 16,292.71 (computation shown in Appendix 2) and 42,861.34 respectively.

Compared to the raw and the deseasonalized MSE of Nave Model, 22,343.33 and 75,437.27,.

this forecasting model is an improvement but (state why its not good to be used) this is not

a suitable model for forecasting the production of milkfish.

Simple Exponential Smoothing

From the computed Simple Exponential Model both raw and deseasonalized data, the

forecast for the third quarter of 2013 is 1,008.87 kg and 1,016.56, r espectively.

0.00

200.00

400.00

600.00

800.00

1,000.00

1,200.00

1,400.00

1,600.00

2006-1

2006-3

2007-1

2007-3

2008-1

2008-3

2009-1

2009-3

2010-1

2010-3

2011-1

2011-3

2012-1

2012-3

2013-1

2013-3

P

r

o

d

i

n

k

g

Time- quarter

Raw Xt

Deseasoned Xt

Moving Average

Deseasoned MA


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Figure 6. Forecast vs data with simple exponential smoothing.

The MSE for raw and deseasonalized data for Simple Exponential Smoothing model

is 43,946.61 and 73,275.64 respectively as shown in Appendix 3., which is very high

compared to the MSE of the Nave Model Compared to the raw and the deseasonalized MSE

of Nave Model, 22,343.33 and 75,437.27, what is the decision.

Time Series Regression

As shown in the Figure 5, a straight line trend was drawn. Before coming out with the

increasing linear trend it was identified that the following figures are necessary, the slope

b=56.1, the intercepta=109.1, and theFt =109.1 + 56.1t.

0.00

200.00

400.00

600.00

800.00

1,000.00

1,200.00

1,400.00

1,600.00

2006-1

2006-3

2007-1

2007-3

2008-1

2008-3

2009-1

2009-3

2010-1

2010-3

2011-1

2011-3

2012-1

2012-3

2013-1

2013-3

P

r

o

d

i

n

k

g

time- quarter

Raw Xt

Deseasoned Xt

SES

Deseasoned SES


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Figure 7. Forecast using the time regression vs the data.

A good forecast was shown in the graph, forecasting the next harvest of 1,848.2 kg for raw

data and 735.66 kg for the deseasonalized data, if we ignore all other externalities such as

calamities, expansion, and etc., it is a good guess of what will be the harvest for the next few

quarters, however based on the historical data, the MSE of the Nave Model both raw and

deseasonalized are 22,343.33 and 75,437.27, better than the nave forecast but highercompared to all others, which in this case, less accurate.

Linear Trend Exponential Smoothing

0.00

200.00

400.00

600.00

800.00

1,000.00

1,200.00

1,400.00

1,600.00

2006-1

2006-3

2007-1

2007-3

2008-1

2008-3

2009-1

2009-3

2010-1

2010-3

2011-1

2011-3

2012-1

2012-3

2013-1

2013-3

P

r

o

d

i

n

k

g

T- quarter

Raw Xt

Deseasoned Xt

TSR

Deseasoned TSR


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Figure 8. Comparison of exponential smoothing with a linear trend data vs forecast.

Solving for Linear Exponential Smoothing is shown in Appendix 5.

There was an MSE of 27,146.89 for the raw data and 60,228.27 for the deseasonalizeddata. Forecast for the total production of milkfish for the third quarter of 2013 for raw data

is 1,139.86 and for the deaseasonalized data is 1,345.13.

Non Linear Exponential Smoothing

The computations shows that there is an MSE of 19,596.88 for raw data and 56,851.15 forthe deaseasonalized data. Forecast for the third quarter of 2013 for raw data is 1,345.13 kgs

and 1,250.16 when deseasonalized.

0.00

200.00

400.00

600.00

800.00

1,000.00

1,200.00

1,400.00

1,600.00

2006-1

2006-3

2007-1

2007-3

2008-1

2008-3

2009-1

2009-3

2010-1

2010-3

2011-1

2011-3

2012-1

2012-3

2013-1

2013-3

P

ro

d

i

n

k

g

time- quarter

Raw Xt

Deseasoned Xt

ESLT

Deseasoned ESLT


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Figure 9. Comparison of exponential smoothing with a non-linear trend data vs

forecast.

Solutions for solving the forecast and error for this model is shown in Appendix 6.

Summary/Implications

The increasing trends in milkfish production is due to the different fisheries development,

technology and innovations that were used and adapted by the said fish farm as an answer

to the previous decreasing trends due to climate change, calamities and other supply shocks

that brought an adverse decline of production. They had been open to expansion of their

farms; training of their caretakers for better fish-handling and harvesting; built stronger

dikes that are able to hold strong water pressure; invested for a machine that collects

harmful algae and turn them into fish feeds; invested for a hatchery for fry stocking; exports

fresh milkfish not only to other towns inside Iloilo but also to Bacolod and Manila through

roll-on, roll-off ships at the Dumangas Port; and most importantly help maintains the

cleanliness of coasts alongside Iloilo.

0.00

200.00

400.00

600.00

800.00

1,000.00

1,200.00

1,400.00

1,600.00

2006-1

2006-3

2007-1

2007-3

2008-1

2008-3

2009-1

2009-3

2010-1

2010-3

2011-1

2011-3

2012-1

2012-3

2013-1

2013-3

Pr

o

d

i

n

k

g

time- quarter

Raw Xt

Deseasoned Xt

SNT

Deseasoned SNT


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Table 2. Summary of Forecasting Models

Quantity Data NaveForecast

Moving

Averages

Time Series

Regression

Simple

Exponenti

al

Smooting

Exponential

Smoothing

in a Linear

Trend

Forecast

Smoothing in

a Nonlinear

Trend

Forecast

t Xt Ft Ft+1 = (Xt+ Xt-1 +Xt-2)/3

Ft= a + bt Ft+1= Ft+

et,1=.9Ft 1=.9

2=.01

Ft 1=.9

2=.01=.9

0

2006-1 720.00 639.04 712.67 639.04 630.81

2006-2 695.00 720.00 666.46 719.27 740.13 725.14

2006-3 715.00 695.00 693.88 697.43 727.29 707.65

2006-4 735.00 715.00 710.00 721.30 713.24 743.88 721.06

2007-1 775.00 735.00 715.00 748.72 732.82 763.45 738.46

2007-2 755.00 775.00 741.67 776.14 770.78 801.53 775.00

2007-3 770.00 755.00 755.00 803.56 756.58 786.87 759.42

2007-4 790.00 770.00 766.67 830.98 768.66 798.73 770.71

2008-1 790.00 790.00 771.67 858.40 787.87 817.83 789.44

2008-2 735.00 790.00 783.33 885.82 789.79 819.47 790.91

2008-3 425.00 735.00 771.67 913.24 740.48 769.28 740.87

2008-4 530.00 425.00 650.00 940.66 456.55 481.82 454.57

2009-1 625.00 530.00 563.33 968.08 522.65 548.06 521.58

2009-2 780.00 625.00 526.67 995.50 614.77 640.95 614.76

2009-3 850.00 780.00 645.00 1,022.92 763.48 791.13 764.71

2009-4 935.00 850.00 751.67 1,050.34 841.35 869.74 842.93

2010-1 995.00 935.00 855.00 1,077.76 925.63 954.75 927.46

2010-2 1,025.00 995.00 926.67 1,105.18 988.06 1,017.66 989.88

2010-3 1,180.00 1,025.00 985.00 1,132.60 1,021.31 1,051.02 1,022.88

2010-4 1,230.00 1,180.00 1,066.67 1,160.02 1,164.13 1,195.15 1,166.36

2011-1 1,310.00 1,230.00 1,145.00 1,187.44 1,223.41 1,254.91 1,225.53

2011-2 1,340.00 1,310.00 1,240.00 1,214.86 1,301.34 1,333.43 1,303.47

2011-3 1,395.00 1,340.00 1,293.33 1,242.28 1,336.13 1,368.35 1,337.95

2011-4 1,420.00 1,395.00 1,348.33 1,269.70 1,389.11 1,421.61 1,390.81

2012-1 1,490.00 1,420.00 1,385.00 1,297.12 1,416.91 1,449.42 1,418.35

2012-2 1,540.00 1,490.00 1,435.00 1,324.54 1,482.69 1,515.61 1,484.22

2012-3 1,580.00 1,540.00 1,483.33 1,351.96 1,534.27 1,567.47 1,535.792012-4 1,635.00 1,580.00 1,536.67 1,379.38 1,575.43 1,608.78 1,576.84

2013-1 1,650.00 1,635.00 1,585.00 1,406.80 1,629.04 1,662.67 1,630.48

2013-2 1,685.00 1,650.00 1,621.67 1,434.22 1,647.90 1,681.44 1,649.09

2013-3 1,685.00 1,656.67 1,461.64 1,681.29 1,714.85 1,682.39

MSE 4,178.33 15,305.2

2

28,888.41 4,930.86 2,055.56 4,722.52


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Conclusion and Recommendation

Brackish water fish farming had been a major contributor to the country s

agricultural and economic development,and it was known that the town of Dumangas had

been a big producer of milkfish, through the help of the Local Government Units, the Bureau

of Fisheries and Aquatic Resources, and the Department of Science Technology milkfish

farming and industry in the future would have an increasing trend, with the new

developments and innovations in the field of fisheries partnered with the programs and

projects of the LGUs the forecasts for a high production in the near future will be reached.

This programs and projects should not just be doable as it would yield high profit

for us, but also courses of actions that would answer environmental problems and

incorporate technology into it.

Appendices

Appendix 1. Raw data of illera milkfish fish farm production.

Year Quarter t Production in Kgs

2006 1 1 750

2 2 685


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3 3 715

4 4 775

2007 1 5 795

2 6 695

3 7 705

4 8 790

2008 1 9 815

2 10 685

3 11 525

4 12 635

2009 1 13 825

2 14 735

3 15 895

4 16 965

2010 1 17 995

2 18 865

3 19 915

4 20 995

2011 1 21 1125

2 22 905

3 23 965

4 24 1185

2012 1 25 1245

2 26 955

3 27 1005

4 28 1210

2013 1 29 1285

2 30 1065

TOTAL 26705

Appendix 2. Nave Forecasting Model

Table 3. Nave forecasting model

Quarter Data Forecast ErrorAboslute

Error

Absolute Percentage

Error

Squared

Error

t Xt Ft et=Xt- Ft |et| |et/Xt|x 100 e2

2006-1 1.00 1 750

2006-2 2.00 2 685 750 -65

2006-3 3.00 3 715 685 30

2006-4 4.00 4 775 715 60


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2007-1 5.00 5 795 775 20

2007-2 6.00 6 695 795 -100

2007-3 7.00 7 705 695 10

2007-4 8.00 8 790 705 85

2008-1 9.00 9 815 790 25

2008-2 10.00 10 685 815 -130

2008-3 11.00 11 525 685 -160

2008-4 12.00 12 635 525 110

2009-1 13.00 13 825 635 190

2009-2 14.00 14 735 825 -90

2009-3 15.00 15 895 735 160

2009-4 16.00 16 965 895 70 70

2010-1 17.00 17 995 965 30 30

2010-2 18.00 18 865 995 -130 130

2010-3 19.00 19 915 865 50 50

2010-4 20.00 20 995 915 80 802011-1 21.00 21 1125 995 130 130

2011-2 22.00 22 905 1125 -220 220

2011-3 23.00 23 965 905 60 60

2011-4 24.00 24 1185 965 220 220

2012-1 25.00 25 1245 1185 60 60

2012-2 26.00 26 955 1245 -290 290

2012-3 27.00 27 1005 955 50 50

2012-4 28.00 28 1210 1005 205 205

2013-1 29.00 29 1285 1210 75 75

2013-2 30.00 30 1065 1285 -220 220

2013-3 31.00 31 1065

e2= 335,150.00

MSE= e2 / 15= 335,150.00/15= 22,343.33

Appendix 3. Moving average

Table 4. Moving Average, N=3

Quarter tData Forecast Error Forecast for t +1 if N=3 Squared

Error

Xt Ft et=Xt-Ft Ft+1=(Xt+Xt-1+Xt-2)/3 e2

2006-1 1 750.00

2006-2 2 685.00

2006-3 3 715.00 F4 716.67


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2006-4 4 775.00 716.67 58.33 F5 725.00

2007-1 5 795.00 725.00 70.00 F6 761.67

2007-2 6 695.00 761.67 (66.67) F7 755.00

2007-3 7 705.00 755.00 (50.00) F8 731.67

2007-4 8 790.00 731.67 58.33 F9 730.00

2008-1 9 815.00 730.00 85.00 F10 770.00

2008-2 10 685.00 770.00 (85.00) F11 763.33

2008-3 11 525.00 763.33 (238.33) F12 675.00

2008-4 12 635.00 675.00 (40.00) F13 615.00

2009-1 13 825.00 615.00 210.00 F14 661.67

2009-2 14 735.00 661.67 73.33 F15 731.67

2009-3 15 895.00 731.67 163.33 F16 818.33

2009-4 16 965.00 818.33 146.67 F17 865.0021,511.11

2010-1 17 995.00 865.00 130.00 F18 951.6716,900.00

2010-2 18 865.00 951.67 (86.67) F19 941.677,511.11

2010-3 19 915.00 941.67 (26.67) F20 925.00711.11

2010-4 20 995.00 925.00 70.00 F21 925.004,900.00

2011-1 21 1,125.00 925.00 200.00 F22 1,011.67

40,000.00

2011-2 22 905.00 1,011.67 (106.67) F23 1,008.3311,377.78

2011-3 23 965.00 1,008.33 (43.33) F24 998.331,877.78

2011-4 24 1,185.00 998.33 186.67 F25 1,018.3334,844.44

2012-1 25 1,245.00 1,018.33 226.67 F26 1,131.6751,377.78

2012-2 26 955.00 1,131.67 (176.67) F27 1,128.3331,211.11

2012-3 27 1,005.00 1,128.33 (123.33) F28 1,068.33 15,211.11

2012-4 28 1,210.00 1,068.33 141.67 F29 1,056.6720,069.44

2013-1 29 1,285.00 1,056.67 228.33 F30 1,166.6752,136.11

2013-2 30 1,065.00 1,166.67 (101.67) F31 1,186.6710,336.11


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2013-3 31 1,186.67

e2= 319,975.00

MSE= e2 / 15= 319,975.00/15=21,331.67

Table 5. Moving average, N=4

Quarter tData Forecast Error Forecast for t +1 if N=3

Squared

Error


2006-1 1.00 750.00

2006-2 2.00 685.00

2006-3 3.00 715.00

2006-4 4.00 775.00 F5 731.25

2007-1 5.00 795.00 731.25 63.75 F6 742.50

2007-2 6.00 695.00 742.50 (47.50) F7 745.00

2007-3 7.00 705.00 745.00 (40.00) F8 742.50

2007-4 8.00 790.00 742.50 47.50 F9 746.25

2008-1 9.00 815.00 746.25 68.75 F10 751.25

2008-2 10.00 685.00 751.25 (66.25) F11 748.75

2008-3 11.00 525.00 748.75 (223.75) F12 703.75

2008-4 12.00 635.00 703.75 (68.75) F13 665.00

2009-1 13.00 825.00 665.00 160.00 F14 667.50

2009-2 14.00 735.00 667.50 67.50 F15 680.00

2009-3 15.00 895.00 680.00 215.00 F16 772.50

2009-4 16.00 965.00 772.50 192.50 F17 855.00 37,056.25

2010-1 17.00 995.00 855.00 140.00 F18 897.50 19,600.00

2010-2 18.00 865.00 897.50 (32.50) F19 930.00 1,056.25

2010-3 19.00 915.00 930.00 (15.00) F20 935.00 225.00

2010-4 20.00 995.00 935.00 60.00 F21 942.50 3,600.00

2011-1 21.00 1,125.00 942.50 182.50 F22 975.00 33,306.252011-2 22.00 905.00 975.00 (70.00) F23 985.00 4,900.00

2011-3 23.00 965.00 985.00 (20.00) F24 997.50 400.00

2011-4 24.00 1,185.00 997.50 187.50 F25 1,045.00 35,156.25

2012-1 25.00 1,245.00 1,045.00 200.00 F26 1,075.00 40,000.00

2012-2 26.00 955.00 1,075.00 (120.00) F27 1,087.50 14,400.00


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2012-3 27.00 1,005.00 1,087.50 (82.50) F28 1,097.50 6,806.25

2012-4 28.00 1,210.00 1,097.50 112.50 F29 1,103.75 12,656.25

2013-1 29.00 1,285.00 1,103.75 181.25 F30 1,113.75 32,851.56

2013-2 30.00 1,065.00 1,113.75 (48.75) F31 1,141.25 2,376.56

2013-3 31.00 1,141.25

e2= 244,390.63

MSE= e2 / 15= 244,390.63/15=16,292.71

Table 6.Moving average, N=5.

Quarter tData Forecast Error Forecast for t +1 if N=3

Squared

Error


2006-1 1.00 750.00

2006-2 2.00 685.002006-3 3.00 715.00

2006-4 4.00 775.00

2007-1 5.00 795.00 F6 930.00

2007-2 6.00 695.00 930.00 (235.00) F7 916.25

2007-3 7.00 705.00 916.25 (211.25) F8 921.25

2007-4 8.00 790.00 921.25 (131.25) F9 940.00

2008-1 9.00 815.00 940.00 (125.00) F10 950.00

2008-2 10.00 685.00 950.00 (265.00) F11 922.50

2008-3 11.00 525.00 922.50 (397.50) F12 880.00

2008-4 12.00 635.00 880.00 (245.00) F13 862.50

2009-1 13.00 825.00 862.50 (37.50) F14 871.25

2009-2 14.00 735.00 871.25 (136.25) F15 851.25

2009-3 15.00 895.00 851.25 43.75 F16 903.75

2009-4 16.00 965.00 903.75 61.25 F17 1,013.75 3,751.56

2010-1 17.00 995.00 1,013.75 (18.75) F18 1,103.75 351.56

2010-2 18.00 865.00 1,103.75 (238.75) F19 1,113.75 57,001.56

2010-3 19.00 915.00 1,113.75 (198.75) F20 1,158.75 39,501.56

2010-4 20.00 995.00 1,158.75 (163.75) F21 1,183.75 26,814.06

2011-1 21.00 1,125.00 1,183.75 (58.75) F22 1,223.75 3,451.56

2011-2 22.00 905.00 1,223.75 (318.75) F23 1,201.25 101,601.56

2011-3 23.00 965.00 1,201.25 (236.25) F24 1,226.25 55,814.06


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2011-4 24.00 1,185.00 1,226.25 (41.25) F25 1,293.75 1,701.56

2012-1 25.00 1,245.00 1,293.75 (48.75) F26 1,356.25 2,376.56

2012-2 26.00 955.00 1,356.25 (401.25) F27 1,313.75 161,001.56

2012-3 27.00 1,005.00 1,313.75 (308.75) F28 1,338.75 95,326.56

2012-4 28.00 1,210.00 1,338.75 (128.75) F29 1,400.00 16,576.56

2013-1 29.00 1,285.00 1,400.00 (115.00) F30 1,425.00 13,225.00

2013-2 30.00 1,065.00 1,425.00 (360.00) F31 1,380.00 129,600.00

2013-3 31.00 1,380.00

e2= 708,095.31

MSE= e2 / 15= 708,095.31/15=47,206.35

Appendix 4. Simple Exponential Smoothing

Table 7. Identification of , =0.1

Quarter Data Forecast error Forecast for t +1squared

error

T Xt Ft et=Xt-Ft Ft+1= Ft+ et e2

2006-1 720.00 735.00 15.00 F2 736.50 735.00 15.00 225.00

2006-2 695.00 736.50 (51.50) F3 731.35 736.50 (51.50) 2,652.25

2006-3 715.00 731.35 (16.35) F4 729.72 731.35 (16.35) 267.32

2006-4 735.00 729.72 45.29 F5 734.24 729.72 45.29 2,050.73

2007-1 775.00 734.24 60.76 F6 740.32 734.24 60.76 3,691.35

2007-2 755.00 740.32 (45.32) F7 735.79 740.32 (45.32) 2,053.83

2007-3 770.00 735.79 (30.79) F8 732.71 735.79 (30.79) 947.85

2007-4 790.00 732.71 57.29 F9 738.44 732.71 57.29 3,282.31

2008-1 790.00 738.44 76.56 F10 746.09 738.44 76.56 5,861.79

2008-2 735.00 746.09 (61.09) F11 739.98 746.09 (61.09) 3,732.46

2008-3 425.00 739.98 (214.98) F12 718.49 739.98 (214.98) 46,218.34

2008-4 530.00 718.49 (83.49) F13 710.14 718.49 (83.49) 6,969.92

2009-1 625.00 710.14 114.86 F14 721.62 710.14 114.86 13,193.41

2009-2 780.00 721.62 13.38 F15 722.96 721.62 13.38 178.93

2009-3 850.00 722.96 172.04 F16 740.17 722.96 172.04 29,597.30

e2= 120,922.80

MSE=.01 for warm up sample= e2 / 15= 120,922.80 /15= 8,061.52


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If = 0.2


error

t Xt Ft et=Xt-Ft Ft+1= Ft+ et e2

2006-1 720.00 735.00 15.00 F2 738.00 735.00 15.00 225.00

2006-2 695.00 738.00 (53.00) F3 727.40 738.00 (53.00) 2,809.00

2006-3 715.00 727.40 (12.40) F4 724.92 727.40 (12.40) 153.76

2006-4 735.00 724.92 50.08 F5 734.94 724.92 50.08 2,508.01

2007-1 775.00 734.94 60.06 F6 746.95 734.94 60.06 3,607.68

2007-2 755.00 746.95 (51.95) F7 736.56 746.95 (51.95) 2,698.68

2007-3 770.00 736.56 (31.56) F8 730.25 736.56 (31.56) 995.97

2007-4 790.00 730.25 59.75 F9 742.20 730.25 59.75 3,570.39

2008-1 790.00 742.20 72.80 F10 756.76 742.20 72.80 5,300.16

2008-2 735.00 756.76 (71.76) F11 742.41 756.76 (71.76) 5,149.24

2008-3 425.00 742.41 (217.41) F12 698.93 742.41 (217.41) 47,265.62

2008-4 530.00 698.93 (63.93) F13 686.14 698.93 (63.93) 4,086.44

2009-1 625.00 686.14 138.86 F14 713.91 686.14 138.86 19,282.04

2009-2 780.00 713.91 21.09 F15 718.13 713.91 21.09 444.70

2009-3 850.00 718.13 176.87 F16 753.50 718.13 176.87 31,283.09

e2= 129,379.79

MSE=0.2 for warm up sample= e2 / 15= 129,379.79 /15= 8,625.32

If = 0.3


error


2006-1 720.00 735.00 15.00 F2 739.50 735.00 15.00 225.002006-2 695.00 739.50 (54.50) F3 723.15 739.50 (54.50) 2,970.25

2006-3 715.00 723.15 (8.15) F4 720.71 723.15 (8.15) 66.42

2006-4 735.00 720.71 54.30 F5 736.99 720.71 54.30 2,947.95

2007-1 775.00 736.99 58.01 F6 754.40 736.99 58.01 3,364.75

2007-2 755.00 754.40 (59.40) F7 736.58 754.40 (59.40) 3,527.82


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2007-3 770.00 736.58 (31.58) F8 727.10 736.58 (31.58) 997.10

2007-4 790.00 727.10 62.90 F9 745.97 727.10 62.90 3,955.94

2008-1 790.00 745.97 69.03 F10 766.68 745.97 69.03 4,764.78

2008-2 735.00 766.68 (81.68) F11 742.18 766.68 (81.68) 6,671.76

2008-3 425.00 742.18 (217.18) F12 677.02 742.18 (217.18) 47,165.67

2008-4 530.00 677.02 (42.02) F13 664.42 677.02 (42.02) 1,765.98

2009-1 625.00 664.42 160.58 F14 712.59 664.42 160.58 25,787.05

2009-2 780.00 712.59 22.41 F15 719.31 712.59 22.41 502.14

2009-3 850.00 719.31 175.69 F16 772.02 719.31 175.69 30,865.54

e2= 135,578.14


If = 0.4


error


2006-1 720.00 735.00 15.00 F2 741.00 735.00 15.00 225.00

2006-2 695.00 741.00 (56.00) F3 718.60 741.00 (56.00) 3,136.00

2006-3 715.00 718.60 (3.60) F4 717.16 718.60 (3.60) 12.96

2006-4 735.00 717.16 57.84 F5 740.30 717.16 57.84 3,345.47

2007-1 775.00 740.30 54.70 F6 762.18 740.30 54.70 2,992.53

2007-2 755.00 762.18 (67.18) F7 735.31 762.18 (67.18) 4,512.83

2007-3 770.00 735.31 (30.31) F8 723.18 735.31 (30.31) 918.49

2007-4 790.00 723.18 66.82 F9 749.91 723.18 66.82 4,464.39

2008-1 790.00 749.91 65.09 F10 775.95 749.91 65.09 4,236.66

2008-2 735.00 775.95 (90.95) F11 739.57 775.95 (90.95) 8,271.21

2008-3 425.00 739.57 (214.57) F12 653.74 739.57 (214.57) 46,039.31

2008-4 530.00 653.74 (18.74) F13 646.24 653.74 (18.74) 351.21

2009-1 625.00 646.24 178.76 F14 717.75 646.24 178.76 31,953.57

2009-2 780.00 717.75 17.25 F15 724.65 717.75 17.25 297.68

2009-3 850.00 724.65 170.35 F16 792.79 724.65 170.35 29,019.81

e2= 139,777.12


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If = 0.5


error


2006-1 720.00 735.00 15.00 F2 742.50 735.00 15.00 225.00

2006-2 695.00 742.50 (57.50) F3 713.75 742.50 (57.50) 3,306.25

2006-3 715.00 713.75 1.25 F4 714.38 713.75 1.25 1.56

2006-4 735.00 714.38 60.63 F5 744.69 714.38 60.63 3,675.39

2007-1 775.00 744.69 50.31 F6 769.84 744.69 50.31 2,531.35

2007-2 755.00 769.84 (74.84) F7 732.42 769.84 (74.84) 5,601.59

2007-3 770.00 732.42 (27.42) F8 718.71 732.42 (27.42) 751.96

2007-4 790.00 718.71 71.29 F9 754.36 718.71 71.29 5,082.13

2008-1 790.00 754.36 60.64 F10 784.68 754.36 60.64 3,677.76

2008-2 735.00 784.68 (99.68) F11 734.84 784.68 (99.68) 9,935.65

2008-3 425.00 734.84 (209.84) F12 629.92 734.84 (209.84) 44,032.35

2008-4 530.00 629.92 5.08 F13 632.46 629.92 5.08 25.81

2009-1 625.00 632.46 192.54 F14 728.73 632.46 192.54 37,071.76

2009-2 780.00 728.73 6.27 F15 731.86 728.73 6.27 39.31

2009-3 850.00 731.86 163.14 F16 813.43 731.86 163.14 26,613.05

e2= 142,570.93

MSE=0.5for warm up sample= e2 / 15= 142,570.93 /15= 9,504.73

If = 0.6


error


2006-1 720.00 735.00 15.00 F2 744.00 735.00 15.00 225.00

2006-2 695.00 744.00 (59.00) F3 708.60 744.00 (59.00) 3,481.00

2006-3 715.00 708.60 6.40 F4 712.44 708.60 6.40 40.96

2006-4 735.00 712.44 62.56 F5 749.98 712.44 62.56 3,913.75

2007-1 775.00 749.98 45.02 F6 776.99 749.98 45.02 2,027.16


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2007-2 755.00 776.99 (81.99) F7 727.80 776.99 (81.99) 6,722.43

2007-3 770.00 727.80 (22.80) F8 714.12 727.80 (22.80) 519.66

2007-4 790.00 714.12 75.88 F9 759.65 714.12 75.88 5,758.01

2008-1 790.00 759.65 55.35 F10 792.86 759.65 55.35 3,063.91

2008-2 735.00 792.86 (107.86) F11 728.14 792.86 (107.86) 11,633.55

2008-3 425.00 728.14 (203.14) F12 606.26 728.14 (203.14) 41,267.31

2008-4 530.00 606.26 28.74 F13 623.50 606.26 28.74 826.14

2009-1 625.00 623.50 201.50 F14 744.40 623.50 201.50 40,601.05

2009-2 780.00 744.40 (9.40) F15 738.76 744.40 (9.40) 88.38

2009-3 850.00 738.76 156.24 F16 832.50 738.76 156.24 24,410.79

e2= 144,579.11


If = 0.7

Quarter Data Forecast error Forecast for t +1 squared errort Xt Ft et=Xt-Ft Ft+1= Ft+ et e2

2006-1 720.00 735.00 15.00 F2 745.50 735.00 15.00 225.00

2006-2 695.00 745.50 (60.50) F3 703.15 745.50 (60.50) 3,660.25

2006-3 715.00 703.15 11.85 F4 711.45 703.15 11.85 140.42

2006-4 735.00 711.45 63.56 F5 755.93 711.45 63.56 4,039.24

2007-1 775.00 755.93 39.07 F6 783.28 755.93 39.07 1,526.19

2007-2 755.00 783.28 (88.28) F7 721.48 783.28 (88.28) 7,793.37

2007-3 770.00721.48 (16.48) F8 709.95 721.48 (16.48) 271.72

2007-4 790.00 709.95 80.05 F9 765.98 709.95 80.05 6,408.77

2008-1 790.00 765.98 49.02 F10 800.30 765.98 49.02 2,402.61

2008-2 735.00 800.30 (115.30) F11 719.59 800.30 (115.30) 13,292.95

2008-3 425.00 719.59 (194.59) F12 583.38 719.59 (194.59) 37,864.69

2008-4 530.00 583.38 51.62 F13 619.51 583.38 51.62 2,664.98


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33

2009-1 625.00 619.51 205.49 F14 763.35 619.51 205.49 42,224.92

2009-2 780.00 763.35 (28.35) F15 743.51 763.35 (28.35) 803.94

2009-3 850.00 743.51 151.49 F16 849.55 743.51 151.49 22,950.38

e2= 146,269.44

MSE=0.7for warm up sample= e2 / 15= 146,269.44/15= 9,751.30

If = 0.8


error


2006-1 720.00 735.00 15.00 F2 747.00 735.00 15.00 225.00

2006-2 695.00 747.00 (62.00) F3 697.40 747.00 (62.00) 3,844.00

2006-3 715.00 697.40 17.60 F4 711.48 697.40 17.60 309.76

2006-4 735.00 711.48 63.52 F5 762.30 711.48 63.52 4,034.79

2007-1 775.00 762.30 32.70 F6 788.46 762.30 32.70 1,069.55

2007-2 755.00 788.46 (93.46) F7 713.69 788.46 (93.46) 8,734.62

2007-3 770.00 713.69 (8.69) F8 706.74 713.69 (8.69) 75.55

2007-4 790.00 706.74 83.26 F9 773.35 706.74 83.26 6,932.50

2008-1 790.00 773.35 41.65 F10 806.67 773.35 41.65 1,734.92

2008-2 735.00 806.67 (121.67) F11 709.33 806.67 (121.67) 14,803.48

2008-3 425.00 709.33 (184.33) F12 561.87 709.33 (184.33) 33,978.99

2008-4 530.00 561.87 73.13 F13 620.37 561.87 73.13 5,348.47

2009-1 625.00 620.37 204.63 F14 784.07 620.37 204.63 41,872.06

2009-2 780.00 784.07 (49.07) F15 744.81 784.07 (49.07) 2,408.32

2009-3 850.00 744.81 150.19 F16 864.96 744.81 150.19 22,555.55

e2= 147,927.56


If = 0.9


error


2006-1 750.00 735.00 15.00 F2 748.50 750.00 735.00 225.00


35/57

34

2006-2 685.00 748.50 (63.50) F3 691.35 685.00 748.50 4,032.25

2006-3 715.00 691.35 23.65 F4 712.64 715.00 691.35 559.32

2006-4 775.00 712.64 62.37 F5 768.76 775.00 712.64 3,889.39

2007-1 795.00 768.76 26.24 F6 792.38 795.00 768.76 688.35

2007-2 695.00 792.38 (97.38) F7 704.74 695.00 792.38 9,482.15

2007-3 705.00 704.74 0.26 F8 704.97 705.00 704.74 0.07

2007-4 790.00 704.97 85.03 F9 781.50 790.00 704.97 7,229.46

2008-1 815.00 781.50 33.50 F10 811.65 815.00 781.50 1,122.43

2008-2 685.00 811.65 (126.65) F11 697.66 685.00 811.65 16,040.16

2008-3 525.00 697.66 (172.66) F12 542.27 525.00 697.66 29,813.19

2008-4 635.00 542.27 92.73 F13 625.73 635.00 542.27 8,599.50

2009-1 825.00 625.73 199.27 F14 805.07 825.00 625.73 39,709.87

2009-2 735.00 805.07 (70.07) F15 742.01 735.00 805.07 4,910.18

2009-3 895.00 742.01 152.99 F16 879.70 895.00 742.01 23,406.78

e2= 149,708.10

MSE=.09 for warm up sample= e2 / 15= 149,708.10 /15=9,980.54

Since MSE=.09 for warm up sample gives the minimum value then 0.9 is the most fitting , to

be used for the simple exponential smoothing model.

Table 8. Simple exponential smoothing, =0.9

Quarte

rData Forecast error Forecast for t +1

squared

error


2006-1 1.00 750.00 735.00 15.00 F2 736.50 1.00 750.00

2006-2 2.00 685.00 736.50 (51.50) F3 731.35 2.00 685.00

2006-3 3.00 715.00 731.35 (16.35) F4 729.72 3.00 715.00

2006-4 4.00 775.00 729.72 45.29 F5 734.24 4.00 775.00

2007-1 5.00 795.00 734.24 60.76 F6 740.32 5.00 795.00

2007-2 6.00 695.00 740.32 (45.32) F7 735.79 6.00 695.00

2007-3 7.00 705.00 735.79 (30.79) F8 732.71 7.00 705.00

2007-4 8.00 790.00 732.71 57.29 F9 738.44 8.00 790.00

2008-1 9.00 815.00 738.44 76.56 F10 746.09 9.00 815.00


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35

2008-2 10.00 685.00 746.09 (61.09) F11 739.98 10.00 685.00

2008-3 11.00 525.00 739.98 (214.98) F12 718.49 11.00 525.00

2008-4 12.00 635.00 718.49 (83.49) F13 710.14 12.00 635.00

2009-1 13.00 825.00 710.14 114.86 F14 721.62 13.00 825.00

2009-2 14.00 735.00 721.62 13.38 F15 722.96 14.00 735.00

2009-3 15.00 895.00 722.96 172.04 F16 740.17 15.00 895.00

2009-4 16.00 965.00 740.17 224.83 F17 762.65 16.00 965.00 50,550.69

2010-1 17.00 995.00 762.65 232.35 F18 785.88 17.00 995.00 53,987.14

2010-2 18.00 865.00 785.88 79.12 F19 793.80 18.00 865.00 6,259.37

2010-3 19.00 915.00 793.80 121.20 F20 805.92 19.00 915.00 14,690.55

2010-4 20.00 995.00 805.92 189.08 F21 824.82 20.00 995.00 35,752.80

2011-1 21.00 1,125.00 824.82 300.18 F22 854.84 21.00 1,125.00 90,105.45

2011-2 22.00 905.00 854.84 50.16 F23 859.86 22.00 905.00 2,515.84

2011-3 23.00 965.00 859.86 105.14 F24 870.37 23.00 965.00 11,054.91

2011-4 24.00 1,185.00 870.37 314.63 F25 901.83 24.00 1,185.00 98,990.83

2012-1 25.00 1,245.00 901.83 343.17 F26 936.15 25.00 1,245.00 117,762.41

2012-2 26.00 955.00 936.15 18.85 F27 938.04 26.00 955.00 355.28

2012-3 27.00 1,005.00 938.04 66.96 F28 944.73 27.00 1,005.00 4,484.16

2012-4 28.00 1,210.00 944.73 265.27 F29 971.26 28.00 1,210.00 70,366.84

2013-1 29.00 1,285.00 971.26 313.74 F30 1,002.63 29.00 1,285.00 98,433.25

2013-2 30.00 1,065.00 1,002.63 62.37 F31 1,008.87 30.00 1,065.00 3,889.60

2013-3 31.00 1,008.87 31.00

e2= 659,199.11

MSE= e2/15= 659,199.11 /15= 43,946.61

Appendix 5. Time Series Regression

Table 9.Linear series eegression, a=703.6607 b=2.89286.

Year TData Forecast Error

Squared

Error

Xt Ft= a + bt et= Xt-Ft tX t2 e2

2006-1 1 750.00 F1 706.55 43.45 750.00 1.00

2006-2 2 685.00 F2 709.45 (24.45) 1,370.00 4.00

2006-3 3 715.00 F3 712.34 2.66 2,145.00 9.00


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36

2006-4 4 775.00 F4 715.23 59.77 3,100.00 16.00

2007-1 5 795.00 F5 718.13 76.88 3,975.00 25.00

2007-2 6 695.00 F6 721.02 (26.02) 4,170.00 36.00

2007-3 7 705.00 F7 723.91 (18.91) 4,935.00 49.00

2007-4 8 790.00 F8 726.80 63.20 6,320.00 64.00

2008-1 9 815.00 F9 729.70 85.30 7,335.00 81.00

2008-2 10 685.00 F10 732.59 (47.59) 6,850.00 100.00

2008-3 11 525.00 F11 735.48 (210.48) 5,775.00 121.00

2008-4 12 635.00 F12 738.38 (103.38) 7,620.00 144.00

2009-1 13 825.00 F13 741.27 83.73 10,725.00 169.00

2009-2 14 735.00 F14 744.16 (9.16) 10,290.00 196.00

2009-3 15 895.00 F15 747.05 147.95 13,425.00 225.00

2009-4 16 965.00 F16 749.95 215.05 88,785.00 1,240.00

2010-1 17 995.00 F17 752.84 242.16 46,248.03

2010-2 18 865.00 F18 755.73 109.27 58,641.79

2010-3 19 915.00 F19 758.63 156.37 11,939.46

2010-4 20 995.00 F20 761.52 233.48 24,453.13

2011-1 21 1,125.00 F21 764.41 360.59 54,513.89

2011-2 22 905.00 F22 767.30 137.70 130,024.60

2011-3 23 965.00 F23 770.20 194.80 18,960.29

2011-4 24 1,185.00 F24 773.09 411.91 37,948.41

2012-1 25 1,245.00 F25 775.98 469.02 169,670.39

2012-2 26 955.00 F26 778.88 176.12 219,977.70

2012-3 27 1,005.00 F27 781.77 223.23 31,019.99

2012-4 28 1,210.00 F28 784.66 425.34 49,832.56

2013-1 29 1,285.00 F29 787.55 497.45 180,913.45

2013-2 30 1,065.00 F30 790.45 274.55 247,452.88

2013-3 31 F31 793.34 75,379.62

120 11,025.00 88,785.00 1,240.00 1,356,976.20

MSE= e2/15= 1,356,976.20/15=90,465.08

= t/n

= 120/30

=8


38/57

37

= X/n

= 11,025.00/30

=88,785.00

b=(tX-n )/ (t2-n

2)= (88,785.00 - (30811,025.00))/ (1,240.00-(308))

= 2.89286

a=-b=88,785.00- (2.89286)(8)

=703.66071

F=a + bt= 703.66071+ (2.89286t)

Appendix 6. Linear Exponential Smoothing

Table 10.Identification of 1 and 2of linear exponential smooting, 1=0.1 and 2=0.01

Yeart

DataForec

astError

Level at the

End of t

Trend at

the end of

t

Forecast for

t+1

Squared

Error

Xt Ftet = Xt-

FtSt = Ft + 1et

Tt = Tt-1 +

2etFt+1 = St + Tt e2

0 - S0 703.66 T0 2.09 F1 705.75 1,958.06

2006-1 1 750.00 705.75 44.25 S1 710.17 T1 2.53 F2 712.71 767.67

2006-2 2 685.00 712.71 (27.71) S2 709.94 T2 2.25 F3 712.19 7.89

2006-3 3 715.00 712.19 2.81 S3 712.47 T3 2.28 F4 714.75 3,629.52

2006-4 4 775.00 714.75 60.25 S4 720.78 T4 2.89 F5 723.66 5,088.77

2007-1 5 795.00 723.66 71.34 S5 730.80 T5 3.60 F6 734.40 1,552.09

2007-2 6 695.00 734.40 (39.40) S6 730.46 T6 3.20 F7 733.66 821.48

2007-3 7 705.00 733.66 (28.66) S7 730.80 T7 2.92 F8 733.71 3,168.18

2007-4 8 790.00 733.71 56.29 S8 739.34 T8 3.48 F9 742.82 5,209.52

2008-1 9 815.00 742.82 72.18 S9 750.04 T9 4.20 F10 754.24 4,794.64

2008-2 10 685.00 754.24 (69.24) S10 747.32 T10 3.51 F11 750.83 50,998.86

2008-3 11 525.00 750.83(225.83

)S11 728.25 T11 1.25 F12 729.50 8,929.93

2008-4 12 635.00 729.50 (94.50) S12 720.05 T12 0.31 F13 720.36 10,950.49

2009-1 13 825.00 720.36 104.64 S13 730.82 T13 1.35 F14 732.17 7.99


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38

MSE1=.1,2=0.01for warm up sample= e2 / 15= 123,858.39/15= 8,257.23

Table 11. Identification of 1 and 2 of linear exponential smooting, 1=0.1 and 2=0.02

MSE1=.1,2=0.02 for warm up sample= e2 / 15= 127,737.43 /15= 8,515.83

Table 12.Identification of 1 and 2 of linear exponential smooting, 1=0.1 and 2=0.03

2009-2 14 735.00 732.17 2.83 S14 732.46 T14 1.38 F15 733.84 25,973.30

2009-3 15 895.00 733.84 161.16 S15 749.95 T15 2.99 F16 752.95 1,958.06

2009-4 16 752.95 767.67

e2= 123,858.39

Yeart

DataForec

astError

Level at the

End of t

Trend at the

end of t

Forecast for

t+1

Squared

Error

Xt Ftet = Xt-

FtSt = Ft + 1et

Tt = Tt-1 +


0 - S0 703.66 T0 2.09 F1 705.75

2006-1 1 750.00 705.75 44.25 S1 710.17 T1 2.97 F2 713.15 1,958.06

2006-2 2 685.00 713.15 (28.15) S2 710.33 T2 2.41 F3 712.75 792.38

2006-3 3 715.00 712.75 2.25 S3 712.97 T3 2.46 F4 715.43 5.08

2006-4 4 775.00 715.43 59.57 S4 721.38 T4 3.65 F5 725.03 3,548.89

2007-1 5 795.00 725.03 69.97 S5 732.03 T5 5.05 F6 737.08 4,895.44

2007-2 6 695.00 737.08 (42.08) S6 732.87 T6 4.21 F7 737.07 1,770.43

2007-3 7 705.00 737.07 (32.07) S7 733.87 T7 3.56 F8 737.43 1,028.77

2007-4 8 790.00 737.43 52.57 S8 742.69 T8 4.62 F9 747.30 2,763.48

2008-1 9 815.00 747.30 67.70 S9 754.07 T9 5.97 F10 760.04 4,582.80

2008-2 10 685.00 760.04 (75.04) S10 752.54 T10 4.47 F11 757.01 5,631.41

2008-3 11 525.00 757.01 (232.01) S11 733.81 T11 (0.17) F12 733.63 53,827.29

2008-4 12 635.00 733.63 (98.63) S12 723.77 T12 (2.14) F13 721.63 9,728.83

2009-1 13 825.00 721.63 103.37 S13 731.96 T13 (0.08) F14 731.89 10,685.95

2009-2 14 735.00 731.89 3.11 S14 732.20 T14 (0.01) F15 732.18 9.69

2009-3 15 895.00 732.18 162.82 S15 748.47 T15 3.24 F16 751.71 26,508.93

2009-4 16 751.71

e2= 127,737.43

Year t DataForec

astError

Level at the

End of t

Trend at the

end of t

Forecast for

t+1

Squared

Error


40/57

39

MSE1=.1,2=0.03 for warm up sample= e2 / 15= 132,234.49 /15=8,815.63

Table 13.Identification of 1 and 2 of linear exponential smooting, 1=0.1 and 2=0.04

Xt Ftet = Xt-

FtSt = Ft + 1et

Tt = Tt-1 +


0 - S0 703.66 T0 2.09 F1 705.75

2006-1 1 750.00 705.75 44.25 S1 710.17 T1 3.42 F2 713.59 1,958.06

2006-2 2 685.00 713.59 (28.59) S2 710.73 T2 2.56 F3 713.29 817.49

2006-3 3 715.00 713.29 1.71 S3 713.46 T3 2.61 F4 716.07 2.92

2006-4 4 775.00 716.07 58.93 S4 721.97 T4 4.38 F5 726.34 3,472.42

2007-1 5 795.00 726.34 68.66 S5 733.21 T5 6.44 F6 739.65 4,713.70

2007-2 6 695.00 739.65 (44.65) S6 735.18 T6 5.10 F7 740.28 1,993.36

2007-3 7 705.00 740.28 (35.28) S7 736.75 T7 4.04 F8 740.79 1,244.73

2007-4 8 790.00 740.79 49.21 S8 745.71 T8 5.52 F9 751.23 2,421.37

2008-1 9 815.00 751.23 63.77 S9 757.61 T9 7.43 F10 765.04 4,066.67

2008-2 10 685.00 765.04 (80.04) S10 757.03 T10 5.03 F11 762.06 6,405.74

2008-3 11 525.00 762.06 (237.06) S11 738.35 T11 (2.08) F12 736.27 56,197.68

2008-4 12 635.00 736.27 (101.27) S12 726.14 T12 (5.12) F13 721.02 10,255.79

2009-1 13 825.00 721.02 103.98 S13 731.42 T13 (2.00) F14 729.42 10,811.41

2009-2 14 735.00 729.42 5.58 S14 729.98 T14 (1.83) F15 728.14 31.16

2009-3 15 895.00 728.14 166.86 S15 744.83 T15 3.17 F16 748.00 27,841.98

2009-4 16 748.00

e2= 132,234.49

Yeart

DataForec

astError

Level at the

End of t

Trend at the

end of t

Forecast for

t+1

Squared

Error

Xt Ftet = Xt-

FtSt = Ft + 1et

Tt = Tt-1 +


0 - S0 703.66 T0 2.09 F1 705.75

2006-1 1 750.00 705.75 44.25 S1 710.17 T1 3.86 F2 714.03 1,958.06

2006-2 2 685.00 714.03 (29.03) S2 711.13 T2 2.70 F3 713.83 842.99

2006-3 3 715.00 713.83 1.17 S3 713.95 T3 2.74 F4 716.69 1.37

2006-4 4 775.00 716.69 58.31 S4 722.52 T4 5.08 F5 727.60 3,399.98

2007-1 5 795.00 727.60 67.40 S5 734.34 T5 7.77 F6 742.11 4,542.93

2007-2 6 695.00 742.11 (47.11) S6 737.40 T6 5.89 F7 743.29 2,219.54


41/57

40

MSE1=0.1,2=0.04 for warm up sample= e2 / 15= 137,159.98 /15= 9,144.00


2007-3 7 705.00 743.29 (38.29) S7 739.46 T7 4.36 F8 743.82 1,466.09

2007-4 8 790.00 743.82 46.18 S8 748.44 T8 6.20 F9 754.64 2,132.80

2008-1 9 815.00 754.64 60.36 S9 760.68 T9 8.62 F10 769.30 3,643.29

2008-2 10 685.00 769.30 (84.30) S10 760.87 T10 5.25 F11 766.11 7,105.67

2008-3 11 525.00 766.11 (241.11) S11 742.00 T11 (4.40) F12 737.60 58,135.29

2008-4 12 635.00 737.60 (102.60) S12 727.34 T12 (8.50) F13 718.84 10,527.55

2009-1 13 825.00 718.84 106.16 S13 729.46 T13 (4.26) F14 725.20 11,269.56

2009-2 14 735.00 725.20 9.80 S14 726.18 T14 (3.86) F15 722.32 96.00

2009-3 15 895.00 722.32 172.68 S15 739.59 T15 3.04 F16 742.63 29,818.85

2009-4 16 742.63

e2= 137,159.98

Yeart

DataForec

astError

Level at the

End of t

Trend at the

end of t

Forecast for

t+1

Squared

Error

Xt Ftet = Xt-

FtSt = Ft + 1et Tt = Tt-1 + 2et Ft+1 = St + Tt e2

0 - S0 703.66 T0 2.09 F1 705.75

2006-1 1 750.00 705.75 44.25 S1 710.17 T1 4.30 F2 714.48 1,958.06

2006-2 2 685.00 714.48 (29.48) S2 711.53 T2 2.83 F3 714.36 868.88

2006-3 3 715.00 714.36 0.64 S3 714.42 T3 2.86 F4 717.28 0.41

2006-4 4 775.00 717.28 57.72 S4 723.05 T4 5.75 F5 728.80 3,331.43

2007-1 5 795.00 728.80 66.20 S5 735.42 T5 9.06 F6 744.48 4,382.53

2007-2 6 695.00 744.48 (49.48) S6 739.53 T6 6.58 F7 746.11 2,447.82

2007-3 7 705.00 746.11 (41.11) S7 742.00 T7 4.53 F8 746.53 1,690.05

2007-4 8 790.00 746.53 43.47 S8 750.87 T8 6.70 F9 757.57 1,889.99

2008-1 9 815.00 757.57 57.43 S9 763.32 T9 9.57 F10 772.89 3,297.77

2008-2 10 685.00 772.89 (87.89) S10 764.10 T10 5.18 F11 769.28 7,724.34

2008-3 11 525.00 769.28 (244.28) S11 744.85 T11 (7.04) F12 737.81 59,671.15

2008-4 12 635.00 737.81 (102.81) S12 727.53 T12 (12.18) F13 715.35 10,570.44

2009-1 13 825.00 715.35 109.65 S13 726.32 T13 (6.69) F14 719.62 12,022.18

2009-2 14 735.00 719.62 15.38 S14 721.16 T14 (5.93) F15 715.24 236.42

2009-3 15 895.00 722.32 172.68 S15 739.59 T15 3.04 F16 742.63 32,315.23

2009-4 16 742.63


42/57

41

MSE1=0.1,2=0.05 for warm up sample= e2 / 15= 142,406.71/15=9,493.78



Table 16.Identification of 1 and 2 of linear exponential smooting, 1=0.1 and 2=0.06.

e2= 142,406.71

Yeart

DataForec

astError

Level at the

End of t

Trend at the

end of t

Forecast for

t+1Squared

Error

Xt Ftet = Xt-


0 - S0 703.66 T0 2.09 F1 705.75

2006-1 1 750.00 705.75 44.25 S1 710.17 T1 4.30 F2 714.48 1,958.06

2006-2 2 685.00 714.48 (29.48) S2 711.53 T2 2.83 F3 714.36 868.88

2006-3 3 715.00 714.36 0.64 S3 714.42 T3 2.86 F4 717.28 0.41

2006-4 4 775.00 717.28 57.72 S4 723.05 T4 5.75 F5 728.80 3,331.43

2007-1 5 795.00 728.80 66.20 S5 735.42 T5 9.06 F6 744.48 4,382.53

2007-2 6 695.00 744.48 (49.48) S6 739.53 T6 6.58 F7 746.11 2,447.82

2007-3 7 705.00 746.11 (41.11) S7 742.00 T7 4.53 F8 746.53 1,690.05

2007-4 8 790.00 746.53 43.47 S8 750.87 T8 6.70 F9 757.57 1,889.99

2008-1 9 815.00 757.57 57.43 S9 763.32 T9 9.57 F10 772.89 3,297.77

2008-2 10 685.00 772.89 (87.89) S10 764.10 T10 5.18 F11 769.28 7,724.34

2008-3 11 525.00 769.28 (244.28) S11 744.85 T11 (7.04) F12 737.81 59,671.15

2008-4 12 635.00 737.81 (102.81) S12 727.53 T12 (12.18) F13 715.35 10,570.44

2009-1 13 825.00 715.35 109.65 S13 726.32 T13 (6.69) F14 719.62 12,022.18

2009-2 14 735.00 719.62 15.38 S14 721.16 T14 (5.93) F15 715.24 236.42

2009-3 15 895.00 722.32 172.68 S15 739.59 T15 3.04 F16 742.63 32,315.23

2009-4 16 742.63

e2= 142,406.71

Yeart

DataForeca

stError

Level at the

End of t

Trend at the

end of t

Forecast for

t+1

Squared

Error

Xt Ftet = Xt-


0 - S0 703.66 T0 2.09 F1 705.75

2006-1 1 750.00 705.75 44.25 S1 710.17 T1 4.74 F2 714.92 1,958.06


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MSE1=0.1,2=0.06 for warm up sample= e2 / 15= 147,908.97 /15=9,860.60


2006-2 2 685.00 714.92 (29.92) S2 711.93 T2 2.95 F3 714.88 895.16

2006-3 3 715.00 714.88 0.12 S3 714.89 T3 2.96 F4 717.85 0.02

2006-4 4 775.00 717.85 57.15 S4 723.56 T4 6.39 F5 729.95 3,266.65

2007-1 5 795.00 729.95 65.05 S5 736.45 T5 10.29 F6 746.74 4,231.94

2007-2 6 695.00 746.74 (51.74) S6 741.57 T6 7.18 F7 748.75 2,677.13

2007-3 7 705.00 748.75 (43.75) S7 744.38 T7 4.56 F8 748.94 1,914.19

2007-4 8 790.00 748.94 41.06 S8 753.04 T8 7.02 F9 760.07 1,686.27

2008-1 9 815.00 760.07 54.93 S9 765.56 T9 10.32 F10 775.88 3,017.80

2008-2 10 685.00 775.88 (90.88) S10 766.79 T10 4.87 F11 771.66 8,258.88

2008-3 11 525.00 771.66 (246.66) S11 746.99 T11 (9.93) F12 737.06 60,839.79

2008-4 12 635.00 737.06 (102.06) S12 726.85 T12 (16.06) F13 710.80 10,415.99

2009-1 13 825.00 710.80 114.20 S13 722.22 T13 (9.20) F14 713.01 13,042.41

2009-2 14 735.00 713.01 21.99 S14 715.21 T14 (7.88) F15 707.33 483.43

2009-3 15 895.00 707.33 187.67 S15 726.09 T15 3.38 F16 729.47 35,221.25

2009-4 16 S0 703.66 T0 2.09 F1 705.75

e2= 147,908.97

Year t

DataForec

ast

ErrorLevel at the

End of t

Trend at the

end of t

Forecast for

t+1

Squared

Error

Xt Ftet = Xt-


0 - S0 703.66 T0 2.09 F1 705.75

2006-1 1 750.00 705.75 44.25 S1 710.17 T1 4.30 F2 714.48 1,958.06

2006-2 2 685.00 714.48 (29.48) S2 711.53 T2 2.83 F3 714.36 868.88

2006-3 3 715.00 714.36 0.64 S3 714.42 T3 2.86 F4 717.28 0.41

2006-4 4 775.00 717.28 57.72 S4 723.05 T4 5.75 F5 728.80 3,331.43

2007-1 5 795.00 728.80 66.20 S5 735.42 T5 9.06 F6 744.48 4,382.53

2007-2 6 695.00 744.48 (49.48) S6 739.53 T6 6.58 F7 746.11 2,447.82

2007-3 7 705.00 746.11 (41.11) S7 742.00 T7 4.53 F8 746.53 1,690.05

2007-4 8 790.00 746.53 43.47 S8 750.87 T8 6.70 F9 757.57 1,889.99

2008-1 9 815.00 757.57 57.43 S9 763.32 T9 9.57 F10 772.89 3,297.77

2008-2 10 685.00 772.89 (87.89) S10 764.10 T10 5.18 F11 769.28 7,724.34

2008-3 11 525.00 769.28 (244.28) S11 744.85 T11 (7.04) F12 737.81 59,671.15


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Table 18. Identification of 1 and 2 of linear exponential smooting, 1=0.1 and 2=0.07.



2008-4 12 635.00 737.81 (102.81) S12 727.53 T12 (12.18) F13 715.35 10,570.44

2009-1 13 825.00 715.35 109.65 S13 726.32 T13 (6.69) F14 719.62 12,022.18

2009-2 14 735.00 719.62 15.38 S14 721.16 T14 (5.93) F15 715.24 236.42

2009-3 15 895.00 722.32 172.68 S15 739.59 T15 3.04 F16 742.63 32,315.23

2009-4 16 742.63

e2= 142,406.71

Yeart

DataForeca

stError

Level at the

End of t

Trend at the

end of t

Forecast for

t+1

Squared

Error

Xt Ftet = Xt-


0 - S0 703.66 T0 2.09 F1 705.75

2006-1 1 750.00 705.75 44.25 S1 710.17 T1 5.19 F2 715.36 1,958.06

2006-2 2 685.00 715.36 (30.36) S2 712.33 T2 3.06 F3 715.39 921.84

2006-3 3 715.00 715.39 (0.39) S3 715.35 T3 3.03 F4 718.38 0.15

2006-4 4 775.00 718.38 56.62 S4 724.04 T4 7.00 F5 731.04 3,205.52

2007-1 5 795.00 731.04 63.96 S5 737.44 T5 11.47 F6 748.91 4,090.62

2007-2 6 695.00 748.91 (53.91) S6 743.52 T6 7.70 F7 751.22 2,906.55

2007-3 7 705.00 751.22 (46.22) S7 746.60 T7 4.47 F8 751.07 2,136.47

2007-4 8 790.00 751.07 38.93 S8 754.96 T8 7.19 F9 762.15 1,515.93

2008-1 9 815.00 762.15 52.85 S9 767.43 T9 10.89 F10 778.32 2,793.21

2008-2 10 685.00 778.32 (93.32) S10 768.99 T10 4.36 F11 773.35 8,709.46

2008-3 11 525.00 773.35 (248.35) S11 748.51 T11 (13.03) F12 735.49 61,677.51

2008-4 12 635.00 735.49 (100.49) S12 725.44 T12 (20.06) F13 705.38 10,097.77

2009-1 13 825.00 705.38 119.62 S13 717.34 T13 (11.69) F14 705.65 14,309.47

2009-2 14 735.00 705.65 29.35 S14 708.59 T14 (9.63) F15 698.95 861.28

2009-3 15 895.00 698.95 196.05 S15 718.56 T15 4.09 F16 722.65 38,434.02

2009-4 16 722.65

e2= 153,617.86


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Yeart

DataForeca

stError

Level at the

End of t

Trend at the

end of t

Forecast for

t+1

Squared

Error

Xt Ftet = Xt-


0 - S0 703.66 T0 2.09 F1 705.75

2006-1 1 750.00 705.75 44.25 S1 710.17 T1 5.63 F2 715.80 1,958.06

2006-2 2 685.00 715.80 (30.80) S2 712.72 T2 3.16 F3 715.89 948.90

2006-3 3 715.00 715.89 (0.89) S3 715.80 T3 3.09 F4 718.89 0.79

2006-4 4 775.00 718.89 56.11 S4 724.50 T4 7.58 F5 732.09 3,147.91

2007-1 5 795.00 732.09 62.91 S5 738.38 T5 12.62 F6 750.99 3,958.08

2007-2 6 695.00 750.99 (55.99) S6 745.39 T6 8.14 F7 753.53 3,135.27

2007-3 7 705.00 753.53 (48.53) S7 748.68 T7 4.25 F8 752.93 2,355.16

2007-4 8 790.00 752.93 37.07 S8 756.64 T8 7.22 F9 763.86 1,374.14

2008-1 9 815.00 763.86 51.14 S9 768.97 T9 11.31 F10 780.28 2,615.65

2008-2 10 685.00 780.28 (95.28) S10 770.75 T10 3.69 F11 774.44 9,078.56

2008-3 11 525.00 774.44 (249.44) S11 749.50 T11 (16.27) F12 733.23 62,220.99

2008-4 12 635.00 733.23 (98.23) S12 723.41 T12 (24.13) F13 699.28 9,649.12

2009-1 13 825.00 699.28 125.72 S13 711.85 T13 (14.07) F14 697.78 15,805.19

2009-2 14 735.00 697.78 37.22 S14 701.51 T14 (11.09) F15 690.42 1,384.96

2009-3 15 895.00 690.42 204.58 S15 710.87 T15 5.28 F16 716.15 41,854.81

2009-4 16 716.15

e2= 159,487.61

Yeart

DataForeca

stError

Level at the

End of t

Trend at the

end of t

Forecast for

t+1

Squared

Error

Xt Ftet = Xt-


0 - S0 703.66 T0 2.09 F1 705.75

2006-1 1 750.00 705.75 44.25 S1 710.17 T1 6.07 F2 716.25 1,958.06

2006-2 2 685.00 716.25 (31.25) S2 713.12 T2 3.26 F3 716.38 976.36

2006-3 3 715.00 716.38 (1.38) S3 716.24 T3 3.14 F4 719.38 1.91

2006-4 4 775.00 719.38 55.62 S4 724.94 T4 8.14 F5 733.08 3,093.73

2007-1 5 795.00 733.08 61.92 S5 739.27 T5 13.71 F6 752.99 3,833.84

2007-2 6 695.00 752.99 (57.99) S6 747.19 T6 8.49 F7 755.68 3,362.56

2007-3 7 705.00 755.68 (50.68) S7 750.62 T7 3.93 F8 754.55 2,568.84


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MSE1=0.1,2=0.09 for warm up sample= e2 / 15= 165,469.19 /15=11,031.28

Table 21. Exponential smoothing with a linear trend, 1= .10, 2=.01

2007-4 8 790.00 754.55 35.45 S8 758.09 T8 7.12 F9 765.22 1,256.80

2008-1 9 815.00 765.22 49.78 S9 770.20 T9 11.60 F10 781.80 2,478.27

2008-2 10 685.00 781.80 (96.80) S10 772.12 T10 2.89 F11 775.01 9,370.31

2008-3 11 525.00 775.01 (250.01) S11 750.01 T11 (19.61) F12 730.40 62,506.33

2008-4 12 635.00 730.40 (95.40) S12 720.86 T12 (28.20) F13 692.67 9,101.65

2009-1 13 825.00 692.67 132.33 S13 705.90 T13 (16.29) F14 689.62 17,511.94

2009-2 14 735.00 689.62 45.38 S14 694.15 T14 (12.20) F15 681.95 2,059.76

2009-3 15 895.00 681.95 213.05 S15 703.26 T15 6.97 F16 710.23 45,388.84

2009-4 16 710.23

e2= 165,469.19

Yeart

Data Forecast ErrorLevel at the

End of t

Trend at the

end of t

Forecast for

t+1

Squared

Error

Xt Ftet = Xt-

FtSt = Ft + 1et

Tt = Tt-1 +


0 - S0 703.66 T0 2.09 F1 705.75

2006-1 1 750.00 705.75 44.25 S1 710.17 T1 2.53 F2 712.71

2006-2 2 685.00 712.71 (27.71) S2 709.94 T2 2.25 F3 712.19

2006-3 3 715.00 712.19 2.81 S3 712.47 T3 2.28 F4 714.75

2006-4 4 775.00 714.75 60.25 S4 720.78 T4 2.89 F5 723.66


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MSE= e2/15= 407,203.35 /15= 27,146.89

2007-1 5 795.00 723.66 71.34 S5 730.80 T5 3.60 F6 734.40

2007-2 6 695.00 734.40 (39.40) S6 730.46 T6 3.20 F7 733.66

2007-3 7 705.00 733.66 (28.66) S7 730.80 T7 2.92 F8 733.71

2007-4 8 790.00 733.71 56.29 S8 739.34 T8 3.48 F9 742.82

2008-1 9 815.00 742.82 72.18 S9 750.04 T9 4.20 F10 754.24

2008-2 10 685.00 754.24 (69.24) S10 747.32 T10 3.51 F11 750.83

2008-3 11 525.00 750.83 (225.83) S11 728.25 T11 1.25 F12 729.50

2008-4 12 635.00 729.50 (94.50) S12 720.05 T12 0.31 F13 720.36

2009-1 13 825.00 720.36 104.64 S13 730.82 T13 1.35 F14 732.17

2009-2 14 735.00 732.17 2.83 S14 732.46 T14 1.38 F15 733.84

2009-3 15 895.00 733.84 161.16 S15 749.95 T15 2.99 F16 752.95

2009-4 16 965.00 752.95 212.05 S16 774.15 T16 5.11 F17 779.27 44,966.39

2010-1 17 995.00 779.27 215.73 S17 800.84 T17 7.27 F18 808.11 46,541.03

2010-2 18 865.00 808.11 56.89 S18 813.80 T18 7.84 F19 821.64 3,236.38

2010-3 19 915.00 821.64 93.36 S19 830.98 T19 8.77 F20 839.75 8,716.12

2010-4 20 995.00 839.75 155.25 S20 855.27 T20 10.33 F21 865.60 24,102.72

2011-1 21 1,125.00 865.60 259.40 S21 891.54 T21 12.92 F22 904.46 67,287.99

2011-2 22 905.00 904.46 0.54 S22 904.51 T22 12.93 F23 917.44 0.29

2011-3 23 965.00 917.44 47.56 S23 922.20 T23 13.40 F24 935.60 2,261.93

2011-4 24 1,185.00 935.60 249.40 S24 960.54 T24 15.90 F25 976.43 62,201.66

2012-1 25 1,245.00 976.43 268.57 S25 1,003.29 T25 18.58 F261,021.8

7

72,128.33

2012-2 26 955.00 1,021.87 (66.87) S26 1,015.18 T26 17.91 F271,033.1

04,471.65

2012-3 27 1,005.00 1,033.10 (28.10) S27 1,030.29 T27 17.63 F281,047.9

2789.36

2012-4 28 1,210.00 1,047.92 162.08 S28 1,064.13 T28 19.25 F291,083.3

826,270.86

2013-1 29 1,285.00 1,083.38 201.62 S29 1,103.54 T29 21.27 F301,124.8

140,651.66

2013-2 30 1,065.00 1,124.81 (59.81) S30 1,118.83 T30 20.67 F311,139.5

03,576.99

2013-3 31 1,139.50

e2= 407,203.35


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Appendix 7. Non Linear Smoothing

Table 22.Identification of 1 and 2 of non linear exponential smooting, 1=.10, 2=.01, =.1

Quarte

r t

Data Forecast ErrorLevel at the End

of t

Trend at the

end of t

Forecast for

t+1

Squared

Error

Xt Ft et=Xt-Ft St= Ft + 1etTt= Tt-1+

2etFt+1=St + Tt e

2

0 0 S0 703.66 T0 2.09 F1 705.96

2006-1 1 750.00 705.96 44.04 S1 710.36 T1 2.74 F2 713.38 2,128.01

2006-2 2 685.00 713.38 (28.38) S2 710.54 T2 2.73 F3 713.54 554.59

2006-3 3 715.00 713.54 1.46 S3 713.69 T3 3.02 F4 717.00 77.83

2006-4 4 775.00 717.00 58.00 S4 722.80 T4 3.90 F5 727.09 4,614.86

2007-1 5 795.00 727.09 67.91 S5 733.88 T5 4.97 F6 739.34 6,572.48

2007-2 6 695.00 739.34 (44.34) S6 734.91 T6 5.02 F7 740.43 735.72

2007-3 7 705.00 740.43 (35.43) S7 736.89 T7 5.17 F8 742.57 207.17

2007-4 8 790.00 742.57 47.43 S8 747.32 T8 6.16 F9 754.09 5,192.95

2008-1 9 815.00 754.09 60.91 S9 760.18 T9 7.38 F10 768.30 8,061.43

2008-2 10 685.00 768.30 (83.30) S10 759.97 T10 7.29 F11 767.99 2,429.49

2008-3 11 525.00 767.99 (242.99) S11 743.69 T11 5.59 F12 749.84 41,747.19

2008-4 12 635.00 749.84 (114.84) S12 738.35 T12 5.00 F13 743.85 5,428.87

2009-1 13 825.00 743.85 81.15 S13 751.97 T13 6.31 F14 758.91 15,321.91

2009-2 14 735.00 758.91 (23.91) S14 756.52 T14 6.70 F15 763.89 453.23

2009-3 15 895.00 763.89 131.11 S15 777.00 T15 8.68 F16 786.55 32,086.69

733.9676

e2= 125,612.44

MSE1=0.1,2=.01, =.1 for warm up sample= e2 / 15= 125,612.44 /15=8,374.16

Table 23. Identification of 1 and 2 of non linear exponential smooting, 1=.10, 2=.01, =.2

Quarte

rt


of t

Trend at the

end of t

Forecast for

t+1

Squared

Error

Xt

Ft

et

=Xt

-Ft

St

= Ft + 1

et

Tt= Tt-1+

2etF

t+1

=St + Tt

e2

0 0 S0 703.66 T0 2.09 F1 704.08

2006-1 1 750.00 704.08 45.92 S1 708.67 T1 0.88 F2 708.852,108.78

2006-2 2 685.00 708.85 (23.85) S2 706.46 T2 (0.06) F3 706.45568.64

2006-3 3 715.00 706.45 8.55 S3 707.30 T3 0.07 F4 707.3273.12


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2006-4 4 775.00 707.32 67.68 S4 714.09 T4 0.69 F5 714.234,580.77

2007-1 5 795.00 714.23 80.77 S5 722.30 T5 0.95 F6 722.496,524.60

2007-2 6 695.00 722.49 (27.49) S6 719.74 T6 (0.09) F7 719.73755.79

2007-3 7 705.00 719.73 (14.73) S7 718.25 T7 (0.16) F8 718.22216.84

2007-4 8 790.00 718.22 71.78 S8 725.40 T8 0.68 F9 725.535,152.37

2008-1 9 815.00 725.53 89.47 S9 734.48 T9 1.03 F10 734.698,003.99

2008-2 10 685.00 734.69 (49.69) S10 729.72 T10 (0.29) F11 729.662,468.88

2008-3 11 525.00 729.66 (204.66) S11 709.19 T11 (2.10) F12 708.7741,886.09

2008-4 12 635.00 708.77 (73.77) S12 701.40 T12 (1.16) F13 701.165,442.58

2009-1 13 825.00 701.16 123.84 S13 713.55 T13 1.01 F14 713.75 15,335.17

2009-2 14 735.00 713.75 21.25 S14 715.87 T14 0.41 F15 715.96451.58

2009-3 15 895.00 715.96 179.04 S15 733.86 T15 1.87 F16 734.2432,056.25

734.24

e2= 125,625.46

MSE1=0.1,2=.01, =.2 for warm up sample= e2 / 15= 125,625.46/15=8,375.03


Quarte

rt


of t

Trend at the

end of t

Forecast for

t+1

Squared

Error


2etFt+1=St + Tt e

2

0 0 S0 703.66 T0 2.09 F1 704.29

2006-1 1 750.00 704.29 45.71 S1 708.86 T1 1.08 F2 709.18 2,089.63

2006-2 2 685.00 709.18 (24.18) S2 706.77 T2 0.08 F3 706.79 584.86

2006-3 3 715.00 706.79 8.21 S3 707.61 T3 0.11 F4 707.64 67.40

2006-4 4 775.00 707.64 67.36 S4 714.38 T4 0.71 F5 714.59 4,536.89

2007-1 5 795.00 714.59 80.41 S5 722.63 T5 1.02 F6 722.94 6,465.62

2007-2 6 695.00 722.94 (27.94) S6 720.14 T6 0.03 F7 720.15 780.45

2007-3 7 705.00 720.15 (15.15) S7 718.64 T7 (0.14) F8 718.59 229.54

2007-4 8 790.00 718.59 71.41 S8 725.73 T8 0.67 F9 725.93 5,099.06

2008-1 9 815.00 725.93 89.07 S9 734.84 T9 1.09 F10 735.17 7,932.69


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2008-2 10 685.00 735.17 (50.17) S10 730.15 T10 (0.17) F11 730.10 2,516.88

2008-3 11 525.00 730.10 (205.10) S11 709.59 T11 (2.10) F12 708.96 42,065.77

2008-4 12 635.00 708.96 (73.96) S12 701.56 T12 (1.37) F13 701.15 5,469.86

2009-1 13 825.00 701.15 123.85 S13 713.54 T13 0.83 F14 713.78 15,338.45

2009-2 14 735.00 713.78 21.22 S14 715.91 T14 0.46 F15 716.04 450.10

2009-3 15 895.00 716.04 178.96 S15 733.94 T15 1.93 F16 734.52 32,025.18

734.24

e2= 125,652.37

MSE1=0.1,2=.01, =.3 for warm up sample= e2 / 15= 125,652.37 /15=8,376.82


Quarter t


of t

Trend at the

end of t

Forecast for

t+1

Squared

Error


Case Study on Milkfish Production of Illera Fish Farm

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