Ch07 - Forecast

8/6/2019 Ch07 - Forecast

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9.1 Introduction to Time Series

Forecasting Forecasting is the process of predicting the future.

Forecasting is an integral part of almost all

business enterprises. Examples

Manufacturing firms forecast demand for their product, toschedule manpower and raw material allocation.

Service organizations forecast customer arrival patterns tomaintain adequate customer service.

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Introduction More examples

Security analysts forecast revenues, profits, and

debt ratios, to make investment recommendations. Firms consider economic forecasts of indicators

(housing starts, changes in gross national profit)

before deciding on capital investments.

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Introduction Good forecasts can lead to

Reduced inventory costs. Lower overall personnel costs. Increased customer satisfaction.

The forecasting process can be based on: Educated guess. Expert opinions. Past history of data values, known as a time

series.

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Components of a TimeSeries

Long-term trend A time series may be stationary or exhibit trend

over time. Long-term trend is typically modeled as a linear,

quadratic or exponential function. Seasonal variation

When a repetitive pattern is observed over sometime horizon, the series is said to have seasonalbehavior.

Seasonal effects are usually associated withcalendar or climatic changes.

Seasonal variation is frequently tied to yearlycycles.

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Cyclical variation An upturn or downturn not tied to seasonal

variation.

Usually results from changes in economicconditions . Random effects

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A stationary time series

Linear trend time series

Linear trend and seasonality time series

Time

Timeseriesvalue

Future


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Steps in the Time Series

Forecasting Process The goal of a time series forecast is toidentify factors that can be predicted.

This is a systematic approach involving the

following steps. Step 1: Hypothesize a form for the time series

model.

Step 2: Select a forecasting technique.

Step 3: Prepare a forecast.

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Forecasting ProcessStep 1: Identify components included in the time series

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Collect historical data. Graph the data vs. time.

Hypothesize a form for the time series

model. Verify this hypothesis statistically.


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Forecasting Process Step 2: Select a Forecasting Technique

Select a forecasting technique from among severaltechniques available. The selection includes

Determination of input parameter values Performance evaluation on past data of each technique

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Step 3: Prepare a Forecast using theselected technique


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7.2 Stationary ForecastingModels

In a stationary model the mean value of the time series is assumed to be constant.

The general form of such a model is

Where:y t = the value of the time series at time period t.

0 = the unchanged mean value of the time series.

t = a random error term at time period t.

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y t = 0 + t

The values of t

are assumedto be

independent

The valuesof t

are assumedto

have amean of 0.


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Stationary ForecastingModels Checking for trend

Use Linear Regression if t is normally distributed. Use a nonparametric test if t is not normally distributed.

Checking for seasonality component Autocorrelation measures the relationship between thevalues of the time series in different periods.

Lag k autocorrelation measures the correlation betweentime series values which are k periods apart.

Autocorrelation between successive periods indicates a

possible trend. Lag 7 autocorrelation indicates one week seasonality

(daily data). Lag 12 autocorrelation indicates 12-month seasonality

(monthly data) . Checking for Cyclical Components

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Moving Average Methods

The last period technique

The forecast for thenext period isthe last observed value.

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t t+1 t t+1t t+1 t t+1t1t yF =+


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t+1 t+1tt-2 t-1 t-2 t-1 tt-2 t-1 tt-2 t-1 tt-2 t-1 tt-2 t-1 t

The moving average

method The forecast is theaverage of

the last n observationsof thetime series. n

y...yyF 1nt1tt1t+

+

+++=


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The weighted moving average

method More recent values of the time seriesget larger weights than past valueswhen performing the forecast.

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1tF += w 1y t + w 2y t-1 +w 3y t-2 + + w ny t-n+1w 1 w 2 w n

w i = 1


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Forecasts for Future Time Periods

The forecast for time period t+ 1 is theforecast for all future time periods:

This forecast is revised only when newdata becomes available.

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...,3,2,1kforyF tkt ==+


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YOHO BRAND YO - YOs

Moving Average Methods -

Galaxy Industries is interested in forecastingweekly demand for its YoHo brand yo-yos.

The yo-yo is a mature product. This yeardemand pattern is expected to repeat nextyear.

To forecast next year demand, the past 52weeks demand records were collected.

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YOHO BRAND YO - YOs

Moving Average Methods - Three forecasting methods were suggested:

Last period technique - suggested by Amy Chang.

Four-period moving average - suggested by Bob Gunther. Four-period weighted moving average - suggested by Carlos

Gonzalez.

Management wants to determine: If a stationary model can be used.

What forecast will be obtained using each method?

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YOHO BRAND YO YOs- Solution

Construct the time series plot

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Week Demand Week Demand Week Demand Week Demand

1 415 14 365 27 351 40 2822 236 15 471 28 388 41 3993 348 16 402 29 336 42 3094 272 17 429 30 414 43 4355 280 18 376 31 346 44 2996 395 19 363 32 252 45 5227 438 20 513 33 256 46 3768 431 21 197 34 378 47 4839 446 22 438 35 391 48 41610 354 23 557 36 217 49 24511 529 24 625 37 427 50 39312 241 25 266 38 293 51 48213 262 26 551 39 288 52 484

Week Demand Week Demand Week Demand Week Demand

1 415 14 365 27 351 40 2822 236 15 471 28 388 41 3993 348 16 402 29 336 42 3094 272 17 429 30 414 43 4355 280 18 376 31 346 44 2996 395 19 363 32 252 45 5227 438 20 513 33 256 46 376

8 431 21 197 34 378 47 4839 446 22 438 35 391 48 41610 354 23 557 36 217 49 24511 529 24 625 37 427 50 39312 241 25 266 38 293 51 48213 262 26 551 39 288 52 484


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0

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

6 0 0

7 0 0

1 5 9

1 3

1 7

2 1

2 5

2 9

3 3

3 7

4 1

4 5

4 9

D e m a n

d

W eeks

S er ies 1

Neither seasonality nor cyclical effects can beobserved


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Is trend present?

Run linear regression to test 1 in the modely t= 0+ 1 t+ t

Excel results

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Coeff. Stand. Err t-Stat P-value Lower 95 Upper 95%

Intercept 369.27 27.79436 13.2857 5E-18 313.44 425.094Weeks 0.3339 0.912641 0.36586 0.71601 -1.49919 2.166990.71601

This large P-value indicatesthat there is little evidence that trend exists

onclusion: A stationary model is appropriat

Ch07 - Forecast

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