Sering Touray

University of The Gambia

School of Business and Public Administration

Division of Economics

Forecasting For Business and Economics

(ECON 313)

Fall Semester 2010.

Topic: Forecasting Real GDP Using

ARIMA Model: The Case of The

Gambia.

December 2010.

Table of Contents

Abstract ...................................................................................................................................................... 3

Chapter 1: Introduction .......................................................................................................................... 4

Chapter 2: Literature Review ................................................................................................................ 5

Chapter 3: Methodology ......................................................................................................................... 7

3.1: Model Specification ........................................................................................................................ 7

3.2: Model Estimation ............................................................................................................................ 8

3.3: Diagnostic Tests ............................................................................................................................. 8

3.4: Forecasting ...................................................................................................................................... 8

Chapter 4: Data Analysis and Discussion ....................................................................................... 10

4.1: Data Analysis ................................................................................................................................ 10

4.2: Findings and Discussions ........................................................................................................... 11

Chapter 5: Conclusions and Recommendations ........................................................................... 13

5.1: Conclusions ................................................................................................................................... 13

5.2: Recommendations ....................................................................................................................... 13

Chapter 6: Appendix ................................................................................................................................ 15

6.1 List of Tables .................................................................................................................................. 15

References ............................................................................................................................................ 20

Data Source .......................................................................................................................................... 21

Abstract

The ability to accurately forecast economic variables remains to be the determining

factor of the reliability of economic models. The paper attempts to forecast the Real

GDP values of The Gambia for the years 2010 and 2011 using data obtained from the

International Monetary Fund (IMF) over the period 1990 through 2009. The paper uses

the Autoregressive Integrated Moving Average (ARIMA) also called the Box Jenkins

model (BJ model) composed of a certain number of the previous values of the variable

in question, the order it is integrated to attain a state of stationarity and the number of

residuals to be included in the model; thus modeled as (p d q). After careful analysis,

the model adopts an ARIMA composed of (2 1 0). Using a one step forecast, the values

of Real GDP for The Gambia for the years 2010 and 2011 were obtained which showed

continuity in the increasing trend of real GDP. This was followed by a series of

diagnosis of the model ran and the values forecasted.

Key words: Real GDP, ARIMA, one step forecast and International Monetary Fund

Chapter 1: Introduction

The Gambia as in most countries computes her GDP annually. This function is usually

executed by the Ministry of Finance which in partnership with other stakeholders

handles the fiscal policy component of the economic policies of The Gambia. According

the statistical appendix on The Gambia published by IMF, the components of GDP

calculation are: agriculture, manufacturing and trade. (Statistical Appendix, 1997). Of

recent, that combination has changed to compose of: agriculture, manufacturing and

services. (Statistical Appendix, 2006).

GDP also as in many economies serves as the measure of economic growth and

development. In the past couple of years, the Gambia’s economic growth has been

attributed to its GDP growth. This achievement earned her not only recognition but also

other economic benefits such as debt relief, grants and aid etc.

As viewed by most economists, Real GDP provides a better measure of estimating the

output as it takes care of price differences. For this reason, the paper uses the real GDP

values of The Gambia in estimating the model.

The paper employs an ARIMA model on real GDP data obtained from IMF for a 20

years period with the object of forecasting the real GDP values for the years 2010 and

2011 using a one-step forecast. Stata 10.0 is the statistical software used to do the

analysis.

Chapter 2: Literature Review

Gross Domestic Product has attracted the views of many economists all other the world.

As a measure of development, it has attracted a lot of controversies from economists as

well as development specialists on issues relating to its ability to measure development.

Despite this seemingly unending debate between economists and development

specialists, there seems to be no other measure of development than GDP (at least not

a single one that has attained the level of fame reached by GDP). As a time series

variable, several models have been developed to enable the ease of forecasting GDP.

ARIMA being one of them has attracted a lot of fame amidst other forecasting models

which has been attributed to its forecasting accuracy. On many occasions, it is reported

that the forecasted values of certain variables by ARIMA tend to be very close to their

actual.

In the example of the ARIMA model given in his text- ‘Basic Econometrics’, Damodar N.

Gujirati showed how the forecasted value of quarterly GDP for the US was close to the

actual: a forecasted value of $4877 billions for the first quarter of 2008; the actual of

which was $4873.7 billons. (Gujirait, 2004).

The ARIMA model has also registered success in the evaluation of interest rates which

is increasing being one of the most watched financial variable. It has been used to

forecast interest rates in India. However, due the clustering effect on the interest rates,

the GARCH model outperformed the ARIMA. (Radha and Thenmozhi, undated).

A related but different study on exchange returns was also done in Nigeria. The author

used the ARIMA model to forecast stock exchange returns in Nigeria. ((Emenike, 2010))

Not only has the success stories of the ARIMA model restricted to forecasting

macroeconomic variables, but also non-economic variables as well. It has been used in

the modeling and predicting traffic characteristics in the UK. The authors of the paper

used a combination of ARIMA and GARCH models to predict the nature of traffic for use

by congestion control. The estimated model was compared to the an FARIMA model

and was found to be better. (Zhou & Sun, undated).

A paper on the production potentials of Pakistan in the area of wheat has also been

examined using ARIMA. In the paper, the authors using the past trend of wheat

production estimated the production of wheat over the period 2002-2022. (Igbal et al,

2005).

Despite its fame and success, the ease of estimating the parameters in the ARIMA

model is regarded by some as problematic. (Igbal et al, 2005). To other authors, the

Autocorrelation Function (ACF) and the Partial Autocorrelation Function (PACF) and the

Akiake Information Criterion provide good estimation of the parameters of the ARIMA

model. (Emenike, 2010)

The forecasting of GDP continues to receive a lot of attention from econometricians.

Several other models have also been used in forecasting GDP in different parts of the

world. The pseudo-real time forecasting model was used in forecasting short term

values of GDP using large monthly data sets. (Barhoumi, Benk, et al, April 2008).

A similar paper was also written to forecast the monthly values of French GDP using a

revised version of the Opium model. (Barhoumi, Brunhes-Lesage et al, September

2008).

Chapter 3: Methodology

3.1: Model Specification

An advantage of the use of the ARIMA model is the provision of a clear cut algorithm to

be followed through the entire process of model estimation and result generation. The

steps being:

◦ Model Identification, choosing p, d and q

◦ Estimation of parameters of the chosen model

◦ Diagnostic checking

◦ Forecasting (Gujirati, 2004)

However, before employing the ARIMA model, a pre-estimation test on the data was

done. Given the fact that, real GDP is a time series data, a stationarity test had to be

done. The Augmented Dickey Fuller (ADF)- which takes care of autocorrelation

problem, was done on the data to ascertain its stationarity level. It showed that the data

was only stationary after its first difference and thus was an I(1).

ARIMA as a time series forecasting techniques is composed of three components. An

Autoregressive (AR) process-p, an Integrated (I) process-d and a Moving Average (MA)

process-q. On the basis of this, the chosen model for the paper was:

Δdyt =δ+θ1 Δdyt-1+θ2 Δ

dyt-2+----- + θpyt-p+et-lα et-1-α2 et-2 αqe t-2

Where yt represents Real GDP,

θ= coefficients of the AR processes up to p lags,

Α= coefficients of the MA processes up to q lags

Δdyt= the difference of Real GDP d times

3.2: Model Estimation

The identification of the ARIMA parameters of the ARIMA model followed suit. As in

most publications, the Autocorrelation Function (ACF) and Partial Autocorrelation

Function were used to estimate the values of p and q. Since the data was integrated at

order 1, the d in the ARIMA model was estimated to be 1. After due analysis of the

statistical significance of the results obtained from the ACF and PACF, it was concluded

that the Real GDP of The Gambia for the period 1990-2009 obtained from IMF was not

explained by a MA process. On the other hand, it was found that the real GDP values

followed an AR process; i.e real GDP was explained by some of its previous values.

Therefore, the following model was estimated:

Δyt =δ+θ1 Δyt-1+θ2 Δyt-2

The real GDP values obtained which were expressed in millions of Dalasis, were left in

their functional forms (linear) and thus the estimated model did not change.

3.3: Diagnostic Tests

The estimation of the model was followed by a series of diagnostic tests to ascertain

that the estimated model is the better model in forecasting the real GDP values of The

Gambia. The residuals obtained were tested for autocorrelation using the Durbin

Watson (DW) tests, the Augmented Dickey Fuller test and a graphical representation of

the residuals was done to ascertain if they are white noise. In addition to this, several

other combinations of p, d and q were tested but all proved that the chosen model was

the better one.

3.4: Forecasting

The one-step forecasting technique was used to obtain the forecasted values of real

GDP. The one step forecasting technique performs an out of sample forecast for an

additional period (Parlow, 2010). Its also generates forecasted values of all except one

preceding periods. Graphically representing the forecasted values against their actual

values, the goodness of fit of the chosen model could be ascertained.

The forecasted values were also tested for accuracy purposes. This was done using the

Root Mean Square Error (RMSE) which calculates the error between the forecasted

values and their corresponding actuals (Parlow, 2010).

Chapter 4: Data Analysis and Discussion

4.1: Data Analysis

The real GDP values obtained for The Gambia from the International Monetary Fund’s

website over the period 1990 through 2009 showed an increasing trend with structural

breaks at some time. This renders it unfit for time series analysis at its state. The first

difference however, showed a state of stationarity. Refer to Appendix, Tables 1 and 2.

The application of the ARIMA model on the obtained data started with the estimation of

the values of p, d and q using the ACF and PACF (graphically and with a correlogram)

(See Appendix, tables 5, 6, and 7) resulted in the model ARIMA (2 1 0). This conclusion

was reached after the examination of statistical significance of the results such as their

p- values. At a significance level of 5 per cent, it was proved that MA process was not

significant even up to lag 6 leading to the conclusion that the GDP figures were not

explained by the preceding values of their residuals (Refer to Appendix, Table 8), but

were explained by its two previous values (See Appendix, Table 9). Since it was

difference at order 1 to be stationary, the integrated process was one. For the results of

the ARIMA (2 1 0) please refer to the Appendix, Table 10.

Economically, it appears to be significant that real GDP is explained by its two previous

values. Considering the size of The Gambian economy and the nature of its sectors;

service being the biggest contributor to GDP (The Ministry of Finance, 2009), it follows

sense to argue that the values of GDP are affected by its close lags. In addition to this,

the output of the service industry the largest of which comes from the banking sector is

pretty much short term. Its does not take three, four to five years to obtain the output of

such an industry; after all, most of the transactions are monetary in nature.

Agriculture on the other hand employs about 60% of The Gambia’s labour force and

contributes about 20% to GDP. If the arguments of the perfectly competitive markets

given its assumptions are anything to go by, supply is fixed in the short run and thus,

farmers cannot alter their productions within a farming season thus minimizing the effect

of agricultural production in the long run. Even if they do alter their productions in the

succeeding season, the agricultural paradox argues that anticipated effect on income

might not be attained.

Basically, given the size of The Gambian economy and its lack of industries, it holds

water to argue that indeed the finding that GDP is explained by its previous values up to

lag two is justifiable. This will probably be greater if the size of the economy was bigger

and more presence of industries.

In addition to the afore-mentioned propositions, the results of the diagnostics showed

that indeed the estimated model somehow fitted the data. The residuals obtained which

were tested using the ADF showed that they were white noise and no autocorrelation

problem was detected from the Durbin Watson test. Refer to Appendix, Tables 11, 12

and 13.

4.2: Findings and Discussions

Ceteris Paribus, the one-step forecast used to forecast the values of real GDP for the

years 2010 and 2011 revealed that real GDP will continue to increase in both years.

The model predicts a 2.2% increment in real GDP for the year 2010- D21.89 (in

billions), which is a drop from 5.6% in the previous year- D21.42 (in billions). For the

year 2011, the model predicts a further increase in real GDP to D22.38 (in billions) but

with a constant growth rate of 2.2%. See Appendix, Table 14 for a graphical

representation of the results.

The drop in the growth rate of real GDP could be attributed to the now settling down

effects of the financial crisis on remittances and ultimately income of most Gambians. In

addition to this, the 2010 rainy season floods which was declared a state of emergency

due to the devastating nature of the floods on compounds, farms, livestock etc. might

lead to a drop in the values of GDP.

Deviations from the forecasted value should be surprising. Some economic variables (or

at least variables whose economic effects can be calculated) have witnessed some

changes. The introduction of the new tourism logo and efforts made to market the

potentials of The Gambia, the establishment of The Gambia Import- Export Promotion

Agency (GIEPA) which is the reformed version of The Gambia Investment Promotion

Free Zone Agency (GIPFZA), the improvement in the revenue collection abilities of the

Gambia Revenue Authority (GRA), the Gambia Radio and Television Service’s satellite,

the imposition of airport tax etc. could lead to a drama of offsetting of effects. Despite

the fact that some of the afore-mentioned variables have witnessed changes a year or

two ago, their effects might start to show (if not already) and ultimately affect GDP.

On another front, the drive to maintaining the single digit inflation by the Central Bank

and government’s massive construction projects might also contribute affecting GDP.

The estimated model used in this paper, did not cover the scope of the relationship

between inflation and GDP in context of The Gambia.

The Root Mean Square Error (RMSE) which was computed to ascertain the accuracy of

the model reported a value of 0 .46395528 which considering the nature of the data and

the sample size obtained can be contained.

Chapter 5: Conclusions and Recommendations

5.1: Conclusions

The findings of the paper justified by the predictions of the estimated model and the

prevailing economic climate of The Gambia means well for the economy. The

forecasted fall in the growth rate of GDP is an expectation given the financial crisis and

its effects of all economies of all regions of the world. As a matter of fact, the IMF

forecast of real GDP for 2010 differs from the forecasted value from this model by

D0.599 (in billions) which could be attributed to a difference in the forecasting

technique.

It is also worth noting that ARIMA is an atheoretic model and thus predictions might not

follow economic expectations. It is for this reason, that I cited some of the possibilities of

deviations in the preceding chapter.

ARIMA has registered success stories in the studies it has been used. Thus

expectations of not much deviation from its usual trend seem to be statistically

significant.

5.2: Recommendations

Having looked at the findings of the paper, the following recommendations have been

reached.

1. The prediction of a slight increment in GDP could be taken as a good omen for

the economy. However, it would be important if a study on the distribution of the

GDP could be studied. This would unveil non-performing sectors to provide an

opportunity of improving them in a bid to avoiding the occurrence of an 80-20

rule. This is particularly necessary for the Finance Ministry. Having had over the

bulletins of their quest to fight poverty in the coming year, it would be important to

figure out through a study the sectors that need to be adjusted to alleviate

poverty. Without an idea of the components of the economy and their relationship

to the welfare of the people, such innovations as poverty alleviations could be

futile.

2. There is need for the Minister of Finance to control issues such as unplanned

expenditures in the economy. This could lead not only to deviations in the

forecasted values of real GDP but anticipated outcome and policy effects.

Unplanned expenditures must be based on genuine economic reasons and not

just a mere desire to spend.

3. There is the need to centralize data especially on key macroeconomic variables.

One of the limitations of the study has been the unavailability of data from

Gambian sources. Many a times, data obtained from different sources tend to

differ. In some cases, one can only trust the source of the data and not the data.

This leads to disparities in forecast values and ultimately a threat to policy

making. Using international organizations as reservoirs for data on The Gambia

is not only unsecure but also unreliable. For the purpose of reliable forecasts for

efficient policy making, needed data most be provided accurately and readily

available. The absence of this however, has proved to be a deterring factor to

most studies in The Gambia. The government of The Gambia through her

agencies most make efforts to ensure that data unavailability at local levels get to

be a thing of the past.

4. There is the need to conduct a further study using a non- atheoretic model with a

larger sample size to obtain more beneficial forecast values of real GDP. The

literature obtained on ARIMA showed explicitly showed that in most of the

studies done using ARIMA a large sample size has always been obtained.

Chapter 6: Appendix

6.1 List of Tables

Analysis of Real GDP

Table 1: Real GDP at its original level

10

15

20

25

rgdp

1990 1995 2000 2005 2010year

Table 2: First difference of Real GDP

1990

1995

2000

2005

2010

year

-.5 0 .5 1 1.5drgdp

Table 3: Augmented Dickey Fuller Test for stationarity

Test Statistic 1% Critical value

5% Critical value

10% Critical value

Z(t) 1.529 3.750 3.000 2.630

MacKinnon approximate p-value for Z(t) = 0.9976

Table 4: Augmented Dickey Fuller Test for stationarity on first difference

Test Statistic 1% Critical value

5% Critical value

10% Critical value

Z(t) -3.133 -3.750 -3.000 -2.630

MacKinnon approximate p-value for Z(t) = 0.0242

Table 5: Correlogram of ACF and PACF

8 -0.0641 0.3517 42.463 0.0000 7 0.0321 0.5402 42.312 0.0000 6 0.1496 0.1044 42.277 0.0000 5 0.2960 0.2192 41.574 0.0000 4 0.4126 0.1060 39.003 0.0000 3 0.5322 0.4410 34.323 0.0000 2 0.6708 0.1682 26.993 0.0000 1 0.8311 1.0565 15.995 0.0001 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] -1 0 1 -1 0 1

Table 6: Autocorrelation Function (ACF)

-0.5

00.0

00.5

0

Auto

corr

ela

tions o

f drg

dp

0 2 4 6 8Lag

Bartlett's formula for MA(q) 95% confidence bands

Table 7: Partial Autocorrelation Function (PACF) -0

.40

-0.2

00.0

00.2

00.4

0

Part

ial auto

corr

ela

tions o

f drg

dp

0 2 4 6 8Lag

95% Confidence bands [se = 1/sqrt(n)]

Table 8: AR processes at lag 6

Log likelihood = -11.62963

Drgdp Coef. OPG Std. Err.

Z P>|z| [95% Conf. Interval]

drgdp _cons

.610351 .0987149 6.18 0.000 .4168734 .8038287

ARMA

Ar

L1. .0222502 .2466456 0.09 0.928 -.4611664 .5056668

L2. -.2380724 .3692183 -0.64 0.519 -.961727 .4855822

L3. .1548211 .4569445 0.34 0.735 -.7407736 1.050416

L4. -.0806445 .5336262 -0.15 0.880 -1.126533 .9652436

L5. -.0806445 .4382332 0.05 0.962 -.8377855 .880057

L6. -.3099892 .5754493 -0.54 0.590 -1.437849 .8178707

/sigma .4374344 .0813722 5.38 0.000 .2779478 .5969211

Table 9: MA processes at lag 6

Log likelihood = -10.70634

Drgdp Coef. OPG Std. Err. z P>z [95% Conf.

drgdp

_cons 0.615313 0.103954 5.92 0 0.411567 0.819058

ARMA ma L1. -0.17597 . . . . .

L2. -0.3514 . . . .

L3. 0.361696 6101.016 0 1 -11957.4 11958.13

L4. 0.023669 130.6556 0 1 -256.057 256.1039

L5. -0.18572 1026.623 0 1 -2012.33 2011.959

L6. -0.67227 3716.236 0 1 -7284.36 7283.016

/sigma 0.362261 1001.361 0 1 -1962.268 1962.993

Table 10: ARIMA (2 1 0)

Drgdp Coef. OPG Std. Err. z P>z [95% Conf.

drgdp

_cons _cons .6052706 0.116684 5.19 0.000 .3765742 0.833967

ARMA Ar

L1. -.008395 0.269368 -0.03 0.975 -.5363465 0.519557

L2. - .2232385 0.356829 -0.63 0.532 .922611 0.476134

/sigma .4634502 .0930337 04.98 0.000 .2811074 .6457929

Table 11: Diagnostic Tests: Augmented Dickey Fuller Test on the residuals

Test Statistic 1% Critical value

5% Critical value

10% Critical value

Z(t) -4.297 -3.750 -3.000 -2.630

MacKinnon approximate p-value for Z(t) = 0.0004

Table 12: Durbin Watson test for autocorrelation

Durbin-Watson d-statistic( 3, 18) = 1.846441

Table 13: White Noise Test: Plot of the residuals

.5.6

.7.8

.9

xb p

redic

tion,

one-s

tep

1990 1995 2000 2005 2010year

Table 14: Graph of forecasted value against their actuals

10

15

20

25

1990 1995 2000 2005 2010year

rgdp y prediction, one-step

References

1. Barhoumi, K., et al, (2008), ‘Short-term forecasting of GDP using large monthly

datasets a pseudo real-time forecast evaluation exercise’ European Central

Bank. Available at http://ssrn.com/abstract=1084910

2. Barhoumi, K., Brunhes-Lesage, V., et al, (2008) ‘Monthly Forecasting Of French

Gdp: A Revised Version Of The Optim Model’, Banque De France, Available at:

http://ssrn.com/abstract=1678444

3. Emenike K. O., (2010), ‘Forecasting Nigerian Stock Exchange Returns: Evidence

from Autoregressive Integrated Moving Average (ARIMA) Model’, University of

Nigeria, Nigeria.

4. Gujirati, D. N., (2004), ‘Basic Econometrics’ (fourth edition), McGraw Hill

Companies.

5. Igbal, N., et al. (2005), ‘Use of the ARIMA Model for Forecasting Wheat Area and

Production in Pakistan’, Journal of Agriculture and Social Sciences, vol. 1813–

2235/2005/01–2–120–122.

6. International Monetary Fund (1997), ‘The Gambia- Statistical Annex’,

Washington DC.

7. International Monetary Fund (2006), ‘The Gambia- Statistical Appendix’,

Washington DC.

8. Parlow A, (2010), ‘Unit Root Tests and Box Jenkins’, University of Wisconsin

Madison, USA.

9. Pesaran, M. H., et al (2004), ‘Forecasting Time Series Subject to Multiple

Structural Breaks’, Institute for the Study of Labour (IZA), Germany.

10. Radha S., and Thenmozhi M., (undated): ‘Forecasting short term interest rates

using ARMA, ARMA-GARCH and ARMA-EGARCH models’, Indian Institute of

Technology Madras, Chennai.

11. The Ministry of Finance of The Gambia (2009), ‘Budget Speech’, Banjul.

12. Zhou, B., et al, (undated), ‘Traffic Modeling and Prediction using ARIMA/GARCH

Model’, University of Surrey, United Kingdom.

Data Source

1. International Monetary Fund, World Economic Outlook Database, October 2010.

Available at: www.imf.org.