IB /z>0*r//3/£0 ANALYZING INFLATION RATE AND ECONOMIC GROWTH RATE OF SRI LANKA: TIME SERIES APPROACH X l B R A f V Y J j j l J V f c R S I T Y OF vifJRATUWA. SRI U W U . M O R A T U W A R. P. S.Prasadanie (06/8108) Dissertation submitted in partial fulfillment of the requirements for the degree Master of Science in Operational Research Department of Mathematics October 2011 U n i v e r s i t y o f M o r a t u w a I I University of Moratuwa = 5 = = = = = = Sri Lanka "~ T-H II 1 0 2 4 6 9 (OW69 1 0 2 4 6 9 Declaration I hereby certify that this dissertation entitled "Analyzing Inflation Rate and Economic Growth Rate of Sri Lanka: Time Series Approach" is entirely my own work. It has not been accepted for any degree or diploma in any university and to the best of my knowledge and belief or it is not being submitted for any other degree. Candidate: Miss R. P. S. Prasadanie. Signature: Date: Supervisor: Dr. T. S. G Peiris Department of Mathematics, University of Moratuwa 11 Abstract Inflation rate (INR) and Economic growth rate (EGR) are two main economic indicators for any country. These measurements are mainly represents the economic condition of the country, living condition of the people and total production of the country by agriculture, industry and service sectors. As a developing country, these indicators are most important to evaluate the current achievement of development and controlling the economy. In particular forecasting INR and EGR is immense useful for decision makers in policy implementation. Thus yearly data on INR and EGR during 1952-2006 of Sri Lanka is analyzed to forecast those values and to find the association between these two series. Result found that ARIMA (1,1,1) was the best fitted model for INR series. It was found that the errors of fitted model are white noise. The percentage error for the observed data (1952-2006) varies 0 to 17%. The model predicted the INR during 2007 and 2008 as 12.58 and 13.26, and the corresponding percentage errors are 10.1% and 16.6% respectively. ARIMA (1,1,0) was identified as the best fitted model for EGR series. It was found that the errors of fitted model are also white noise and the percentage error for the observed series (1952-2006) varies 0 to 23%. The predicted values for the EGR for 2007 and 2008 are 7.25 and 7.37, and the percentage errors are 6.58% and 22.8% respectively. There was a significant correlation coefficient between INR and EGR (r = 0.447 p = 0.001). The Granger Casualty test confirmed that the INR Granger causes with EGR. The order of the VAR model was decided by the minimum value criteria of sequential modified LR test statistic, Final prediction error (FPE), Akaike information criterion (AIC), Schwarz information criterion (SIC) and Hannan-Quinn information criterion (HQ). The best fitted VAR model identified is: INR, = 0 . 5 2 6 8 6 8 * I N R ( M ) + 0.557582*EGR ( ,_ 1) + 1.454656 (R 2 = 0.46, p < 0.05). It was not able to improve the model. Further more errors were found as random. The percentage errors of predicted values of INR for 2007 in and 2008 using univariate ARIMA model much lower than that of from the VAR model. Therefore it is recommended to use the above ARIMA model to forecast INR values for planning purposes. As this study was limited only for the two variables, it is suggested that the investigation to be carried out to improve the models by using other external variables such as exchange rate and borrow sum. Another drawback of this study is that both best fitted models got the positive percentage errors confirming that the fitted models always tend to over forecast. Therefore, it is also recommended to explore the possibility of improving such models as well. IV Acknowledgments I acknowledged with utmost gratitude in mind, the proper direction, encouragement and support extended to me by the supervisor of this study Dr. T. S. G Peiris, Senior Lecturer in Statistics and the course coordinator of the MSc (Operational Research) in the Department of Mathematics, University of Moratuwa. Further, my indebted gratitude and thanks go to the former coordinator of the MSc (Operational Research) to Mr T.M.J.A Cooray, Senior Lecturer in the Department of Mathematics, University of Moratuwa. 1 acknowledge with thanks to all the lecturers and all the staff members in the Department of Mathematics, who helped me in numerous way. v Contents Declaration Abstract Acknowledgement Contents List of tables List of figures CHAPTER 1- Introduction 1.1 Introduction to the study 1.1.1 Inflation rate 1.1.2. Economic growth rate 1.2 Objectives of the study 1.3 Data used 1.4 Structure of the report CHAPTER 2- Related work in other countries 2.1 General studies on inflation rate and economic growth rate 2.2 Inflation rate and economic growth rate of USA. 2.3 Inflation rate and economic growth rate of Japan. 2.4 Inflation rate and economic growth rate of India . 2.5 Summary CHAPTER 3- Statistical Methodology 3.1 Basic explanatory analysis 3.2. Inferential statistics 3.3.1 Jarque Bera test vi • 3.2.2 Normal probability plot 12 3.3 Time series 13 3.3.1 Stationarity of the time series 13 3.3.2 Unit root 14 3.3.3 Dicky Fuller test 14 3.3.4 Sample Auto Correlation Function (ACF) 14 3.3.5 Partial Auto Correlation Function (PACF) 15 3.3.6 Differencing 16 3.3.7 Autoregressive Process of order p-AR(p) 17 3.3.8 Moving Average Process of order q-MA(q) 17 3.3.9 Autoregressive Moving Average of order p,q-ARMA(p,q) 18 3.3.10 ARMA (1,1) process 18 3.3.11 Box-Jenkins model identification 19 3.3.12 Granger Causality test 21 3.3.13 Cointegration 22 3.3.14 Vector Autoregression(VAR) Model 22 3.3.15 Lag selection criteria 23 Chapter 4 - Time Series Model for {INR t} series 4.1 Description 24 4.1.1 Descriptive Statistics. 26 4.2 Analyze of Time Series Plot of INR 28 4.2.1 Trend analysis of INR 29 4.2.2 ACF for INR 30 4.2.3 First difference series of INR 31 4.2.4 ACF and PACF of first difference series. 34 4.2.5 Dickey Fuller test to confirm the property of stationary 36 vii 4.3 Model fitting 38 4.4 Model identification 48 4.5 Forecasting. 51 4.6 Summary 52 Chapter 5 - Time Series Model for {EGR t} series • 5.1 Description 53 5.1.1 Descriptive Statistics. 55 5.2 Analyze of Time Series Plot of EGR 57 5.2.1 Trend analysis of EGR 57 5.2.2 ACF for EGR 59 5.2.3 First difference series of EGR 60 5.2.4 ACF and PACF of first difference series. 6 3 5.2.5 Dickey Fuller test to confirm the property of stationary 65 5.3 Model fitting 67 5.4 Model identification 78 5.5 Forecasting. 85 5.6 Summary 86 Chapter 6 - Model fitting by VAR methodology. 6.1 Introduction 87 6.2 Pair wise correlation of INR and EGR 87 6.1.2 Granger Causality test for INR and EGR 88 6.1.3 Johansen cointegration test for INR and EGR 89 6.2 Model fitting by using VAR methodology 91 • 6.3 Forecasting by using VAR model 93 6.4 Comparison of VAR and univariate ARIMA 94 viii Chapter 7- Conclusions and Recommendations. 95 References 96 Appendixes Appendix I - Inflation rates of Sri Lanka 1952-2006 97 Appendix II - Economic growth rates of Sri Lanka 1952-2006 98 Appendix III - Residuals of ARIMA( 1,1,1) of INR 99 Appendix IV - Residuals of ARIMA( 1,1,0) of EGR 101 ix List of tables Table No P a S e Table 4.1- INR 1952-2006 25 Table 4.2- Descriptive statistics of INR 26 Table 4.3- Accuracy measures 30 Table 4.4- Autocorrelations of INR 30 Table 4.5- First difference series of INR 32 Table 4.6- Autocorrelations for first differenced series of INR 34 Table 4.7- Partial autocorrelations for first differenced series of INR 35 Table 4.8- DF summary for INR (without trend and intercept) 36 Table 4.9- DF summary for INR (with intercept) 36 Table 4.10- DF summary for INR (with trend and intercept) 37 Table 4.11- Modified Box-Pierce (Ljung-Box) Chi-Square statistic 38 Table 4.12- Final Estimates of Parameters 38 Table 4.13- Modified Box-Pierce (Ljung-Box) Chi-Square statistic 40 Table 4.14- Final Estimates of Parameters 40 Table 4.15- Modified Box-Pierce (Ljung-Box) Chi-Square statistic 42 Table 4.16- Final Estimates of Parameters 42 Table 4.17- Modified Box-Pierce (Ljung-Box) Chi-Square statistic 44 Table 4.18- Final Estimates of Parameters 44 Table 4.19- Modified Box-Pierce (Ljung-Box) Chi-Square statistic 46 Table 4.20- Final Estimates of Parameters 46 Table 4.21- Summary of the model statistics for INR 48 Table 4.22- Parameters estimates of ARIMA( 1,1,1) 50 Table 4.23- Foecasting INR by using ARIMA(1,1,1) 51 Table 5.1-INR 1952-2006 54 Table 5.2- Descriptive statistics of EGR 55 Table 5.3- Accuracy of Trend Measures 58 X Table 5.4- Autocorrelations for EGR 59 Table 5.5- First difference series of EGR 61 Table 5.6- Autocorrelations for first differenced series of EGR 63 Table 5.7- Partial autocorrelations for first differenced series of EGR 64 Table 5.8- DF test summary for EGR (without trend and intercept) 65 Table 5.9- DF test summary for EGR (with intercept) 66 Table 5.10- DF test summary for EGR (with trend and intercept) 66 Table 5.11- Modified Box-Pierce (Ljung-Box) Chi-Square statistic 67 Table 5.12- Final Estimates of Parameters 68 Table 5.13- Modified Box-Pierce (Ljung-Box) Chi-Square statistic 69 Table 5.14- Final Estimates of Parameters 70 Table 5.15- Modified Box-Pierce (Ljung-Box) Chi-Square statistic 71 Table 5.16- Final Estimates of Parameters 72 Table 5.17- Modified Box-Pierce (Ljung-Box) Chi-Square statistic 74 Table 5.18- Final Estimates of Parameters 74 Table 5.19- Modified Box-Pierce (Ljung-Box) Chi-Square statistic 76 Table 5.20- Final Estimates of Parameters 76 Table 5.21- Summary of the model statistics for EGR 78 Table 5.22- Parameter estimates of ARIMA (1,1,0) 80 Table 5.23- Parameter estimates of ARIMA (1,1,0) after removing the 81 constant Table 5.24- Forecasting EGR by using ARIMA (1,1,0) 85 Table 6.1- Correlations between INR and EGR 87 Table 6.2- Summary of Granger causality test 88 Table 6.3- Summary of Johansen Cointegration test 89 Table 6.4- Unrestricted Adjustment Coefficients of INR and EGR 89 Table 6.5- Adjustment Coefficients of INR and EGR 90 xi Table 6.6- Summary of VAR lag order selection criteria Table 6.7- Vector autoregression estimates Table 6.8- Summary of forested values of INR Table 6.9- Summary of forested values of EGR Table 6.10- Comparison of model for prediction INR Table 6.11- Comparison of model for prediction EGR xii • List of Figures Figure No Page Figure 3.1- Normal probability plot 12 Figure 4.1- Histogram of INR 27 Figure 4.2- Normal probability plot of INR 27 Figure 4.3- Time series plot of INR 1952-2006 28 Figure 4.4- Trend analysis of INR-linear 29 Figure 4.5- Trend analysis of INR-Quadratic 29 Figure 4.6-ACF for INR 31 Figure 4.7- First difference series of INR 33 Figure 4.8- ACF of first difference series of INR 34 Figure 4.9- PACF of first difference series of INR 35 Figure 4.10- ACF of ARIMA( 1,1,0) 39 Figure 4.11-PACF of ARIMA( 1,1,0) 39 Figure 4.12-ACF of ARIMA(1,1,1) 41 Figure 4.13-PACF of ARIMA( 1,1,1) 41 Figure 4.14- ACF of ARIMA(0,1,1) 43 Figure 4.15-PACF of ARIMA(0,1,1) 43 Figure 4.16- ACF of ARIMA(2,1,1) 45 Figure 4.17-PACF of ARIMA(2,1,1) 45 Figure 4.18- ACF of ARIMA(2,1,0) 47 Figure 4.19- PACF of ARIMA(2,1,0) 47 Figure 4.20- Histogram of residuals of ARIMA( 1,1,1) 49 Figure 4.21- Normal PP of residuals of ARIMA( 1,1,1) 50 Figure 4.22- Forecasting INR by ARIMA( 1,1,1) 51 Figure 5.1- Histogram of EGR 55 xiii • Figure .5.2- Normal probability plot of EGR 56 Figure 5.3- Time series plot of EGR 57 Figure 5.4- Trend analysis of EGR -linear 57 Figure 5.5- Trend analysis of EGR -Quadratic 58 Figure 5.6- ACF for EGR 60 • Figure 5.7- Time series plot for first difference series of EGR 62 Figure 5.8- ACF of first difference series of EGR 63 Figure 5.9- PACF of first difference series of EGR 64 Figure 5.10- ACF of ARIMA( 1,1,0) 68 Figure 5.11-PACF of ARIMA(1,1,0) 69 Figure 5.12- ACF of ARIMA( 1,0,1) 70 Figure 5.13-PACF of ARIMA(1,0,1) 71 Figure 5.14- ACF of ARIMA( 1,1,0) 72 Figure 5.15- PACF of A R M A ( 1,1,0) 73 Figure 5.16- ACF of ARIMA(0,1,1) 75 Figure 5.17-PACF of ARIMA(0,1,1) 75 Figure 5.18-ACF of ARIMA(1,1,1) 77 Figure 5.19-PACF of ARIMA(1,1,1) 77 Figure 5.20- Histogram of the residuals of ARIMA( 1,1,0) 79 Figure 5.21- Normal PP of residuals of ARIMA(1,1,0) 80 Figure 5.22- ACF of the residuals of ARIMA( 1,1,0) 81 After removing the constant Figure 5.23- PACF of the residuals of ARIMA(1,1,0) 82 Figure 5.24- Histogram of the residuals of ARIMA( 1,1,0) 83 after removing the constant Figure 5.25- Normal probability plot of the residuals of ARIMA( 1,1,0) 84 * after removing the constant Figure 5.26- Forecasting EGR 85 xiv