Time Series Modelling with Application to Tanzania Inflation Data

Edward  Ngailo; Eliab  Luvanda; Estomih S.  Massawe

doi:10.4236/jdaip.2014.22007

Edward Ngailo, Eliab Luvanda, Estomih S. Massawe^*

Abstract: In this paper, time series modelling is examined with a special application to modelling inflation data in Tanzania. In particular the theory of univariate non linear time series analysis is explored and applied to the inflation data spanning from January 1997 to December 2010. Time series models namely, the autoregressive conditional heteroscedastic (ARCH) (with their extensions to the generalized autoregressive conditional heteroscedasticity ARCH (GARCH)) models are fitted to the data. The stages in the model building namely, identification, estimation and checking have been explored and applied to the data. The best fitting model is selected based on how well the model captures the stochastic variation in the data (goodness of fit). The goodness of fit is assessed through the Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC) and minimum standard error (MSE). Based on minimum AIC and BIC values, the best fit GARCH models tend to be GARCH(1,1) and GARCH(1,2). After estimation of the parameters of selected models, a series of diagnostic and forecast accuracy test are performed. Having satisfied with all the model assumptions, GARCH(1,1) model is found to be the best model for forecasting. Based on the selected model, twelve months inflation rates of Tanzania are forecasted in sample period (that is from January 2010 to December 2010). From the results, it is observed that the forecasted series are close to the actual data series.

Keywords: Time Series, Inflation, Autoregressive

Cite this paper: Ngailo, E. , Luvanda, E. and Massawe, E. (2014) Time Series Modelling with Application to Tanzania Inflation Data. Journal of Data Analysis and Information Processing, 2, 49-59. doi: 10.4236/jdaip.2014.22007.

References

[1] Ahiati, V.S. (2007) Discrete Time Series Analysis with ARMA Models. Revised Edition, Holden-Day, Oakland.

[2] Chatfield, C. (2000) Time Series Forecasting. Chapman and Hall, London.

[3] Webster, D. (2000) Webster’s New Universal Unabridged Dictionary. Barnes and Noble, New York.

[4] Hall, R. (1982) Inflation, Causes and Effects. Chicago University Press, Chicago.

[5] David, F.H. (2001) Modelling UK Inflation, 1875-1991. Journal of Applied Econometrics, 16, 255-275.
http://dx.doi.org/10.1002/jae.615

[6] Engle, R. (1982) The Use of ARCH/GARCH Models in Applied Econometrics. Journal of Economic Perspectives, 15, 157-168. http://dx.doi.org/10.1257/jep.15.4.157

[7] Bollerslev, T. (1986) Generalized Autoregressive Conditional Heteroscedasticity. Journal of Econometrics, 31, 307- 327. http://dx.doi.org/10.1016/0304-4076(86)90063-1

[8] Amos, C. (2010) Time Series Modelling with Application to South African Inflation Data. Master’s Thesis, University of Kwazulu Natal, Kwazulu Natal.

[9] Tsay, R.S. (2002) Analysis of Financial Time Series. John Wiley & Sons, Hoboken.
http://dx.doi.org/10.1002/0471264105

[10] Shephard, N. (1996) Statistical Aspects of ARCH and Stochastic Volatility Time Series in Econometrics, Finance and Other Fields. Chapman and Hall, London.

[11] Bollerslev, T., Chou, R.Y. and Kroner, K.F. (1992) ARCH Modeling in Finance: A Selective Review of the Theory and Empirical Evidence. Journal of Econometrics, 52, 5-59. http://dx.doi.org/10.1016/0304-4076(92)90064-X

[12] Ljung, G.M. and Box, G.E.P. (1978) On a Measure of Lack of Fit in Time Series Models. Biometrika, 65, 297-303. http://dx.doi.org/10.1093/biomet/65.2.297