Time series model of imports and exports in Zanzibar

This study explored issues associated with modelling, identification techniques, diagnostic checking as well as short-term forecasting of univariate time series of imports and exports in Zanzibar using the Box-Jenkins methodology. The procedure used data from first quarter of 1975 to fourth quarter of 1999. Unfavourable characteristics were found in the data just like in other economic time series. This necessitated a transformation of the data from Tshs. into US $ unit of account and subsequently to natural logarithms. Nevertheless, other forms of transformation were attempted such as first and seasonal differencing as suggested by Box-Jenkins. Under those transformations various informal and formal trials, which include a discussion of their practical problems have been performed to achieve stationarity of the series. In the identification stage, the series were plotted and the sample autocorrelations were examined. The stationary series were used and four plausible time series models for import series and three for exports were used to estimate the associated parameters. The formal test statistics such as Ljung-Box Q-statistic and Durbin-Waston statistic were applied to verify the adequacy of the identified models. Diagnostic checking confirmed that ARIMA (2, 1, and 1) model for import series used had no serial correlation at 5 and 10 percent levels of significance, and other test statistics revealed that the model was adequate. The export series used came up with a model called SARIMA (1, 0, 1) x (0,1,1), which fulfilled all criteria for an appropriate model. Finally the adequate models were used to forecast quarterly values of imports and exports for the year 2000. The forecasts were compared with the actual values and empirical evaluation has been performed based on percent prediction limit and errors. In conclusion, since the forecast values are reasonable, the identified models can be considered as adequate for univariate short-term forecasting for the respective series.