This research work was set to examine the activities of the Nigerian Stock Exchange using the All-Share Index monthly data published between the year 2000 and 2015. Based on the plotted ACF graph of the original series, it was observed that the series was non-stationary and also exhibited some elements of seasonality which necessitated the series to be differenced to attain stationarity as well as reducing the seasonal effect. This deseasonalised stationary series data was modeled in order to determine the stability of the parameter estimation. The plots of the ordinary and seasonal differenced series autocorrelation and partial autocorrelation functions suggested some models for selection but the Akaike and Bayesian Information Criterion was used to select the model that really provided the best fit for the series. From the family of the seasonal models generated using R-Console, seasonal ARIMA (2, 1, 1)×(0, 1, 1)12 model was found to be the most adequate model that really captured the dependence in the series and that also tracked the seasonal effect. The adequacy of the chosen model was subsequently checked using both the Shapiro-Wilk and Ljung-Box test approaches. The Shapiro-Wilk test for normality of residuals while Ljung-Box test for dependence in residuals of the fitted model. Method of maximum likelihood was used to determine the estimates of the parameters of the identified models and each parameter was statistically tested for significance. The model was used for a short term forecast (2016-2018).
Key words: Deseasonalised, autocorrelation function, partial autocorrelation function, stationarity, All-Share Index.
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