The error structure was then fitted with the autoregressive integrated moving average (ARIMA) model. The order of p, q, and d in ARIMA model was determined by carefully examination of ACF, PACF, and IACF plots. Maximum likelihood method was used for estimation of parameters.
Chi-Square test on the residuals was used to assess if series was left with white noise. Non-significant Chi-Square statistics indicated that our model fitted well. Residual QQ plots were used to test the departure from normality assumption.
A set of candidate models were arrived at, and final model was selected by the lowest akaike information criterion (AIC), significant parameter estimates (indicator and AR/MA lags), Chi-square test on the residuals, residuals diagnosis plots, and forecast plots. Fitted plots were produced in both log and original scale.