Fig. 5

Plots of the standardised residuals (at the top), ACF of residuals (at the middle) and Ljung-Box statistic (at the bottom). The data points in the standardised residuals plot determine the randomness of the residuals for the actual data period (2008–2017) and the forecasted year (2018). The data points in the ACF of the residuals which ranged from -0.2 to 1.0 at various lags assessed the independence of the autocorrelation function (ACF). The data points of Ljung-Box statistic which ranged from 0.0 to 1.0 at various lags represent the p-values of the residuals. The horizontal dash lines in the ACF of the residuals and Ljung-Box statistic are the significant bounds