Modelling heteroscedasticty of streamflow times series

Figures & data

Fig. 1 (a) ACF of daily streamflows, (b) ACF of the lag-1 differenced logarithmic daily streamflow, (c) p values of the Ljung-Box of the residuals, and (d) p values of the Engle test for SSRs of the ARIMA (13,1,4) model.

Fig. 2 p values of the Engle test for SSRs of the ARIMA-PGARCH error model.

Fig. 3 p values of the Engle test for SSRs of the ARIMA-TGARCH error model.

Fig. 4 p values of the Engle test for SSRs of the ARIMA-EGARCH error model.

Fig. 5 Scatter plot of observed against estimated streamflows for different models.

Fig. 6 Time series plot of observed and estimated streamflows for different models.

Table 1  Evaluation criteria for time series models (italics indicate result is significant)

Criteria	Models
	ARIMA	PGARCH	TGARCH	EGARCH
AME	54.34	58.23	58.33	42.11
PDIFF	11.44	33.7	32.25	19.33
MAE	2.46	2.93	2.92	2.03
RMSE	5.66	7.15	7.1	4.86
RAE	0.27	0.32	0.32	0.22
R ^2 (%)	86	81	81	93
IoAd (%)	94	89	90	96

Fig. 7 QQ plots of time series models.