Evaluation of Combined ARMA-ARCH and BL-ARCH models in Modeling Lake Urmia water level

Abstract

Many nonlinear models have been developed based on the mean errors modeling. However, the non-linear models with Autoregressive conditional heteoscedasticity are based on variance modeling. These models are combined with linear models, partly to increase the accuracy of modeling and predictions. In this study, using data from the Urmia Lake water level data for the period 1973-2012, the models with autocorrelation moving average and Bilinear model and two combined models (Autoregressive conditional heteoscedasticity) and (Bilinear conditional heteoscedasticity) were evaluated. To select the ARMA family models, AICC test were used and regression coefficient (r) and root mean square error (RMSE) tests were used for validation models. The results of validation the ARMA, BL, ARMA-ARCH and BL-ARCH models showed the correlation coefficient of 0.707, 0.618, 0.792 and 0.704 and the mean square root equal 2.838, 4.309, 2.031 and 4.11 between observed and modeling data respectively. Also the results showed that model accuracy increased with combining both linear and nonlinear models, but with combining two nonlinear models is caused reduce the accuracy of the models. Overall the results showed that by combining ARMA and ARCH models, the model error decreased about 28 percentage and combining two non-linear models caused increased model error about 2 percentage.

Keywords

• arma
• autoregressive
• bilinear model
• conditionally heteroscedasticity