Applying Diebold–Mariano Test for Performance Evaluation Between Individual and Hybrid Time-Series Models for Modeling Bivariate Time-Series Data and Forecasting the Unemployment Rate in the USA

Abstract

Unemployment rate forecasting has become a particularly promising domain of comparative studies in recent years because it is a major issue facing the economic forecasting process. Since the time-series data are rarely pure linear or nonlinear, obviously, sometimes contain both components jointly. Therefore, this study introduces a hybrid model that combines two commonly used models, namely, the Linear Autoregressive Moving Average with exogenous variable (ARMAX) model and nonlinear Generalized Autoregressive Conditional Heteroskedasticity with exogenous variable (GARCHX) model whose conditional variance follows a General error distribution (GED). That is, build a hybrid (ARMAX-GARCHX-GED) model employed in modeling bivariate time-series data of the unemployment rate and exchange rate. Usually, the forecasting performance evaluation based on the common classical forecast accuracy criteria such as Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percent Error (MAPE) have some specific limitations in application to choosing the optimal forecasting model. Therefore, in this paper, we employed a modern evaluation criterion based on the methodology advocated by Diebold–Mariano (DM) known as (DM test) as a new criterion for evaluation based on statistical hypothesis tests. This (DM test) has been applied in this study to distinguish the significant differences in forecasting accuracy between hybrid (ARMAX-GARCHX-GED) and individual ARMAX models. From the case study results and according to DM-test it is observed that the differences between the forecasting performances of models are significant and the hybrid model (ARMAX-GARCHX-GED) is more efficient than the individual competitive ARMAX model for the unemployment rate forecasting.