Applying Hybrid time series models for modeling bivariate time series data with different distributions for forecasting unemployment rate in the USA


Firas Ahmmed Mohammed,Moamen Abbas Mousa,



ARMAX,GARCH,GARCHX,Normal distribution,Student-t distribution,General Error distribution (GED),Hybrid model,Unemployment rate,Exchange rate,


Unemployment rate forecasting has become a particularly promising field of research in recent years because it's an important problem in state planning and management. Since the time series data are rarely pure linear or nonlinear obviously, sometimes contain both components jointly. Therefore, this study introduces new hybrid models contain Three commonly used, first is the Stochastic Linear Autoregressive Moving Average with eXogenous variable (ARMAX) model for modeled the relationship between the unemployment rate and exchange rate, second and third are a nonlinear Generalized Autoregressive Conditional Heteroscedasticity (GARCH) and GARCH with eXogenous variable (GARCHX) used When the assumption of homoscedasticity error variance is violated for the purpose of capture the volatility in the residuals of ARMAX model and to enhance the Forecasting ability of ARMAX model by combining it with other nonlinear models. In this case, to have a better forecasting efficiency, we introduce a hybrid methodology of amalgamating the forecasts from a linear time series model (ARMAX) and from a nonlinear time series model (GARCH, GARCHX) with three different distributions (Normal Distribution, Student’s t-distribution and General Error Distribution (GED)), the last two distributions for capturing fat-tailed properties in residuals time series. The hybrid approach specifically (ARMAX-GARCH) and (ARMAXGARCHX) have been used for modeling and forecasting the unemployment rate in the USA. Diverseapproacheshave beenemployed in the parameters vectorestimation. A comparison evaluation was as well been done based on mean absolute error (MAE), mean absolute percentage error (MAPE), as well as Root mean square error (RMSE) between the hybrid and their individual rival model in accordance with forecasting performance. From investigational results, it is perceived that the hybrid model (ARMAX-GARCHX) is more effectualthan other twin hybrid and individual rival models for the data under study. MATLAB, SAS, and EViews software packages have used for the data analysis


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