Optimizing Wavelet Selection for VARX Models: Insights from Iraq’s Government Expenditures and Foreign Reserves
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Abstract
This study seeks to improve the accuracy of the VARX model used for analyzing monthly economic data through noise processing techniques using wavelet transform. A set of wavelet types, including Coiflets, Daubechies, Symlets, biorthogonal, and inverse biorthogonal, are evaluated by testing all different wavelet orders and levels to improve the reliability of the model and its ability to simulate real economic patterns and predict future trends. This research aims to identify the optimal wavelets and appropriate levels and orders based on performance criteria (AIC and BIC). To achieve this goal, a Universal threshold-based algorithm with soft rules is proposed to determine the optimal value, as well as its performance is compared with traditional and non-wavelet-based methods. In the traditional method, the level of analysis (L = 3) and order (N = 3) were applied to all types of wavelets, except for Biorthogonal and Reverse Biorthogonal, where the level (L = 3) and order (N = 8) were applied, which are the default values in MATLAB23. This method was tested using real data. The methodology included applying the study to the monthly data of the Iraqi economy during the period from January 31, 2010, to July 31, 2024, to analyze the impact of external variables such as money supply and oil revenues on internal variables such as government expenditures and official reserves (OR). The results demonstrated the efficiency of the proposed method in reducing noise and estimating the parameters of VAR models, which contributed to improving the overall performance of the model. This comprehensive framework provides significant improvements in the analysis of economic data, by providing accurate forecasts and deep insights to decision-makers, which enhances the reliability of estimates and helps in understanding economic trends more effectively.
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