VAR TIME SERIES ANALYSIS USING WAVELET SHRINKAGE WITH APPLICATION

Abstract

This study investigates the VAR time series data of the overall expenditures and income in the Kurdistan ‎Region of Iraq. It applies multivariate wavelet shrinkage within the VAR model, comparing it to ‎traditional methods to identify the most appropriate model. The chosen model will then be used to ‎predict general expenditures and revenues for the years 2022-2026. The analysis involved assessing the ‎stationarity of the expenditure and revenue time series, which are interrelated variables during the ‎interval 1997-2021, and identifying the overall trend through differencing to achieve stationarity. The ‎proposed method incorporated multivariate wavelet shrinkage in the VAR model to address data ‎contamination in expenditures and revenue using various wavelets like Coiflets, Daubechies, Symlets, ‎and Fejér–Korovkin at different orders. Threshold levels were estimated using the SURE method and soft ‎thresholding rules to denoise the data for the following analysis within the VAR model. Model selection ‎was based on Akaike and Bayes information criteria. The analysis, conducted using MATLAB, indicated ‎the superiority of the proposed method over traditional methods, forecasting a continued rise in ‎expenditures and revenues for the Iraqi Kurdistan region from 2022 to 2026. The findings suggest that ‎advanced techniques can offer more accurate economic forecasts, benefiting regional planning and ‎policy-making.‎

Keywords

• Time Series
• VAR
• Wavelet
• Threshold
• Soft Rule