Bayesian Time Series Modelling with Wavelet Analysis for Forecasting Monthly Inflation

This article treats data noise and outliers in Bayesian ARIMA models through wavelet analysis. Apply the discrete wavelet transformation using Daubechies and Symlets wavelets for orders 10 and 15 to decompose the data of Bayesian ARIMA models into their frequency components. Threshold the wavelet coefficients using a method like soft thresholding, with the threshold selected via Stein’s unbiased risk estimate and soft rule. Simulation experiments were used with real data representing the monthly inflation in the Kurdistan Region of Iraq (2009-2024) with a forecast for the next ten months. The proposed wavelet-based Bayesian ARIMA method provides a robust framework for handling noisy time series data and offers significant improvements over classical methods, making it an appealing choice for practical applications in time series forecasting, particularly when dealing with outliers and noise.