A Coiflets-Based Wavelet Decomposition Method for Improving Parameter Estimation in Combined ARIMA–GARCH Models

This paper proposes a wavelet-based framework to improve parameter estimation and forecasting performance in combined ARIMA–GARCH models for nonlinear and non-normal time series with time-varying variance. Although standard ARIMA–GARCH models are widely used to describe conditional mean and volatility dynamics, they may fail to capture localized and multiscale behavior, since the model structure is typically constructed on a single scale. To address this limitation, the proposed approach integrates discrete wavelet decomposition based on Coiflets wavelets into the ARIMA–GARCH framework. The original series is decomposed into approximation and detail components representing low- and high-frequency dynamics. Each component is modeled separately using ARIMA–GARCH specifications and then recombined through the inverse wavelet transform to reconstruct an improved series representation. The performance of the proposed methodology is evaluated through an extensive simulation study under different data-generating scenarios and sample sizes, as well as through an application to real monthly gold price data from Iraq. The results indicate that the wavelet-based ARIMA–GARCH models provide superior performance compared with the classical specification in terms of information criteria and forecasting accuracy measures. In particular, low-order Coiflets decompositions offer an effective balance between model flexibility and parsimony. Overall, the proposed framework provides a practical and efficient approach for modeling multiscale volatility behavior and improving inference and forecasting in complex time series applications.