Wavelet-based Bayesian Analysis of GARMAX Model

We introduce a wavelet-based Bayesian method for estimating the parameters of the Gegenbauer Autoregressive Moving Average model with an exogenous input (GARMAX). This model accommodates both persistent and cyclical dynamics in the presence of an external predictor. Our approach employs the Whittle likelihood derived from the maximal overlap discrete wavelet transform (MODWT), a redundant transform whose oversampling enhances estimation precision. Leveraging this wavelet-based Whittle likelihood allows for computationally efficient sampling from the posterior distribution while incorporating prior information about the model parameters. We illustrate the method’s accuracy and efficiency through simulation studies, demonstrating its potential as a robust alternative to traditional estimation techniques.