Fisher’s z Distribution-Based Mixture Autoregressive Model

We generalize the Gaussian Mixture Autoregressive (GMAR) model to Fisher’s z (ZMAR) for modeling nonlinear time series. The consists of a mixture K-component autoregressive models with mixing proportions changing over time. This can capture series both heteroskedasticity and multimodal conditional distribution, using distribution as an innovation in MAR model. ZMAR is classified nonlinearity level (or mode) because mode stable its location parameter, whether symmetric or asymmetric. Using Markov Chain Monte Carlo (MCMC) algorithm, e.g., No-U-Turn Sampler (NUTS), we conducted simulation study investigate performance compared GMAR Student t (TMAR) are applied daily IBM stock prices monthly Brent crude oil prices. results show that proposed outperforms existing ones, indicated by Pareto-Smoothed Important Sampling Leave-One-Out cross-validation (PSIS-LOO) minimum criterion.