Nonlinear autoregressive model with stochastic volatility innovations: Semiparametric and Bayesian approach

摘要

The first-order nonlinear autoregressive model with the stochastic volatility as the model of dependent innovations is considered and a semiparametric method is proposed to estimate the unknown function. Optimal filtering technique based on sequential Monte Carlo perspective is used for estimation of the hidden log-volatility in this model. Bayesian paradigm is applied for estimation of both the unknown parameters and hidden process using particle marginal Metropolis–Hastings scheme. Furthermore, an empirical application on simulated data and on the monthly excess returns of S&P 500 index is presented to study the performance of the schemes implemented.