Nonlinear AR(1) with dependent innovations

Volatility clustering is one of the stylized statistical properties of a financial time series that can be described by the stochastic volatility model. In this paper, we expand a first-order nonlinear autoregressive model with the stochastic volatility as the model of dependent innova- tions. The nonlinear part of model is estimated by a semiparametric method and the particle Markov chain Monte Carlo method is used for the optimal filtering of the hidden log-volatility. A simulation study is performed to assess the performance of the proposed methods