Improved stochastic estimator of time-varying autoregressive models with heteroscedastic variance process and application

Motivated by modern research trends in econometric discipline, we propose the derivative-free extended Kalman filtering (DF-EKF) method appropriate for estimating the nonlinear state-space models with multiplicative noise scenario and/or space-dependent diffusion terms. In particular, an autoregressive process with the heteroscedastic variance assumption modeled by a stochastic volatility specification yields such models’ structure and requires a development of effective estimation methods. The discussed models are widely used for estimating the hidden volatility process, that is, usually regarded as a measure of risk. The novel DF-EKF allows to estimate the sophisticated nonlinear SV models’ specifications without derivatives computation and, more importantly, in case of non-additive noise scenario both in the process and measurement equations. The numerical tests substantiate the estimation method developed in this work. Empirical study concerns U.S. market volatility estimation by using S&P500 index in period from November 1927 to June 2020, which includes the U.S. Great Depression and the 2008–2009 global financial crisis.