Simple estimators and inference for higher-order stochastic volatility models

We study the problem of estimating higher-order stochastic volatility [SV(p)] models. Due to the difficulty of evaluating the likelihood function, this remains a challenging problem, even in the relatively simple SV(1) case. We propose simple moment-based winsorized ARMA-type estimators, which are computationally inexpensive and remarkably accurate. The proposed estimators do not require choosing a sampling algorithm, initial parameter values, or an auxiliary model. We show that a Durbin–Levinson-type updating algorithm can be applied to recursively estimate models of increasing order p. The asymptotic distribution of the estimators is established. Due to their computational simplicity, the proposed estimators allow one to perform finite-sample Monte Carlo tests. Simulation results show that the proposed estimators have lower bias and mean squared error than all alternative estimators (including Bayes-type estimators). The proposed estimators are applied to S&P 500 daily returns (1928–2016). We find that an SV(3) model is preferable to an SV(1) model.