A simple estimation method and finite-sample inference for a stochastic volatility model

The aim of the paper is to fulfill the gap for testing hypotheses on parameters of the log-normal stochastic volatility model, more precisely, to propose finite sample exact tests in the sense that the tests have correct levels in small samples. To do this, we examine method-of-moments-based tests and we provide explicit expressions for all the moments and the estimators which simplifies highly the test procedures. We then state the asymptotic distribution of the estimator as well as that of the proposed test statistics for testing the null hypothesis of no persistence in the volatility. We then compare the finite sample properties of the standard asymptotic techniques to that of Monte Carlo tests which are valid in finite samples and allow for test statistics whose null distribution may depend on nuisance parameters. In particular Maximized Monte Carlo tests introduced by Dufour (1995) have the exact level in finite samples when the p-value function is maximized over the entire set of nuisance parameters