Parametric estimation of hidden stochastic model by contrast minimization and deconvolution

Abstract

We study a new parametric approach for particular hidden stochastic models such as the Stochastic Volatility model. This method is based on contrast minimization and deconvolution. After proving consistency and asymptotic normality of the estimation leading to asymptotic confidence intervals, we provide a thorough numerical study, which compares most of the classical methods that are used in practice (Quasi Maximum Likelihood estimator, Simulated Expectation Maximization Likelihood estimator and Bayesian estimators). We prove that our estimator clearly outperforms the Maximum Likelihood Estimator in term of computing time, but also most of the other methods. We also show that this contrast method is the most robust with respect to non Gaussianity of the error and also does not need any tuning parameter.

Parametric estimation of hidden Markov models by least squares type estimation and deconvolution

“…Recently, in [13], the authors generalize this approach to models defined as X i = b θ 0 (X i−1 )+η i , where b θ 0 is the regression function assumed to be known up to θ 0 and for homoscedastic innovations η i . Also, in [21] and [23], the authors propose a consistent estimator for parametric models assuming knowledge of the stationary density f θ 0 up to the unknown parameters θ 0 for the construction of the estimator. For many processes, this density has no analytic expression, and even in some cases where it is known, it may be more complex to apply deconvolution techniques using this density rather than the transition density.…”