Estimation methods for stochastic volatility models: a survey

Abstract

The empirical application of Stochastic Volatility (SV) models has been limited due to the difficulties involved in the evaluation of the likelihood function. However, recently there has been fundamental progress in this area due to the proposal of several new estimation methods that try to overcome this problem, being at the same time, empirically feasible. As a consequence, several extensions of the SV models have been proposed and their empirical implementation is increasing. In this paper, we review the main estimators of the parameters and the volatility of univariate SV models proposed in the literature. We describe the main advantages and limitations of each of the methods both from the theoretical and empirical point of view. We complete the survey with an application of the most important procedures to the S&P 500 stock price index.

Multivariate Stochastic Volatility: A Review

“…While this general set of estimation methods can all be used to estimate certain MSV models, only a small subset of them has been applied in the literature, namely, quasi-maximum likelihood, simulated maximum likelihood, and Markov chain Monte Carlo. Consequently, in this review we will focus on these three estimation methods and refer readers to Broto and Ruiz (2004) for a review of the remaining estimation methods.…”

“…In addition to efficiency, other important issues related to estimation include (1) estimation of the latent volatility; (2) determination of the optimal filtering, smoothing, and forecasting methods; (3) computational efficiency; (4) applicability for flexible modeling. Broto and Ruiz (2004) provided a recent survey regarding the numerous estimation techniques for univariate SV models, ranging from inefficient methods, such as GMM, quasi-maximum likelihood, and spectral GMM based on the characteristic function, to more efficient methods, such as EMM, indirect inference, numerical maximum likelihood, simulated maximum likelihood and Markov chain Monte Carlo. While this general set of estimation methods can all be used to estimate certain MSV models, only a small subset of them has been applied in the literature, namely, quasi-maximum likelihood, simulated maximum likelihood, and Markov chain Monte Carlo.…”

“…The univariate SV literature was surveyed in Ghysels et al (1996) and Shephard (1996), while estimation methods for univariate SV models were reviewed in Broto and Ruiz (2004). Shephard (2005) collects some of the more important studies on the topic.…”

The inflation and inflation uncertainty relationship for Turkey: a dynamic framework

“…If |φ| = 1 and σ 2 t = 0, the volatility is constant over time. If |φ| < 1, then σ 2 t and y t are considered stationary processes (Broto and Ruiz 2004). Therefore, φ is restricted to less than one in an absolute value.…”

Sequential Monte Carlo for inference of latent ARMA time-series with innovations correlated in time

“…To that end, two classes of problems are contemplated: one where the processes and the observations are linear functions of the states with additive and Gaussian perturbations and another where the functions are nonlinear and/or the noises are not Gaussian. The former class allows for estimating the latent process by optimal methods (e.g., Kalman filtering [16]) while the latter, by resorting to suboptimal methods, based on Bayesian theory [17] or other approximating techniques [18]. Precisely, popular approaches are based on (1) model transformations (e.g., extended Kalman filtering [19]), (2) resorting to QML solutions [15], and (3) Monte Carlo sampling principles.…”