Stat Methods Appl (2017) 26:437–452
Estimation and asymptotic covariance matrix
for stochastic volatility models
Published online: 4 November 2016
© Springer-Verlag Berlin Heidelberg 2016
Abstract In this paper we compute the asymptotic variance-covariance matrix of
the method of moments estimators for the canonical Stochastic Volatility model. Our
procedure is based on a linearization of the initial process via the log-squared transfor-
mation of Breidt and Carriquiry (Modelling and prediction, honoring Seymour Geisel.
Springer, Berlin, 1996). Knowledge of the asymptotic variance-covariance matrix of
the method of moments estimators offers a concrete possibility for the use of the clas-
sical testing procedures. The resulting asymptotic standard errors are then compared
with those proposed in the literature applying different parameter estimates. Applica-
tions on simulated data support our results. Finally, we present empirical applications
on the daily returns of Euro-US dollar and Yen-US dollar exchange rates.
Keywords Stochastic volatility · Asymptotically stationary process · Consistency ·
Asymptotic normality · Asymptotic variance-covariance matrix · Financial returns
JEL Classiﬁcation C01 · C13 · C58
Stochastic Volatility (SV) models have been of growing interest in time series analysis
with numerous ﬁnancial applications like, for example, option pricing, asset allocation
and risk management. For a comprehensive discussion on SV models see, for example,
Taylor (1994). Also of interest is Tsyplakov (2010) survey paper and its references.
Department of Economics “Marco Biagi”, University of Modena and Reggio E,
Viale Berengario 51, 41121 Modena, Italy