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Linear‐representation Based Estimation of Stochastic Volatility Models
Author(s) -
FRANCQ CHRISTIAN,
ZAKOÏAN JEANMICHEL
Publication year - 2006
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2006.00495.x
Subject(s) - mathematics , autoregressive–moving average model , estimator , autoregressive model , stochastic volatility , weighting , volatility (finance) , mean squared error , series (stratigraphy) , monte carlo method , linear model , statistics , econometrics , medicine , paleontology , radiology , biology
. A new way of estimating stochastic volatility models is developed. The method is based on the existence of autoregressive moving average (ARMA) representations for powers of the log‐squared observations. These representations allow to build a criterion obtained by weighting the sums of squared innovations corresponding to the different ARMA models. The estimator obtained by minimizing the criterion with respect to the parameters of interest is shown to be consistent and asymptotically normal. Monte‐Carlo experiments illustrate the finite sample properties of the estimator. The method has potential applications to other non‐linear time‐series models.