Moments structure of ℓ 1 -stochastic volatility models
We consider Taylor’s stochastic volatility model (SVM) when the innovations of the hidden log-volatility process have a Laplace distribution (ℓ 1 exponential density), rather than the standard Gaussian distribution (ℓ 2 ) usually employed. Recently many investigations have employed ℓ 1 metric to allow better modeling of the abrupt changes of regime observed in financial time series. However, the estimation of SVM is known to be difficult because it is a non-linear with an hidden markov process. Moreover, an additional difficulty yielded by the use of ℓ 1 metric is the not differentiability of the likelihood function. An alternative consists in using a generalized or efficient method-of-moments (GMM/EMM) estimation. For this purpose, we derive here the moments and autocovariance function of such ℓ 1 -based stochastic volatility models. Copyright Springer Science+Business Media B.V. 2012
Volume (Year): 46 (2012)
Issue (Month): 6 (October)
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