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Moments structure of ℓ 1 -stochastic volatility models

  • David Neto

    ()

  • Sylvain Sardy

    ()

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    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

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    File URL: http://hdl.handle.net/10.1007/s11135-011-9459-4
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    Article provided by Springer in its journal Quality & Quantity.

    Volume (Year): 46 (2012)
    Issue (Month): 6 (October)
    Pages: 1947-1952

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    Handle: RePEc:spr:qualqt:v:46:y:2012:i:6:p:1947-1952
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    1. Catalin Starica & Clive Granger, 2004. "Non-stationarities in stock returns," Econometrics 0411016, EconWPA.
    2. Andersen, Torben G. & Chung, Hyung-Jin & Sorensen, Bent E., 1999. "Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 91(1), pages 61-87, July.
    3. Sardy, Sylvain & Tseng, Paul, 2004. "On the Statistical Analysis of Smoothing by Maximizing Dirty Markov Random Field Posterior Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 191-204, January.
    4. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204.
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