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Kernel deconvolution of stochastic volatility models

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  • Fabienne Comte

Abstract

. In this paper, we study the problem of the nonparametric estimation of the function m in a stochastic volatility model ht = exp(Xt/2λ)ξt, Xt = m(Xt−1) + ηt, where ξt is a Gaussian white noise. We show that the model can be written as an autoregression with errors‐in‐variables. Then an adaptation of the deconvolution kernel estimator proposed by Fan and Truong [Annals of Statistics, 21, (1993) 1900] estimates the function m with the optimal rate, which depends on the distribution of the measurement error. The rates vary from powers of n to powers of ln(n) depending on the rate of decay near infinity of the characteristic function of this noise. The performance of the method are studied by some simulation experiments and some real data are also examined.

Suggested Citation

  • Fabienne Comte, 2004. "Kernel deconvolution of stochastic volatility models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 563-582, July.
    • Handle: RePEc:bla:jtsera:v:25:y:2004:i:4:p:563-582
    DOI: 10.1111/j.1467-9892.2004.01825.x
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    References listed on IDEAS

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    Cited by:

    1. Van Es, Bert & Spreij, Peter, 2011. "Estimation of a multivariate stochastic volatility density by kernel deconvolution," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 683-697, March.
    2. Jean-Jacques Forneron, 2019. "A Sieve-SMM Estimator for Dynamic Models," Papers 1902.01456, arXiv.org, revised Jan 2023.
    3. Zu, Yang, 2015. "Nonparametric specification tests for stochastic volatility models based on volatility density," Journal of Econometrics, Elsevier, vol. 187(1), pages 323-344.
    4. Yu, Zhuoxi & Wang, Dehui & Shi, Ningzhong, 2009. "Semiparametric estimation of regression functions in autoregressive models," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 165-172, January.

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