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Box--Cox realized asymmetric stochastic volatility models with generalized Student's t -error distributions

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  • Didit B. Nugroho
  • Takayuki Morimoto

Abstract

This study proposes a class of non-linear realized stochastic volatility (SV) model by applying the Box--Cox (BC) transformation, instead of the logarithmic transformation, to the realized estimator. The non-Gaussian distributions such as Student's t , non-central Student's t , and generalized hyperbolic skew Student's t -distributions are applied to accommodate heavy-tailedness and skewness in returns. The proposed models are fitted to daily returns and realized kernel of six stocks: SP500, FTSE100, Nikkei225, Nasdaq100, DAX, and DJIA using an Markov chain Monte Carlo Bayesian method, in which the Hamiltonian Monte Carlo (HMC) algorithm updates BC parameter and the Riemann manifold HMC algorithm updates latent variables and other parameters that are unable to be sampled directly. Empirical studies provide evidence against both the logarithmic transformation and raw versions of realized SV model.

Suggested Citation

  • Didit B. Nugroho & Takayuki Morimoto, 2016. "Box--Cox realized asymmetric stochastic volatility models with generalized Student's t -error distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(10), pages 1906-1927, August.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:10:p:1906-1927
    DOI: 10.1080/02664763.2015.1125862
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    Cited by:

    1. Makoto Takahashi & Yuta Yamauchi & Toshiaki Watanabe & Yasuhiro Omori, 2024. "Realized Stochastic Volatility Model with Skew-t Distributions for Improved Volatility and Quantile Forecasting," Papers 2401.13179, arXiv.org, revised Oct 2024.
    2. Tsionas, Mike G. & Philippas, Dionisis & Philippas, Nikolaos, 2022. "Multivariate stochastic volatility for herding detection: Evidence from the energy sector," Energy Economics, Elsevier, vol. 109(C).
    3. Abanto-Valle, Carlos A. & Rodríguez, Gabriel & Garrafa-Aragón, Hernán B., 2021. "Stochastic Volatility in Mean: Empirical evidence from Latin-American stock markets using Hamiltonian Monte Carlo and Riemann Manifold HMC methods," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 272-286.
    4. Taylor, Nick, 2017. "Realised variance forecasting under Box-Cox transformations," International Journal of Forecasting, Elsevier, vol. 33(4), pages 770-785.
    5. Didit Budi Nugroho & Takayuki Morimoto, 2019. "Incorporating Realized Quarticity into a Realized Stochastic Volatility Model," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(4), pages 495-528, December.

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