Data cloning estimation for asymmetric stochastic volatility models

Abstract

The paper proposes the use of data cloning (DC) to the estimation of general univariate asymmetric stochastic volatility (ASV) models with flexible distributions for the standardized returns. These models are able to capture the asymmetric volatility, the leptokurtosis and the skewness of the distribution of returns. Data cloning is a general technique to compute maximum likelihood estimators, along with their asymptotic variances, by means of a Markov chain Monte Carlo (MCMC) methodology. The main aim of this paper is to illustrate how easily general univariate ASV models can be estimated and consequently studied via data cloning. Changes of specifications, priors and sampling error distributions are done with minor modifications of the code. Using an intensive simulation study, the finite sample properties of the estimators of the parameters are evaluated and compared to those of a benchmark estimator that is also user-friendly. The results show that the proposed estimator is computationally efficient, and can be an effective alternative to the existing estimation methods applied to ASV models. Finally, we use data cloning to estimate the parameters of general ASV models and forecast the one-step-ahead volatility of S&P 500 and FTSE-100 daily returns.

Keywords:

• Asymmetric volatility
• data cloning
• non-Gaussian nonlinear time series models
• skewed and heavy-tailed distributions

JEL classification:

• C11
• C13
• C15
• C58

Notes

1 For more examples on the negative correlation between returns and future volatility (see Yu, 2005), and on the threshold stochastic volatility (see Asai and McAleer, 2004, 2005, 2011), Chen et al. (2008, 2013), Elliott et al. (2011), Ghosh et al. (2015), Wu and Zhou (2015), and Wirjanto et al. (2016), among others.

2 Models’ extension to the multivariate context is beyond the scope of this paper and it is left for future research.

3 The Gaussianity of η_t when $m({ϵ}_t;\theta )=0$ is justified in Andersen et al. (2001) and Andersen et al. (2001, 2003).

4 See code example in Appendix.

5 See Fernández and Steel (1998) for the specification of the skew-Student-t distribution

6 The SE is defined as ${(R{V}_{t+1}-\widehat{{\sigma }_{t+1}})}^2$ while the Qlike is defined as $\mathit{Qlike}\equiv \frac{R{V}_{t+1}}{\widehat{{\sigma }_{t+1}}}-\left(\frac{R{V}_{t+1}}{\widehat{{\sigma }_{t+1}}}\right)-1.$ $R{V}_{t+1}$ corresponds to the realized volatility obtained with intradaily returns (5-minutes) calculated in https://realized.oxford-man.ox.ac.uk/data.

Additional information

Funding

The first author was financially supported by FCT - Fundação para a Ciěncia e a Tecnologia, Portugal, through the projects UID/MAT/00006/2013 and UID/MAT/00006/2019. The third author acknowledges financial support from Spanish Ministry of Economy and Competitiveness, research projects ECO2015-70331-C2-2-R and ECO2015-65701-P, and FCT grant UID/GES/00315/2019.