Shape-constrained semiparametric additive stochastic volatility models

ABSTRACT

Nonparametric stochastic volatility models, although providing great flexibility for modelling the volatility equation, often fail to account for useful shape information. For example, a model may not use the knowledge that the autoregressive component of the volatility equation is monotonically increasing as the lagged volatility increases. We propose a class of additive stochastic volatility models that allow for different shape constraints and can incorporate the leverage effect – asymmetric impact of positive and negative return shocks on volatilities. We develop a Bayesian fitting algorithm and demonstrate model performance on simulated and empirical datasets. Unlike general nonparametric models, our model sacrifices little when the true volatility equation is linear. In nonlinear situations we improve the model fit and the ability to estimate volatilities over general, unconstrained, nonparametric models.

KEYWORDS:

• Bayesian isotonic regression
• leverage effect
• Markov chain Monte Carlo
• nonlinear time series
• particle filter
• state space model

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Peter Craigmile and Jiangyong Yin were supported in part by the National Science Foundation (NSF) under grant DMS-0906864. Xinyi Xu, Jiangyong Yin and Steven MacEachern were supported in part by the NSF under grant DMS-1209194. Peter Craigmile is additionally supported in part by the NSF under grants SES-1024709, DMS-1407604 and SES-1424481, and the National Cancer Institute of the National Institutes of Health under Award Number 1R21CA212308-01, and the project title is ‘Evaluating how licensing-law strategies will change neighborhood disparities in tobacco retailer density’. Xinyi Xu and Steven MacEachern are supported under grant DMS-1613110.

Notes on contributors

Jiangyong Yin

Jiangyong Yin was a Ph.D. student at The Ohio State University, and is currently working at CapitalG, San Francisco, California.

Peter F. Craigmile

Peter F. Craigmile is Professor at Department of Statistics, The Ohio State University.

Xinyi Xu

Xinyi Xu is an Associate Professor at Department of Statistics, The Ohio State University.

Steven MacEachern

Steven MacEachern is Professor at Department of Statistics, The Ohio State University.