Nonparametric specification tests for stochastic volatility models based on volatility density

Abstract

Zu, Yang (2015) Nonparametric specification tests for stochastic volatility models based on volatility density. Journal of Econometrics, Access from the University of Nottingham repository: http://eprints.nottingham.ac.uk/45843/1/svtestvol.pdf Copyright and reuse:The The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. JEL Classification: C58, C12, C14.

Consistent nonparametric specification tests for stochastic volatility models based on the return distribution

“…Notice that the return sequence (X i ) n i=1 is a sequence of stochastic integrals of the volatility process with respect to an independent Brownian motion B over small fixed intervals. By the following lemma from Zu (2015), the return series inherit the stationarity, ergodicity and the β-mixing properties from the volatility process.…”

“…From a practical perspective, the stochastic volatility model considered in Corradi and Swanson in more appropriate to be used with interest rate data, where mean-reversion is often observed; while our model is more appropriate for equity and exchange rate price data, where unit-root behaviour is often observed. Zu (2015) analyzes an alternative approach to a similar testing problem, by comparing the nonparametric kernel deconvolution estimator of the volatility density with its parametric counterpart.…”

Nonparametric Density Estimation by B-Spline Duality

“…The application of nonparametric density estimators is widespread and growing in finance and financial econometrics. These estimators are often introduced to estimate transition densities (see Aït-Sahalia, 1996), the diffusion matrix (see Bandi and Moloche, 2017), state price densities (see Zhang et al, 2009;Song and Xiu, 2016;Beare and Schmidt, 2014), realized variance and stock volatilities (see Van Es, Spreij, and Zanten, 2003;Zu, 2015), implied volatilities (see Chen and Xu, 2014), as well as bond yields. In quantitative risk management, density estimates enable the calculation of risk measures, such as value-at-risk and expected shortfall (see Wang and Zhao, 2016;Cai and Wang, 2008;Opschoor, Dijk, and van der Wel, 2017).…”

The realized empirical distribution function of stochastic variance with application to goodness-of-fit testing

“…Inspired by the above, a common approach is to compare (conditional) moments of the integrated variance of a parametric model with a nonparametric estimator hereof (see, e.g., Bollerslev and Zhou, 2002;Corradi and Distaso, 2006;Dette and Podolskij, 2008;Dette, Podolskij, and Vetter, 2006;Todorov, 2009;Todorov, Tauchen, and Grynkiv, 2011;Vetter and Dette, 2012). Zu (2015) proposes a test based on a de-convolution kernel density estimator of the distribution of the integrated variance, Lin, Lee, andGuo (2013, 2016) resort to a characteristic function approach, while Bull (2017) proposes a wavelet-based test.…”