Modeling Autoregressive Conditional Skewness and Kurtosis with Multi‐Quantile CAViaR

Halbert White, Tae‐Hwan Kim and Simone Manganelli

in Volatility and Time Series Econometrics

Published in print March 2010 | ISBN: 9780199549498
Published online May 2010 | e-ISBN: 9780191720567 | DOI:

Series: Advanced Texts in Econometrics

 Modeling Autoregressive Conditional Skewness and Kurtosis with Multi‐Quantile CAViaR

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This chapter extends Engle and Manganelli's (2004) univariate CAViaR model to a multi-quantile version, MQ-CAViaR. This allows for both a general vector autoregressive structure in the conditional quantiles and the presence of exogenous variables. The MQ-CAViaR model is then used to specify conditional versions of the more robust skewness and kurtosis measures discussed in Kim and White (2004). The chapter is organized as follows. Section 2 develops the MQ-CAViaR data generating process (DGP). Section 3 proposes a quasi-maximum likelihood estimator for the MQ-CAViaR process, and proves its consistency and asymptotic normality. Section 4 shows how to consistently estimate the asymptotic variance—covariance matrix of the MQ-CAViaR estimator. Section 5 specifies conditional quantile-based measures of skewness and kurtosis based on MQ-CAViaR estimates. Section 6 contains an empirical application of our methods to the S&P 500 index. The chapter also reports results of a simulation experiment designed to examine the finite sample behavior of our estimator. Section 7 contains a summary and concluding remarks.

Keywords: MQ-CAViaR model; skewness; kurtosis; data generating process; covariance matrix

Chapter.  14129 words.  Illustrated.

Subjects: Econometrics and Mathematical Economics

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