Modeling Autoregressive Conditional Skewness and Kurtosis with Multi-Quantile CAViaR

Halbert White, Tae Hwan Kim, Simone Manganelli

Research output: Chapter in Book/Report/Conference proceedingChapter

13 Citations (Scopus)


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 MQCAViaR 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.

Original languageEnglish
Title of host publicationVolatility and Time Series Econometrics
Subtitle of host publicationEssays in Honor of Robert Engle
PublisherOxford University Press
ISBN (Electronic)9780191720567
ISBN (Print)9780199549498
Publication statusPublished - 2010 May 1

Bibliographical note

Publisher Copyright:
© Oxford University Press, 2013.

All Science Journal Classification (ASJC) codes

  • Economics, Econometrics and Finance(all)


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