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Volatility and Time Series EconometricsEssays in Honor of Robert Engle$
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Tim Bollerslev, Jeffrey Russell, and Mark Watson

Print publication date: 2010

Print ISBN-13: 9780199549498

Published to Oxford Scholarship Online: May 2010

DOI: 10.1093/acprof:oso/9780199549498.001.0001

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Modeling Autoregressive Conditional Skewness and Kurtosis with Multi‐Quantile CAViaR

Modeling Autoregressive Conditional Skewness and Kurtosis with Multi‐Quantile CAViaR

(p.231) 12 Modeling Autoregressive Conditional Skewness and Kurtosis with Multi‐Quantile CAViaR
Volatility and Time Series Econometrics

Halbert White

Tae‐Hwan Kim

Simone Manganelli

Oxford University Press

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

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