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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

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

Halbert White

Tae‐Hwan Kim

Simone Manganelli

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199549498.003.0012

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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