Inter-Quantile Ranges and Volatility of Financial Data

34 Pages Posted: 8 Sep 2016 Last revised: 5 Oct 2016

See all articles by Thomas Dimpfl

Thomas Dimpfl

University of Tuebingen - Department of Statistics and Econometrics

Dirk G. Baur

University of Western Australia - Business School; Financial Research Network (FIRN)

Date Written: September 7, 2016

Abstract

We propose to estimate the variance of a time series of financial returns through a quantile autoregressive model (QAR) and demonstrate that the return QAR model contains all information that is commonly captured in two separate equations for the mean and variance of a GARCH-type model. In particular, QAR allows to characterize the entire distribution of returns conditional on a positive or negative return of any given size. We show theoretically and in an empirical application that the inter-quantile range spanned by conditional quantile estimates identifies the asymmetric response of volatility to lagged returns, resulting in broader conditional densities for negative returns than for positive returns. Finally, we estimate the conditional variance based on the estimated conditional density and illustrate its accuracy with an evaluation of Value-at-Risk and variance forecasts.

Keywords: quantile autoregression (QAR), asymmetric volatility, inter-quantile range

JEL Classification: G01, G02, G14, G15

Suggested Citation

Dimpfl, Thomas and Baur, Dirk G., Inter-Quantile Ranges and Volatility of Financial Data (September 7, 2016). Available at SSRN: https://ssrn.com/abstract=2835951 or http://dx.doi.org/10.2139/ssrn.2835951

Thomas Dimpfl (Contact Author)

University of Tuebingen - Department of Statistics and Econometrics ( email )

Germany

Dirk G. Baur

University of Western Australia - Business School ( email )

School of Business
35 Stirling Highway
Crawley, Western Australia 6009
Australia

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

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