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Time-Varying Quantiles
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When
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2.00pm on Friday 17th March
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Where
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B617, Leverhulme Library, Columbia House
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Presentations
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Speaker
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Andrew Harvey
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From
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University of Cambridge
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Abstract
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A time-varying quantile can be fitted to a sequence of observations by formulating a time series model for the corresponding population quantile and iteratively applying a suitably modified state space signal extraction algorithm. Quantiles estimated in this way provide
information on various aspects of a time series, including dispersion, asymmetry and, for financial applications, value at risk. Tests for the constancy of quantiles, and associated contrasts, are constructed using indicator variables; these tests have a similar form to stationarity tests and, under the null hypothesis, their asymptotic distributions belong to the Cramér von Mises family. Estimates of the quantiles at the end of the series provide the basis for forecasting. As such they offer an alternative to conditional quantile autoregressions and, at the same time, give some insight into their structure and potential drawbacks. Finally it is shown that, because the state space form can handle irregularly spaced observations, our algorithm can be easily adapted to provide a viable means of computing spline-based non-parametric quantile regression estimates.
KEYWORDS: Cubic splines; Kalman filter; quantile regression; state space smoother; stationarity tests; stochastic volatility, value at risk.
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For further information
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Thomas Hewlett (Postgraduate Administrator) Ext. 6879
Department of Statistics, Columbia House
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