Quantiles, Expectiles and Splines
AbstractA 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. It is shown that such time-varying quantiles satisfy the defining property of fixed quantiles in having the appropriate number of observations above and below. Expectiles are similar to quantiles except that they are defined by tail expectations. Like quantiles, time-varying expectiles can be estimated by a state space signal extraction algorithm and they satisfy properties that generalize the moment conditions associated with fixed expectiles. Time-varying quantiles and expectiles provide information on various aspects of a time series, such as dispersion and asymmetry, while estimates at the end of the series provide the basis for forecasting. Because the state space form can handle irregularly spaced observations, the proposed algorithms can be easily adapted to provide a viable means of computing spline-based non-parametric quantile and expectile regressions.
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Bibliographic InfoPaper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0660.
Date of creation: Feb 2007
Date of revision:
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Web page: http://www.econ.cam.ac.uk/index.htm
Asymmetric least squares; cubic splines; dispersion; non-parametric regression; quantile regression; signal extraction; state space smoother.;
Other versions of this item:
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-05-19 (All new papers)
- NEP-ECM-2007-05-19 (Econometrics)
- NEP-ETS-2007-05-19 (Econometric Time Series)
- NEP-FOR-2007-05-19 (Forecasting)
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