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Quantiles, Expectiles and Splines

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Author Info
DeRossi, G.
Harvey, A.

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Abstract

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. 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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File URL: http://www.econ.cam.ac.uk/dae/repec/cam/pdf/cwpe0660.pdf
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Publisher Info
Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0660.

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Length: 29
Date of creation: Feb 2007
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Handle: RePEc:cam:camdae:0660

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Related research
Keywords: Asymmetric least squares; cubic splines; dispersion; non-parametric regression; quantile regression; signal extraction; state space smoother.;

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Clive Granger & Chor-yiu Sin, 1999. "Modelling the Absolute Returns of Different Stock Indices: Exploring the Forecastability of an Alternative Measure of Risk," University of California at San Diego, Economics Working Paper Series 1999-12, Department of Economics, UC San Diego. [Downloadable!]
    Other versions:
  2. DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics 0649, Faculty of Economics, University of Cambridge. [Downloadable!]
  3. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
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  4. Busettti, F. & Harvey, A., 2007. "Tests of time-invariance," Cambridge Working Papers in Economics 0701, Faculty of Economics, University of Cambridge. [Downloadable!]
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  5. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-47, July. [Downloadable!] (restricted)
  6. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August. [Downloadable!] (restricted)
  7. Andrew Harvey & Siem Jan Koopman, 2000. "Signal extraction and the formulation of unobserved components models," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 84-107.
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  8. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October. [Downloadable!] (restricted)
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  9. Bosch, Ronald J. & Ye, Yinyu & Woodworth, George G., 1995. "A convergent algorithm for quantile regression with smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 19(6), pages 613-630, June. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Chollete, Loran & Pena, Victor de la & Lu, Ching-Chih, 2009. "International Diversification: A Copula Approach," UiS Working Papers in Economics and Finance 2009/27, University of Stavanger. [Downloadable!]
  2. Chollete, Loran & de la Pena , Victor & Lu, Ching-Chih, 2009. "International Diversification: An Extreme Value Approach," UiS Working Papers in Economics and Finance 2009/26, University of Stavanger. [Downloadable!]
  3. Harvey, A., 2008. "Dynamic distributions and changing copulas," Cambridge Working Papers in Economics 0839, Faculty of Economics, University of Cambridge. [Downloadable!]
  4. Tobias Adrian & Markus K. Brunnermeier, 2008. "CoVaR," Staff Reports 348, Federal Reserve Bank of New York. [Downloadable!]
  5. Busetti, F. & Harvey, A., 2008. "When is a copula constant? A test for changing relationships," Cambridge Working Papers in Economics 0841, Faculty of Economics, University of Cambridge. [Downloadable!]
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