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Quantiles, expectiles and splines

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Author Info
De Rossi, Giuliano
Harvey, Andrew

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Abstract

A time-varying quantile can be fitted 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 quantiles satisfy the defining property of fixed quantiles in having the appropriate number of observations above and below. 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. Because the state space form can handle irregularly spaced observations, the proposed algorithms can be adapted to provide a viable means of computing spline-based non-parametric quantile and expectile regressions.

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File URL: http://www.sciencedirect.com/science/article/B6VC0-4VBMNJV-2/2/bcad3a8a461731626a948472a805656c
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Publisher Info
Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 152 (2009)
Issue (Month): 2 (October)
Pages: 179-185
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Handle: RePEc:eee:econom:v:152:y:2009:i:2:p:179-185

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Web page: http://www.elsevier.com/locate/jeconom

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Related research
Keywords: Asymmetric least squares Cubic splines Quantile regression Signal extraction State space smoother;

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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. Tobias Adrian & Markus K. Brunnermeier, 2008. "CoVaR," Staff Reports 348, Federal Reserve Bank of New York. [Downloadable!]
  2. 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!]
  3. 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!]
  4. Harvey, A., 2008. "Dynamic distributions and changing copulas," Cambridge Working Papers in Economics 0839, Faculty of Economics, University of Cambridge. [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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