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
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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- DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics 0649, Faculty of Economics, University of Cambridge.
- Busettti, F. & Harvey, A., 2007.
"Tests of time-invariance,"
Cambridge Working Papers in Economics
0657, Faculty of Economics, University of Cambridge.
- Koenker,Roger, 2005.
Cambridge University Press, number 9780521608275.
- 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.
- Robert Engle & Simone Manganelli, 2000. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Econometric Society World Congress 2000 Contributed Papers 0841, Econometric Society.
- Engle, Robert F & Manganelli, Simone, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series qt06m3d6nv, Department of Economics, UC San Diego.
- 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.
- Harvey, A.C. & Koopman, S.J.M., 1999.
"Signal Extraction and the Formulation of Unobserved Components Models,"
1999-44, Tilburg University, Center for Economic Research.
- 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.
- Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999.
"Statistical algorithms for models in state space using SsfPack 2.2,"
Royal Economic Society, vol. 2(1), pages 107-160.
- Koopman, S.J.M. & Shephard, N. & Doornik, J.A., 1998. "Statistical Algorithms for Models in State Space Using SsfPack 2.2," Discussion Paper 1998-141, Tilburg University, Center for Economic Research.
- Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-47, July.
- Durbin, James & Koopman, Siem Jan, 2001.
"Time Series Analysis by State Space Methods,"
Oxford University Press, number 9780198523543.
- Tom Doan, . "SEASONALDLM: RATS procedure to create the matrices for the seasonal component of a DLM," Statistical Software Components RTS00251, Boston College Department of Economics.
- 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.
- 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.
- Tobias Adrian & Markus K. Brunnermeier, 2011.
NBER Working Papers
17454, National Bureau of Economic Research, Inc.
- 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.
- Fabio Busetti & Andrew Harvey, 2011. "When is a Copula Constant? A Test for Changing Relationships," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(1), pages 106-131, Winter.
- Zhijie Xiao & Roger Koenker, 2009. "Conditional Quantile Estimation for GARCH Models," Boston College Working Papers in Economics 725, Boston College Department of Economics.
- Yuta Kurose & Yasuhiro Omori, 2012. "Bayesian Analysis of Time-Varying Quantiles Using a Smoothing Spline," CIRJE F-Series CIRJE-F-845, CIRJE, Faculty of Economics, University of Tokyo.
- 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.
- Harvey, A., 2008. "Dynamic distributions and changing copulas," Cambridge Working Papers in Economics 0839, Faculty of Economics, University of Cambridge.
- Jason Ng & Catherine S. Forbes & Gael M. Martin & Brendan P.M. McCabe, 2011. "Non-Parametric Estimation of Forecast Distributions in Non-Gaussian, Non-linear State Space Models," Monash Econometrics and Business Statistics Working Papers 11/11, Monash University, Department of Econometrics and Business Statistics.
- Cathy Q. Ning & Loran Chollete, 2009.
"The Dependence Structure of Macroeconomic Variables in the US,"
005, Ryerson University, Department of Economics.
- Chollete, Loran & Ning, Cathy, 2009. "The Dependence Structure of Macroeconomic Variables in the US," UiS Working Papers in Economics and Finance 2009/31, University of Stavanger.
- Rubia, Antonio & Sanchis-Marco, Lidia, 2013. "On downside risk predictability through liquidity and trading activity: A dynamic quantile approach," International Journal of Forecasting, Elsevier, vol. 29(1), pages 202-219.
- Chollete, Lorán & de la Peña, Victor & Lu, Ching-Chih, 2011. "International diversification: A copula approach," Journal of Banking & Finance, Elsevier, vol. 35(2), pages 403-417, February.
- Harvey, Andrew, 2010. "Tracking a changing copula," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 485-500, June.
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