Quantiles, Expectiles and Splines
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.
|Date of creation:||Feb 2007|
|Date of revision:|
|Contact details of provider:|| Web page: http://www.econ.cam.ac.uk/index.htm|
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.:
- Koenker,Roger, 2005.
Cambridge University Press, number 9780521845731, 1.
- Durbin, James & Koopman, Siem Jan, 2001.
"Time Series Analysis by State Space Methods,"
Oxford University Press, number 9780198523543, July.
- 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.
- Neil Shephard & Jurgen Doornik & Siem Jan Koopman, 1998.
"Statistical algorithms for models in state space using SsfPack 2.2,"
Economics Series Working Papers
1998-W06, University of Oxford, Department of Economics.
- 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.
- 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.
- DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics 0649, Faculty of Economics, University of Cambridge.
- Robert Engle & Simone Manganelli, 2000.
"CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles,"
Econometric Society World Congress 2000 Contributed Papers
0841, Econometric Society.
- 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.
- 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.
- Busettti, F. & Harvey, A., 2007.
"Tests of time-invariance,"
Cambridge Working Papers in Economics
0657, Faculty of Economics, University of Cambridge.
- 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.
- Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-47, July.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:cam:camdae:0702. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Jake Dyer)
If references are entirely missing, you can add them using this form.