IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this article

Adaptive estimation of autoregressive models with time-varying variances

Listed author(s):
  • Xu, Ke-Li
  • Phillips, Peter C.B.

Stable autoregressive models of known finite order are considered with martingale differences errors scaled by an unknown nonparametric time-varying function generating heterogeneity. An important special case involves structural change in the error variance, but in most practical cases the pattern of variance change over time is unknown and may involve shifts at unknown discrete points in time, continuous evolution or combinations of the two. This paper develops kernel-based estimators of the residual variances and associated adaptive least squares (ALS) estimators of the autoregressive coefficients. These are shown to be asymptotically efficient, having the same limit distribution as the infeasible generalized least squares (GLS). Comparisons of the efficient procedure and the ordinary least squares (OLS) reveal that least squares can be extremely inefficient in some cases while nearly optimal in others. Simulations show that, when least squares work well, the adaptive estimators perform comparably well, whereas when least squares work poorly, major efficiency gains are achieved by the new estimators.

(This abstract was borrowed from another version of this item.)

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(07)00130-3
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 142 (2008)
Issue (Month): 1 (January)
Pages: 265-280

as
in new window

Handle: RePEc:eee:econom:v:142:y:2008:i:1:p:265-280
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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.:

as in new window
  1. Cătălin Stărică & Clive Granger, 2005. "Nonstationarities in Stock Returns," The Review of Economics and Statistics, MIT Press, vol. 87(3), pages 503-522, August.
  2. Joon Y. Park & Peter C.B. Phillips, 1998. "Nonlinear Regressions with Integrated Time Series," Cowles Foundation Discussion Papers 1190, Cowles Foundation for Research in Economics, Yale University.
  3. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(03), pages 458-467, December.
  4. Kim, Tae-Hwan & Leybourne, Stephen & Newbold, Paul, 2002. "Unit root tests with a break in innovation variance," Journal of Econometrics, Elsevier, vol. 109(2), pages 365-387, August.
  5. Mark W. Watson, 1999. "Explaining the increased variability in long-term interest rates," Economic Quarterly, Federal Reserve Bank of Richmond, issue Fall, pages 71-96.
  6. Margaret M. McConnell & Gabriel Perez Quiros, 1997. "Output fluctuations in the United States: what has changed since the early 1980s?," Research Paper 9735, Federal Reserve Bank of New York.
  7. Gonçalves, Sílvia & KILIAN, Lutz, 2003. "Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form," Cahiers de recherche 01-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  9. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
  10. Hamori, Shigeyuki & Tokihisa, Akira, 1997. "Testing for a unit root in the presence of a variance shift1," Economics Letters, Elsevier, vol. 57(3), pages 245-253, December.
  11. Catalin Starica & Stefano Herzel & Tomas Nord, 2005. "Why does the GARCH(1,1) model fail to provide sensible longer- horizon volatility forecasts?," Econometrics 0508003, EconWPA.
  12. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  13. Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, vol. 63(5), pages 1113-1132, September.
  14. Kuersteiner, Guido M., 2001. "Optimal instrumental variables estimation for ARMA models," Journal of Econometrics, Elsevier, vol. 104(2), pages 359-405, September.
  15. D van Dijk & D R Osborn & M Sensier, 2002. "Changes in variability of the business cycle in the G7 countries," The School of Economics Discussion Paper Series 0204, Economics, The University of Manchester.
  16. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, December.
  17. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2001. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," CIRJE F-Series CIRJE-F-124, CIRJE, Faculty of Economics, University of Tokyo.
  18. Giuseppe Cavaliere, 2005. "Unit Root Tests under Time-Varying Variances," Econometric Reviews, Taylor & Francis Journals, vol. 23(3), pages 259-292.
  19. Kuersteiner, Guido M., 2002. "Efficient Iv Estimation For Autoregressive Models With Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 18(03), pages 547-583, June.
  20. Busetti, Fabio & Taylor, A M Robert, 2003. "Variance Shifts, Structural Breaks, and Stationarity Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 510-531, October.
  21. Yu, K. & Jones, M.C., 2004. "Likelihood-Based Local Linear Estimation of the Conditional Variance Function," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 139-144, January.
  22. Joon Y. Park & Heetaik Chung, 2004. "Nonstationary Nonlinear Heteroskedasticity in Regression," Econometric Society 2004 Far Eastern Meetings 508, Econometric Society.
  23. de Pooter, M.D. & van Dijk, D.J.C., 2004. "Testing for changes in volatility in heteroskedastic time series - a further examination," Econometric Institute Research Papers EI 2004-38, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  24. Jörg Polzehl & Vladimir Spokoiny, 2006. "Varying coefficient GARCH versus local constant volatility modeling. Comparison of the predictive power," SFB 649 Discussion Papers SFB649DP2006-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  25. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
  26. Peter C.B. Phillips & Ke-Li Xu, 2007. "Tilted Nonparametric Estimation of Volatility Functions," Cowles Foundation Discussion Papers 1612, Cowles Foundation for Research in Economics, Yale University, revised Jul 2010.
  27. Jianqing Fan & Qiwei Yao, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
  28. Silvia Goncalves & Lutz Kilian, 2007. "Asymptotic and Bootstrap Inference for AR(∞) Processes with Conditional Heteroskedasticity," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 609-641.
  29. B. Abraham & W. Wei, 1984. "Inferences about the parameters of a time series model with changing variance," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 31(1), pages 183-194, December.
  30. Sílvia Gonçalves & Lutz Kilian, 2003. "Asymptotic and Bootstrap Inference for AR( Infinite ) Processes with Conditional Heteroskedasticity," CIRANO Working Papers 2003s-28, CIRANO.
  31. Peter C.B. Phillips & Mico Loretan, 1990. "Testing Covariance Stationarity Under Moment Condition Failure with an Application to Common Stock Returns," Cowles Foundation Discussion Papers 947, Cowles Foundation for Research in Economics, Yale University.
  32. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
  33. Thomas Mikosch & Catalin Starica, 2004. "Non-stationarities in financial time series, the long range dependence and the IGARCH effects," Econometrics 0412005, EconWPA.
  34. Peter C. B. Phillips & Ke-Li Xu, 2006. "Inference in Autoregression under Heteroskedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 289-308, 03.
  35. Delgado, Miguel A. & Hidalgo, Javier, 2000. "Nonparametric inference on structural breaks," Journal of Econometrics, Elsevier, vol. 96(1), pages 113-144, May.
  36. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  37. Li, W K & Ling, Shiqing & McAleer, Michael, 2002. " Recent Theoretical Results for Time Series Models with GARCH Errors," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 245-269, July.
  38. Cavaliere, Giuseppe, 2004. "Testing stationarity under a permanent variance shift," Economics Letters, Elsevier, vol. 82(3), pages 403-408, March.
  39. Peña, Daniel & Galeano, Pedro, 2004. "Variance changes detection in multivariate time series," DES - Working Papers. Statistics and Econometrics. WS ws041305, Universidad Carlos III de Madrid. Departamento de Estadística.
  40. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
  41. Robert F. Engle & Jose Gonzalo Rangel, 2005. "The Spline GARCH Model for Unconditional Volatility and its Global Macroeconomic Causes," Working Papers 2005/13, Czech National Bank, Research Department.
  42. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 140(2), pages 919-947, October.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:142:y:2008:i:1:p:265-280. 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: (Shamier, Wendy)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.