Averaging estimators for autoregressions with a near unit root
This paper uses local-to-unity theory to evaluate the asymptotic mean-squared error (AMSE) and forecast expected squared error from least-squares estimation of an autoregressive model with a root close to unity. We investigate unconstrained estimation, estimation imposing the unit root constraint, pre-test estimation, model selection estimation, and model average estimation. We find that the asymptotic risk depends only on the local-to-unity parameter, facilitating simple graphical comparisons. Our results strongly caution against pre-testing. Strong evidence supports averaging based on Mallows weights. In particular, our Mallows averaging method has uniformly and substantially smaller risk than the conventional unconstrained estimator, and this holds for autoregressive roots far from unity. Our averaging estimator is a new approach to forecast combination.
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.
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.
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.:
- Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
- Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992.
"Efficient Tests for an Autoregressive Unit Root,"
NBER Technical Working Papers
0130, National Bureau of Economic Research, Inc.
- Stock, James H, 1996. "VAR, Error Correction and Pretest Forecasts at Long Horizons," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(4), pages 685-701, November.
- Marco Aiolfi & Carlos Capistrán & Allan Timmermann, 2010.
2010-04, Banco de México.
- Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, 07.
- Eugene Canjels & Mark W. Watson, 1994.
"Estimating Deterministic Trends in the Presence of Serially Correlated Errors,"
NBER Technical Working Papers
0165, National Bureau of Economic Research, Inc.
- Eugene Canjels & Mark W. Watson, 1997. "Estimating Deterministic Trends In The Presence Of Serially Correlated Errors," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 184-200, May.
- Eugene Canjels & Mark W. Watson, 1994. "Estimating deterministic trends in the presence of serially correlated errors," Working Paper Series, Macroeconomic Issues 94-19, Federal Reserve Bank of Chicago.
- R. Bhansali, 1996. "Asymptotically efficient autoregressive model selection for multistep prediction," Annals of the Institute of Statistical Mathematics, Springer, vol. 48(3), pages 577-602, September.
- Stock, James H. & Watson, Mark W., 2006. "Forecasting with Many Predictors," Handbook of Economic Forecasting, Elsevier.
- Francis X. Diebold & Lutz Kilian, 1999.
"Unit Root Tests are Useful for Selecting Forecasting Models,"
New York University, Leonard N. Stern School Finance Department Working Paper Seires
99-063, New York University, Leonard N. Stern School of Business-.
- Diebold, Francis X & Kilian, Lutz, 2000. "Unit-Root Tests Are Useful for Selecting Forecasting Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 265-73, July.
- Francis X. Diebold & Lutz Kilian, 1999. "Unit Root Tests Are Useful for Selecting Forecasting Models," NBER Working Papers 6928, National Bureau of Economic Research, Inc.
- Inoue, Atsushi & Kilian, Lutz, 2003.
"On the selection of forecasting models,"
Working Paper Series
0214, European Central Bank.
- Hjort N.L. & Claeskens G., 2003. "Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 879-899, January.
- Gonzalo, Jesus & Pitarakis, Jean-Yves, 1998. "Specification via model selection in vector error correction models," Economics Letters, Elsevier, vol. 60(3), pages 321-328, September.
- Michael P. Clements & David F.Hendry, 2001.
"Forecasting with difference-stationary and trend-stationary models,"
Royal Economic Society, vol. 4(1), pages S1-S19.
- Clements, M.P. & Hendry, D.P., 1998. "Forecasting with Difference-Stationary and Trend-Stationary Models," The Warwick Economics Research Paper Series (TWERPS) 516, University of Warwick, Department of Economics.
- David Hendry & Michael P. Clements, 2000. "Forecasting with Difference-Stationary and Trend-Stationary Models," Economics Series Working Papers 5, University of Oxford, Department of Economics.
- Hansen, Bruce E., 2008. "Least-squares forecast averaging," Journal of Econometrics, Elsevier, vol. 146(2), pages 342-350, October.
- Phillips, Peter C B, 1988.
"Regression Theory for Near-Integrated Time Series,"
Econometric Society, vol. 56(5), pages 1021-43, September.
- Ing, Ching-Kang & Wei, Ching-Zong, 2003. "On same-realization prediction in an infinite-order autoregressive process," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 130-155, April.
- Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
- Aznar, Antonio & Salvador, Manuel, 2002. "Selecting The Rank Of The Cointegration Space And The Form Of The Intercept Using An Information Criterion," Econometric Theory, Cambridge University Press, vol. 18(04), pages 926-947, August.
- Kapetanios, George, 2004. "The Asymptotic Distribution Of The Cointegration Rank Estimator Under The Akaike Information Criterion," Econometric Theory, Cambridge University Press, vol. 20(04), pages 735-742, August.
- Hansen, Bruce E., 1995.
"Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power,"
Cambridge University Press, vol. 11(05), pages 1148-1171, October.
- Bruce E. Hansen, 1995. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power," Boston College Working Papers in Economics 300., Boston College Department of Economics.
- Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
- Ing, Ching-Kang, 2003. "Multistep Prediction In Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 19(02), pages 254-279, April.
- Chao, John C. & Phillips, Peter C. B., 1999.
"Model selection in partially nonstationary vector autoregressive processes with reduced rank structure,"
Journal of Econometrics,
Elsevier, vol. 91(2), pages 227-271, August.
- John C. Chao & Peter C.B. Phillips, 1997. "Model Selection in Partially Nonstationary Vector Autoregressive Processes with Reduced Rank Structure," Cowles Foundation Discussion Papers 1155, Cowles Foundation for Research in Economics, Yale University.
- Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
- Kemp, Gordon C.R., 1999. "The Behavior Of Forecast Errors From A Nearly Integrated Ar(1) Model As Both Sample Size And Forecast Horizon Become Large," Econometric Theory, Cambridge University Press, vol. 15(02), pages 238-256, April.
- Pesaran, M. Hashem & Timmermann, Allan, 2007. "Selection of estimation window in the presence of breaks," Journal of Econometrics, Elsevier, vol. 137(1), pages 134-161, March.
- Tae-Hwan Kim & Stephen J. Leybourne & Paul Newbold, 2004. "Asymptotic mean-squared forecast error when an autoregression with linear trend is fitted to data generated by an I(0) or I(1) process," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 583-602, 07.
- Francis X. Diebold & Jose A. Lopez, 1996.
"Forecast Evaluation and Combination,"
NBER Technical Working Papers
0192, National Bureau of Economic Research, Inc.
- Hansen, Bruce E., 2009. "Averaging Estimators For Regressions With A Possible Structural Break," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1498-1514, December.
- Franses, Philip Hans & Kleibergen, Frank, 1996. "Unit roots in the Nelson-Plosser data: Do they matter for forecasting?," International Journal of Forecasting, Elsevier, vol. 12(2), pages 283-288, June.
When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:158:y:2010:i:1:p:142-155. 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: (Zhang, Lei)
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.