Bias-corrected estimation in potentially mildly explosive autoregressive models
This paper provides a comprehensive Monte Carlo comparison of different finite-sample bias-correction methods for autoregressive processes. We consider classic situations where the process is either stationary or exhibits a unit root. Importantly, the case of mildly explosive behaviour is studied as well. We compare the empirical performance of an indirect inference estimator (Phillips, Wu, and Yu, 2011), a jackknife approach (Chambers, 2013), the approximately median-unbiased estimator by Roy and Fuller (2001) and the bootstrap- aided estimator by Kim (2003). Our findings suggest that the indirect inference approach o ers a valuable alternative to other existing techniques. Its performance (measured by its bias and root mean squared error) is balanced and highly competitive across many different settings. A clear advantage is its applicability for mildly explosive processes. In an empirical application to a long annual US Debt/GDP series we consider rolling window estimation of autoregressive models. We find substantial evidence for time-varying persistence and periods of explosiveness during the Civil War and World War II. During the recent years, the series is nearly explosive again. Further applications to commodity and interest rate series are considered as well.
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.:
- Chambers, Marcus J., 2013.
"Jackknife estimation of stationary autoregressive models,"
Journal of Econometrics,
Elsevier, vol. 172(1), pages 142-157.
- Chambers, Marcus J, 2010. "Jackknife Estimation of Stationary Autoregressive Models," Economics Discussion Papers 2786, University of Essex, Department of Economics.
- Efthymios Pavlidis & Ivan Paya & David Peel, 2012. "A New Test for Rational Speculative Bubbles using Forward Exchange Rates: The Case of the Interwar German Hyperinflation," Working Papers 18599597, Lancaster University Management School, Economics Department.
- Peter C.B. Philips & Yangru Wu & Jun Yu, 2009.
"Explosive Behavior in the 1990s Nasdaq : When Did Exuberance Escalate Asset Values?,"
Finance Working Papers
23050, East Asian Bureau of Economic Research.
- Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, 02.
- Peter C.B. Phillips & Yangru Wu & Jun Yu, 2009. "Explosive Behavior in the 1990s Nasdaq: When Did Exuberance Escalate Asset Values?," Cowles Foundation Discussion Papers 1699, Cowles Foundation for Research in Economics, Yale University.
- Peter C.B. PHILIPS & Yangru WU & Jun YU, 2009. "Explosive Behavior in the 1990s Nasdaq: When Did Exuberance Escalate Asset Values?," Working Papers 19-2009, Singapore Management University, School of Economics.
- Peter C. B. Phillips & Yangru Wu & Jun Yu, 2007. "Explosive Behavior in the 1990s Nasdaq: When Did Exuberance Escalate Asset Values?," Working Papers 222007, Hong Kong Institute for Monetary Research.
- Christian GouriÃƒÂ©roux & Peter C. B. Phillips & Jun Yu, 2006.
"Indirect Inference for Dynamic Panel Models,"
Development Economics Working Papers
22421, East Asian Bureau of Economic Research.
- Peter C. B. Phillips, 2012. "Folklore Theorems, Implicit Maps, and Indirect Inference," Econometrica, Econometric Society, vol. 80(1), pages 425-454, 01.
- Gourieroux, C. & Monfort, A. & Renault, E., 1992.
92.279, Toulouse - GREMAQ.
- Baur, Dirk G. & Dimpfl, Thomas & Jung, Robert C., 2012.
"Stock return autocorrelations revisited: A quantile regression approach,"
University of Tuebingen Working Papers in Economics and Finance
24, University of Tuebingen, Faculty of Economics and Social Sciences.
- Baur, Dirk G. & Dimpfl, Thomas & Jung, Robert C., 2012. "Stock return autocorrelations revisited: A quantile regression approach," Journal of Empirical Finance, Elsevier, vol. 19(2), pages 254-265.
- Hansen,B.E., 1998.
"The grid bootstrap and the autoregressive model,"
26, Wisconsin Madison - Social Systems.
- Kim, Jae-Young, 2000. "Detection of change in persistence of a linear time series," Journal of Econometrics, Elsevier, vol. 95(1), pages 97-116, March.
- James G. MacKinnon & Anthony A. Smith Jr., 1995.
"Approximate Bias Correction in Econometrics,"
919, Queen's University, Department of Economics.
- Mackinnon, J.G. & Smith, A.A., 1996. "Approximate Bias Correction in Econometrics," G.R.E.Q.A.M. 96a14, Universite Aix-Marseille III.
- James G. MacKinnon & Anthony A. Smith, Jr., . "Approximate Bias Correction in Econometrics," GSIA Working Papers 1997-36, Carnegie Mellon University, Tepper School of Business.
- Smith, A A, Jr, 1993. "Estimating Nonlinear Time-Series Models Using Simulated Vector Autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S63-84, Suppl. De.
- Phillips, Peter C.B. & Magdalinos, Tassos, 2007.
"Limit theory for moderate deviations from a unit root,"
Journal of Econometrics,
Elsevier, vol. 136(1), pages 115-130, January.
- Peter C.B. Phillips & Tassos Magdalinos, 2004. "Limit Theory for Moderate Deviations from a Unit Root," Cowles Foundation Discussion Papers 1471, Cowles Foundation for Research in Economics, Yale University.
- Diba, Behzad T & Grossman, Herschel I, 1988. "Explosive Rational Bubbles in Stock Prices?," American Economic Review, American Economic Association, vol. 78(3), pages 520-30, June.
- Robert Taylor & Stephen Leybourne & David Harvey, 2004.
"Modified Tests for a Change in Persistence,"
Econometric Society 2004 Australasian Meetings
64, Econometric Society.
- James H. Stock & Mark W. Watson, 1994.
"Evidence on Structural Instability in Macroeconomic Time Series Relations,"
NBER Technical Working Papers
0164, National Bureau of Economic Research, Inc.
- Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 11-30, January.
- James H. Stock & Mark W. Watson, 1994. "Evidence on structural instability in macroeconomic times series relations," Working Paper Series, Macroeconomic Issues 94-13, Federal Reserve Bank of Chicago.
- Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
- Stephen Leybourne & Robert Taylor & Tae-Hwan Kim, 2007. "CUSUM of Squares-Based Tests for a Change in Persistence," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(3), pages 408-433, 05.
- Rossi, Barbara, 2005.
"Confidence Intervals for Half-Life Deviations From Purchasing Power Parity,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 23, pages 432-442, October.
- Rossi, Barbara, 2002. "Confidence Intervals for Half-life Deviations from Purchasing Power Parity," Working Papers 02-08, Duke University, Department of Economics.
- Roy, Anindya & Fuller, Wayne A, 2001. "Estimation for Autoregressive Time Series with a Root Near 1," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 482-93, October.
- Simon van Norden, 1995.
"Regime Switching as a Test for Exchange Rate Bubbles,"
9502001, EconWPA, revised 09 Aug 1995.
- van Norden, Simon, 1996. "Regime Switching as a Test for Exchange Rate Bubbles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 219-51, May-June.
- Andrews, Donald W K & Chen, Hong-Yuan, 1994. "Approximately Median-Unbiased Estimation of Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 187-204, April.
- Schotman, Peter & van Dijk, Herman K., 1991. "A Bayesian analysis of the unit root in real exchange rates," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 195-238.
- Dirk G. Baur & Thomas K. McDermott, .
"Is gold a safe haven? International evidence,"
The Institute for International Integration Studies Discussion Paper Series
- Bao, Yong & Ullah, Aman, 2007. "The second-order bias and mean squared error of estimators in time-series models," Journal of Econometrics, Elsevier, vol. 140(2), pages 650-669, October.
- Tom Engsted & Thomas Q. Pedersen, 2014.
"Bias-Correction in Vector Autoregressive Models: A Simulation Study,"
MDPI, Open Access Journal, vol. 2(1), pages 45, March.
- Tom Engsted & Thomas Q. Pedersen, 2011. "Bias-correction in vector autoregressive models: A simulation study," CREATES Research Papers 2011-18, Department of Economics and Business Economics, Aarhus University.
- Lof, Matthijs, 2012. "Heterogeneity in stock prices: A STAR model with multivariate transition function," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1845-1854.
- Chong, Terence Tai-Leung, 2001.
"Structural Change In Ar(1) Models,"
Cambridge University Press, vol. 17(01), pages 87-155, February.
- Jörg Breitung & Robinson Kruse, 2013. "When bubbles burst: econometric tests based on structural breaks," Statistical Papers, Springer, vol. 54(4), pages 911-930, November.
- Clark, Steven P. & Coggin, T. Daniel, 2011. "Was there a U.S. house price bubble? An econometric analysis using national and regional panel data," The Quarterly Review of Economics and Finance, Elsevier, vol. 51(2), pages 189-200, May.
- repec:acb:camaaa:2011-11 is not listed on IDEAS
- Chambers, Marcus J. & Kyriacou, Maria, 2012. "Jackknife bias reduction in autoregressive models with a unit root," MPRA Paper 38255, University Library of Munich, Germany.
- Shi, Shuping & Arora, Vipin, 2012.
"An application of models of speculative behaviour to oil prices,"
Elsevier, vol. 115(3), pages 469-472.
- Shu-ping Shi & Vipin Arora, 2011. "An Application Of Models Of Speculative Behaviour To Oil Prices," CAMA Working Papers 2011-11, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
- Abadir, Karim M., 1993. "Ols Bias in a Nonstationary Autoregression," Econometric Theory, Cambridge University Press, vol. 9(01), pages 81-93, January.
- Kim, Jae H., 2003. "Forecasting autoregressive time series with bias-corrected parameter estimators," International Journal of Forecasting, Elsevier, vol. 19(3), pages 493-502.
- Casella, Alessandra, 1989. "Testing for rational bubbles with exogenous or endogenous fundamentals : The German hyperinflation once more," Journal of Monetary Economics, Elsevier, vol. 24(1), pages 109-122, July.
When requesting a correction, please mention this item's handle: RePEc:aah:create:2013-10. 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: ()
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.