Bootstrap LR tests of stationarity, common trends and cointegration
AbstractThe paper considers likelihood ratio (LR) tests of stationarity, common trends and cointegration for multivariate time series. As the distribution of these tests is not known, a bootstrap version is proposed via a state space representation. The bootstrap samples are obtained from the Kalman filter innovations under the null hypothesis. Monte Carlo simulations for the Gaussian univariate random walk plus noise model show that the bootstrap LR test achieves higher power for medium-sized deviations from the null hypothesis than a locally optimal and one-sided LM test, that has a known asymptotic distribution. The power gains of the bootstrap LR test are significantly larger for testing the hypothesis of common trends and cointegration in multivariate time series, as the alternative asymptotic procedure -obtained as an extension of the LM test of stationarity- does not possess properties of optimality. Finally, it is showed that the (pseudo) LR tests maintain good size and power properties also for non-Gaussian series. As an empirical illustration, we find evidence of two common stochastic trends in the volatility of the US dollar exchange rate against european and asian/pacific currencies.
Download InfoIf 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.
Bibliographic InfoPaper provided by Bank of Italy, Economic Research and International Relations Area in its series Temi di discussione (Economic working papers) with number 799.
Date of creation: Mar 2011
Date of revision:
Kalman filter; state-space models; unit roots;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-07-13 (All new papers)
- NEP-ECM-2011-07-13 (Econometrics)
- NEP-ETS-2011-07-13 (Econometric Time Series)
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.:
- Caner, Mehmet & Kilian, Lutz, 2000.
"Size Distortions Of Tests Of The Null Hypothesis Of Stationarity: Evidence And Implications For The PPP Debate,"
CEPR Discussion Papers
2425, C.E.P.R. Discussion Papers.
- Caner, M. & Kilian, L., 2001. "Size distortions of tests of the null hypothesis of stationarity: evidence and implications for the PPP debate," Journal of International Money and Finance, Elsevier, vol. 20(5), pages 639-657, October.
- Kilian, L. & Caner, M., 1999. "Size Distortions of Tests of the Null Hypothesis of Stationarity: Evidence and Implications for the PPP Debate," Papers 99-05, Michigan - Center for Research on Economic & Social Theory.
- Russell Davidson & James G. MacKinnon, 2004.
"The Power of Bootstrap and Asymptotic Tests,"
1035, Queen's University, Department of Economics.
- Robert Taylor & Peter Burridge, 2004.
"Bootstrapping the HEGY Seasonal Unit Root Tests,"
Econometric Society 2004 North American Summer Meetings
125, Econometric Society.
- Jeremy Berkowitz & Lutz Kilian, 1996.
"Recent developments in bootstrapping time series,"
Finance and Economics Discussion Series
96-45, Board of Governors of the Federal Reserve System (U.S.).
- Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992.
"Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?,"
Journal of Econometrics,
Elsevier, vol. 54(1-3), pages 159-178.
- Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
- Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
- JAMES G. MacKINNON, 2006.
"Bootstrap Methods in Econometrics,"
The Economic Record,
The Economic Society of Australia, vol. 82(s1), pages S2-S18, 09.
- A. W. Coats, 1996. "Introduction," History of Political Economy, Duke University Press, vol. 28(5), pages 3-11, Supplemen.
- Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
- Busetti, Fabio & Harvey, Andrew, 2003. "Seasonality Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 420-36, July.
- Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589819, December.
- Andrews, Donald W K, 1993.
"Tests for Parameter Instability and Structural Change with Unknown Change Point,"
Econometric Society, vol. 61(4), pages 821-56, July.
- Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
- Lee, Junsoo, 1996. "On the power of stationarity tests using optimal bandwidth estimates," Economics Letters, Elsevier, vol. 51(2), pages 131-137, May.
- Fabio Busetti, 2004.
"Tests of seasonal integration and cointegration in multivariate unobserved component models,"
- Fabio Busetti, 2006. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 419-438.
- Fabio Busetti, 2003. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Temi di discussione (Economic working papers) 476, Bank of Italy, Economic Research and International Relations Area.
- Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
- Canova, Fabio & Hansen, Bruce E, 1995. "Are Seasonal Patterns Constant over Time? A Test for Seasonal Stability," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 237-52, July.
- Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994.
"Multivariate Stochastic Variance Models,"
Review of Economic Studies,
Wiley Blackwell, vol. 61(2), pages 247-64, April.
- Tom Doan, . "RATS programs to estimate multivariate stochastic volatility models," Statistical Software Components RTZ00093, Boston College Department of Economics.
- Leybourne, S J & McCabe, B P M, 1994. "A Consistent Test for a Unit Root," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 157-66, April.
- Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589833, December.
- Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589826, December.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ().
If references are entirely missing, you can add them using this form.