Testing against stochastic trend and seasonality in the presence of unattended breaks and unit roots
AbstractThis paper considers the problem of testing against stochastic trend and seasonality in the presence of structural breaks and unit roots at frequencies other than those directly under test, which we term unattended breaks and unattended unit roots respectively. We show that under unattended breaks the true size of the Kwiatkowski et. al. (1992) [KPSS] test at frequency zero and the Canova and Hansen (1995) [CH] test at the seasonal frequencies fall well below the nominal level under the null with an associated, often very dramatic, loss of power under the alternative. We demonstrate that a simple modification of the statistics can recover the usual limiting distribution appropriate to the case where there are no breaks, provided unit roots do not exist at any of the unattended frequencies. Where unattended unit roots occur we show that the above statistics converge in probability to zero under the null. However, computing the KPSS and CH statistics after pre-filtering the data is simultaneously efficacious against both unattended breaks and unattended unit roots, in the sense that the statistics retain their usual pivotal limiting null distributions appropriate to the case where neither occurs. The case where breaks may potentially occur at all frequencies is also discussed. The practical relevance of the theoretical contribution of the paper is illustrated through a number of empirical examples.
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 470.
Date of creation: Mar 2003
Date of revision:
stationarity tests; structural breaks; pre-filtering; unattended unit roots;
Other versions of this item:
- Busetti, Fabio & Taylor, A. M. Robert, 2003. "Testing against stochastic trend and seasonality in the presence of unattended breaks and unit roots," Journal of Econometrics, Elsevier, vol. 117(1), pages 21-53, November.
- 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
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.:
- Smith, Jeremy & Otero, Jesus, 1997.
"Structural breaks and seasonal integration,"
Elsevier, vol. 56(1), pages 13-19, September.
- Smith, J. & Otero, J., 1995. "Structural Breaks and Seasonal Integration," The Warwick Economics Research Paper Series (TWERPS) 435, University of Warwick, Department of Economics.
- Harvey, Andrew, 2001. "Testing in Unobserved Components Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(1), pages 1-19, January.
- Graham Elliott & James H. Stock, 1992.
"Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown,"
NBER Technical Working Papers
0122, National Bureau of Economic Research, Inc.
- Elliott, Graham & Stock, James H., 1994. "Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 672-700, August.
- Hyllerberg, S. & Engle, R.F. & Granger, C.W.J. & Yoo, B.S., 1988.
"Seasonal Integration And Cointegration,"
0-88-2, Pennsylvania State - Department of Economics.
- 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?,"
8905, Michigan State - Econometrics and Economic Theory.
- 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.
- Taylor, A M Robert, 2003. "Robust Stationarity Tests in Seasonal Time Series Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 156-63, January.
- Nyblom, Jukka & Harvey, Andrew, 2000.
"Tests Of Common Stochastic Trends,"
Cambridge University Press, vol. 16(02), pages 176-199, April.
- Hannan, E J & Terrell, R D & Tuckwell, N E, 1970. "The Seasonal Adjustment of Economic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(1), pages 24-52, February.
- Perron, Pierre, 1989.
"The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis,"
Econometric Society, vol. 57(6), pages 1361-1401, November.
- Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
- Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
- Philip Hans Franses & Timothy J. Vogelsang, 1998. "On Seasonal Cycles, Unit Roots, And Mean Shifts," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 231-240, May.
- Donald W.K. Andrews, 1988.
"Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation,"
Cowles Foundation Discussion Papers
877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
- Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
- Fabio Busetti & Andrew Harvey, 2003. "Further Comments On Stationarity Tests In Series With Structural Breaks At Unknown Points," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(2), pages 137-140, 03.
- Hylleberg, Svend, 1995. "Tests for seasonal unit roots general to specific or specific to general?," Journal of Econometrics, Elsevier, vol. 69(1), pages 5-25, September.
- 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.
- Hansen, Bruce E., 1992.
"Testing for parameter instability in linear models,"
Journal of Policy Modeling,
Elsevier, vol. 14(4), pages 517-533, August.
- Tom Doan, . "STABTEST: RATS procedure to perform Hansen's stability test for OLS," Statistical Software Components RTS00199, Boston College Department of Economics.
- Fabio Busetti & Silvia Fabiani & Andrew Harvey, 2006.
"Convergence of Prices and Rates of Inflation,"
Oxford Bulletin of Economics and Statistics,
Department of Economics, University of Oxford, vol. 68(s1), pages 863-877, December.
- Wang, Dabin & Tomek, William G., 2004. "Commodity Prices And Unit Root Tests," Working Papers 127145, Cornell University, Department of Applied Economics and Management.
- Wang, Dabin & Tomek, William G., 2004. "Commodity Prices And Unit Root Tests," 2004 Annual meeting, August 1-4, Denver, CO 20141, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
- Su, Chi-Wei & Tsangyao, Chang & Chang, Hsu-Ling, 2011. "Purchasing power parity for fifteen Latin American countries: Stationary test with a Fourier function," International Review of Economics & Finance, Elsevier, vol. 20(4), pages 839-845, October.
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.