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Testing for Periodic Integration with a Changing Mean

Author

Listed:
  • Tomás Barrio

    (University of the Balearic Islands)

  • Mariam Camarero

    (University Jaume I)

  • Cecilio Tamarit

    (University of Valencia)

Abstract

In this paper we extend the test of periodic integration proposed by Boswijk and Franses (J Time Ser Anal 17:221–245, 1996) allowing for a change in the mean. We provide the asymptotic distribution and show that is the square of the distribution obtained by Perron and Vogelsang (J Bus Econ Stat 10:467–470, 1992a, J Bus Econ Stat 10:301–320, 1992b). In a Monte-Carlo experiment we show a good behaviour of the test in terms of size and power. Finally we have illustrated the use of the test in an empirical application to the case of external imbalances in the eurozone.

Suggested Citation

  • Tomás Barrio & Mariam Camarero & Cecilio Tamarit, 2019. "Testing for Periodic Integration with a Changing Mean," Computational Economics, Springer;Society for Computational Economics, vol. 54(1), pages 45-75, June.
  • Handle: RePEc:kap:compec:v:54:y:2019:i:1:d:10.1007_s10614-017-9680-x
    DOI: 10.1007/s10614-017-9680-x
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    1. del Barrio Castro, Tomás & Osborn, Denise R., 2008. "Cointegration For Periodically Integrated Processes," Econometric Theory, Cambridge University Press, vol. 24(1), pages 109-142, February.
    2. Ghysels, Eric & Perron, Pierre, 1993. "The effect of seasonal adjustment filters on tests for a unit root," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 57-98.
    3. Luis C. Nunes & Paulo M. M. Rodrigues, 2011. "On LM‐type tests for seasonal unit roots in the presence of a break in trend," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(2), pages 108-134, March.
    4. Pierre-Olivier Gourinchas & Hélène Rey, 2007. "International Financial Adjustment," Journal of Political Economy, University of Chicago Press, vol. 115(4), pages 665-703, August.
    5. Tomas Barrio Castro & Mariam Camarero & Cecilio Tamarit, 2015. "An analysis of the trade balance for OECD countries using periodic integration and cointegration," Empirical Economics, Springer, vol. 49(2), pages 389-402, September.
    6. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    7. 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.
    8. Mark Holmes & Theodore Panagiotidis & Abhijit Sharma, 2011. "The sustainability of India's current account," Applied Economics, Taylor & Francis Journals, vol. 43(2), pages 219-229.
    9. Perron, Pierre, 1988. "Trends and random walks in macroeconomic time series : Further evidence from a new approach," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 297-332.
    10. Ghysels, Eric, 1990. "Unit-Root Tests and the Statistical Pitfalls of Seasonal Adjustment: The Case of U.S. Postwar Real Gross National Product," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 145-152, April.
    11. Osborn, Denise R., 1991. "The implications of periodically varying coefficients for seasonal time-series processes," Journal of Econometrics, Elsevier, vol. 48(3), pages 373-384, June.
    12. Olekalns, Nilss, 1994. "Testing for unit roots in seasonally adjusted data," Economics Letters, Elsevier, vol. 45(3), pages 273-279.
    13. Perron, Pierre & Vogelsang, Timothy J, 1992. "Nonstationarity and Level Shifts with an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 301-320, July.
    14. Choi,In, 2015. "Almost All about Unit Roots," Cambridge Books, Cambridge University Press, number 9781107097339.
    15. Fountas Stilianos & Wu Jyh-Lin, 1999. "Are the U.S. Current Account Deficits Really Sustainable?," International Economic Journal, Taylor & Francis Journals, vol. 13(3), pages 51-58.
    16. Husted, Steven, 1992. "The Emerging U.S. Current Account Deficit in the 1980s: A Cointegration Analysis," The Review of Economics and Statistics, MIT Press, vol. 74(1), pages 159-166, February.
    17. Arize, Augustine C., 2002. "Imports and exports in 50 countries: Tests of cointegration and structural breaks," International Review of Economics & Finance, Elsevier, vol. 11(1), pages 101-115, April.
    18. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
    19. Gregory, Allan W. & Hansen, Bruce E., 1996. "Residual-based tests for cointegration in models with regime shifts," Journal of Econometrics, Elsevier, vol. 70(1), pages 99-126, January.
    20. Vanessa Berenguer‐Rico & Josep Lluís Carrion‐i‐Silvestre, 2011. "Regime shifts in stock–flow I(2)–I(1) systems: the case of US fiscal sustainability," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(2), pages 298-321, March.
    21. H. Peter Boswijk & Philip Hans Franses, 1996. "Unit Roots In Periodic Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(3), pages 221-245, May.
    22. Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2007. "Efficient tests of the seasonal unit root hypothesis," Journal of Econometrics, Elsevier, vol. 141(2), pages 548-573, December.
    23. Paresh Kumar Narayan & Seema Narayan, 2005. "Are exports and imports cointegrated? Evidence from 22 least developed countries," Applied Economics Letters, Taylor & Francis Journals, vol. 12(6), pages 375-378.
    24. Perron, Pierre, 1997. "Further evidence on breaking trend functions in macroeconomic variables," Journal of Econometrics, Elsevier, vol. 80(2), pages 355-385, October.
    25. Franses, Philip Hans, 1994. "A multivariate approach to modeling univariate seasonal time series," Journal of Econometrics, Elsevier, vol. 63(1), pages 133-151, July.
    26. Perron, Pierre, 1990. "Testing for a Unit Root in a Time Series with a Changing Mean," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 153-162, April.
    27. Maravall, Agustin, 1993. "Stochastic linear trends : Models and estimators," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 5-37, March.
    28. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    29. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030.
    30. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882, January.
    31. Craigwell, Roland & Greenidge, Kevin & Thomas, Chrystal & Drakes, Lisa, 2012. "Threshold Effects of Sovereign Debt: Evidence from the Caribbean," MPRA Paper 40936, University Library of Munich, Germany.
    32. Irandoust Manuchehr & Sjoo Boo, 2000. "The Behavior of the Current Account in Response to Unobservable and Observable Shocks," International Economic Journal, Taylor & Francis Journals, vol. 14(4), pages 41-57.
    33. Uwe Hassler & Paulo M. M. Rodrigues, 2004. "Seasonal Unit Root Tests Under Structural Breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 33-53, January.
    34. del Barrio Castro Tomás & Osborn Denise R, 2011. "Nonparametric Tests for Periodic Integration," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-35, February.
    35. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    36. Perron, Pierre & Vogelsang, Timothy J, 1992. "Testing for a Unit Root in a Time Series with a Changing Mean: Corrections and Extensions," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 467-470, October.
    37. Nag, Biswajit & Mukherjee, Jaydeep, 2012. "The sustainability of trade deficits in the presence of endogenous structural breaks: Evidence from the Indian economy," Journal of Asian Economics, Elsevier, vol. 23(5), pages 519-526.
    38. Dierk Herzer & Nowak-Lehmann Felicitas, 2006. "Is there a long-run relationship between exports and imports in Chile?," Applied Economics Letters, Taylor & Francis Journals, vol. 13(15), pages 981-986.
    39. Harvey, David I. & Leybourne, Stephen J. & Newbold, Paul, 2002. "Seasonal unit root tests with seasonal mean shifts," Economics Letters, Elsevier, vol. 76(2), pages 295-302, July.
    40. Hakkio, Craig S & Rush, Mark, 1991. "Is the Budget Deficit "Too Large?"," Economic Inquiry, Western Economic Association International, vol. 29(3), pages 429-445, July.
    41. Gregory, Allan W & Hansen, Bruce E, 1996. "Tests for Cointegration in Models with Regime and Trend Shifts," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(3), pages 555-560, August.
    42. Peter Boswijk, H. & Franses, Philip Hans, 1995. "Testing for periodic integration," Economics Letters, Elsevier, vol. 48(3-4), pages 241-248, June.
    43. Hansen, Lars Peter & Sargent, Thomas J., 1993. "Seasonality and approximation errors in rational expectations models," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 21-55.
    44. Shigeyuki Hamori, 2009. "The sustainability of trade accounts of the G-7 countries," Applied Economics Letters, Taylor & Francis Journals, vol. 16(17), pages 1691-1694.
    45. Maekawa, Koichi, 1997. "Periodically integrated autoregression with a structural break," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(3), pages 467-473.
    46. 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.
    47. Manuchehr Irandoust & Johan Ericsson, 2004. "Are Imports and Exports Cointegrated? An International Comparison," Metroeconomica, Wiley Blackwell, vol. 55(1), pages 49-64, February.
    48. Osborn, Denise R, 1988. "Seasonality and Habit Persistence in a Life Cycle Model of Consumptio n," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(4), pages 255-266, October-D.
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    More about this item

    Keywords

    Periodic integration; Change in the mean; Trade balance;
    All these keywords.

    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; Diffusion Processes

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