Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Studies in Nonlinear Dynamics & Econometrics

Ed. by Mizrach, Bruce


IMPACT FACTOR 2018: 0.448
5-years IMPACT FACTOR: 0.877

CiteScore 2018: 0.85

SCImago Journal Rank (SJR) 2018: 0.552
Source Normalized Impact per Paper (SNIP) 2018: 0.561

Mathematical Citation Quotient (MCQ) 2018: 0.07

Online
ISSN
1558-3708
See all formats and pricing
More options …
Ahead of print

Issues

Volume 24 (2020)

A wavelet-based variance ratio unit root test for a system of equations

Abdul Aziz Ali / Kristofer Månsson / Ghazi Shukur
Published Online: 2019-11-16 | DOI: https://doi.org/10.1515/snde-2018-0005

Abstract

In this paper, we suggest a unit root test for a system of equations using a spectral variance decomposition method based on the Maximal Overlap Discrete Wavelet Transform. We obtain the limiting distribution of the test statistic and study its small sample properties using Monte Carlo simulations. We find that, for multiple time series of small lengths, the wavelet-based method is robust to size distortions in the presence of cross-sectional dependence. The wavelet-based test is also more powerful than the Cross-sectionally Augmented Im et al. unit root test (Pesaran, M. H. 2007. “A Simple Panel Unit Root Test in the Presence of Cross-section Dependence.” Journal of Applied Econometrics 22 (2): 265–312.) for time series with between 20 and 100 observations, using systems of 5 and 10 equations. We demonstrate the usefulness of the test through an application on evaluating the Purchasing Power Parity theory for the Group of 7 countries and find support for the theory, whereas the test by Pesaran (Pesaran, M. H. 2007. “A Simple Panel Unit Root Test in the Presence of Cross-section Dependence.” Journal of Applied Econometrics 22 (2): 265–312.) finds no such support.

Keywords: system of equations; unit roots; wavelets

References

  • Andrews, D. W. 1991. “Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation.” Econometrica: Journal of the Econometric Society 59: 817–858.CrossrefGoogle Scholar

  • Bahmani-Oskooee, M. 1993. “Purchasing Power Parity Based on Effective Exchange Rate and Cointegration: 25 LDCs’ Experience With its Absolute Formulation.” World Development 21 (6): 1023–1031.CrossrefGoogle Scholar

  • Bahmani-Oskooee, M. 1995. “Real and Nominal Effective Exchange Rates for 22 LDCs: 1971: 1–1990: 4.” Applied Economics 27 (7): 591–604.CrossrefGoogle Scholar

  • Billingsley, P. 1968. Convergence of Probability Measures. New york: John Wiley & Sons.Google Scholar

  • Breitung, J. 2002. “Nonparametric Tests for Unit Roots and Cointegration.” Journal of Econometrics 108 (2): 343–363.CrossrefGoogle Scholar

  • Cheung, Y.-W., M. D. Chinn, and E. Fujii. 2006. “The Chinese Economies in Global Context: The Integration Process and its Determinants.” Journal of the Japanese and International Economies 20 (1): 128–153.CrossrefGoogle Scholar

  • Choi, I. 2001. “Unit Root Tests for Panel Data.” Journal of International Money and Finance 20 (2): 249–272.CrossrefGoogle Scholar

  • Cochrane, J. H. 1988. “How Big is the Random Walk in GNP?” Journal of Political Economy 96 (5): 893–920.CrossrefGoogle Scholar

  • Corbae, D., and S. Ouliaris 1988. “Cointegration and Tests of Purchasing Power Parity.” The Review of Economics and Statistics 70: 508–511.CrossrefGoogle Scholar

  • Corbae, D., and S. Ouliaris. 1991. “A Test of Long-run Purchasing Power Parity Allowing for Structural Breaks.” Economic Record 67 (1): 26–33.CrossrefGoogle Scholar

  • Dickey, D. A., and W. A. Fuller. 1979. “Distribution of the Estimators for Autoregressive Time Series with a Unit Root.” Journal of the American statistical association 74 (366a): 427–431.Google Scholar

  • Fan, Y., and R. Gençay. 2010. “Unit Root Tests with Wavelets.” Econometric Theory 26 (05): 1305–1331.CrossrefWeb of ScienceGoogle Scholar

  • Fisher, R. 1932. Statistical Methods for Research Workers (Edinburgh: Oliver and Boyd, 1925). Edinburgh: Oliver and Boyd.Google Scholar

  • Frankel, J. A, and A. K Rose. 1996. “A Panel Project on Purchasing Power Parity: Mean Reversion Within and Between Countries.” Journal of International Economics 40: (1): 209–224.CrossrefGoogle Scholar

  • Gençay, R., F. Selçuk, and B. J. Whitcher. 2001. An Introduction to Wavelets and Other Filtering Methods in Finance and Economics. San Diego: Academic Press.Google Scholar

  • Glen, J. D. 1992. “Real Exchange Rates in the Short, Medium, and Long Run.” Journal of International Economics 33 (1–2): 147–166.CrossrefGoogle Scholar

  • Granger, C. 1966. “The Typical Spectral Shape of an Economic Variable.” Econometrica 54: 257–287.Google Scholar

  • Hamilton, J. D. 1994. Time Series Analysis, Vol. 2. Princeton: Princeton University Press.Google Scholar

  • Hegwood, N. D., and D. H. Papell. 1998. “Quasi Purchasing Power Parity.” International Journal of Finance & Economics 3 (4): 279–289.CrossrefGoogle Scholar

  • Im, K. S., M. H. Pesaran, and Y. Shin. 2003. “Testing for Unit Roots in Heterogeneous Panels.” Journal of econometrics 115 (1): 53–74.CrossrefGoogle Scholar

  • Kwiatkowski, D., P. C. Phillips, P. Schmidt, and Y. Shin. 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 54 (1–3): 159–178.CrossrefGoogle Scholar

  • Layton, A. P., and J. P. Stark. 1990. “Cointegration as an Empirical Test of Purchasing Power Parity.” Journal of Macroeconomics 12 (1): 125–136.CrossrefGoogle Scholar

  • Levin, A., C.-F. Lin, and C.-S. J. Chu. 2002. “Unit Root Tests in Panel Data: Asymptotic and Finite-sample Properties.” Journal of econometrics 108 (1): 1–24.CrossrefGoogle Scholar

  • Li, Y., and G. Shukur. 2013. “Testing for Unit Roots in Panel Data Using a Wavelet Ratio Method.” Computational Economics 41 (1): 59–69.Web of ScienceCrossrefGoogle Scholar

  • Lothian, J. R., and M. P. Taylor. 1996. “Real Exchange Rate Behavior: The Recent Float From the Perspective of the Past two Centuries.” Journal of Political Economy 104 (3): 488–509.CrossrefGoogle Scholar

  • Maddala, G. S., and S. Wu. 1999. “A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test.” Oxford Bulletin of Economics and statistics 61 (S1): 631–652.CrossrefGoogle Scholar

  • Murray, C. J., and D. H. Papell. 2002. “The Purchasing Power Parity Persistence Paradigm.” Journal of International Economics 56 (1): 1–19.CrossrefGoogle Scholar

  • Murray, C. J., and D. H. Papell. 2005. “Do Panels Help Solve the Purchasing Power Parity Puzzle?” Journal of Business & Economic Statistics 23 (4): 410–415.CrossrefGoogle Scholar

  • Newey, W. K., and K. D. West. 1987. “A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation-consistent Covariance Matrix.” Econometrica 55: 703–708.CrossrefGoogle Scholar

  • Percival, D. B. 1995. “On Estimation of the Wavelet Variance.” Biometrika 82 (3): 619–631.CrossrefGoogle Scholar

  • Percival, D. B., and A. T. Walden. 2000. Wavelet Methods for Time Series Analysis (Cambridge Series in Statistical and Probabilistic Mathematics). Cambridge: Cambridge University Press.Google Scholar

  • Pesaran, M. H. 2007. “A Simple Panel Unit Root Test in the Presence of Cross-section Dependence.” Journal of Applied Econometrics 22 (2): 265–312.CrossrefGoogle Scholar

  • Schmidt, P., and P. C. Phillips. 1966. “LM Tests for a Unit Root in the Presence of Deterministic Trends“. Oxford Bulletin of Economics and Statistics 34: 150–161.Google Scholar

  • Stock, J. H. 1994. “Unit Roots, Structural Breaks and Trends.” In Handbook of Econometrics, edited by R. Engle and D. McFadden, Vol. 4, chapter 46, 2752–2753. North Holland: Elsevier located in Amsterdam.Google Scholar

  • Tanaka, K. 1990. “Testing for a Moving Average Unit Root.” Econometric Theory 6 (04): 433–444.CrossrefGoogle Scholar

  • Taylor, M. P. 1988. “An Empirical Examination of Long-run Purchasing Power Parity Using Cointegration Techniques.” Applied Economics 20 (10): 1369–1381.CrossrefGoogle Scholar

  • Taylor, A. M. 2002. “A Century of Purchasing Power Parity.” Review of Economics and Statistics 84 (1): 139–150.CrossrefGoogle Scholar

  • Zivot, E., and J. Wang. 2006. Modelling Financial Time Series with S-Plus. New York: Springer-Verlag.Google Scholar

About the article

Published Online: 2019-11-16


Citation Information: Studies in Nonlinear Dynamics & Econometrics, 20180005, ISSN (Online) 1558-3708, DOI: https://doi.org/10.1515/snde-2018-0005.

Export Citation

© 2019 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in