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A Frequency Domain Test of Time Reversibility

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  • Melvin J. Hinich
  • Philip Rothman

Abstract

We introduce a frequency-domain test of time reversibility, the REVERSE test. It is based on the bispectrum. We analytically establish the asymptotic distribution of the test and also explore its finite-sample properties through Monte-Carlo simulation. Following other researchers who demonstrated that the problem of business-cycle asymmetry can be stated as whether macroeconomic fluctuations are time irreversible, we use the REVERSE test as a frequency-domain test of business-cycle asymmetry. Our empirical results show that time irreversibility is the rule rather than the exception for a representative set of macroeconomic time series for five OECD countries.
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  • Melvin J. Hinich & Philip Rothman, "undated". "A Frequency Domain Test of Time Reversibility," Working Papers 9706, East Carolina University, Department of Economics.
  • Handle: RePEc:wop:eacaec:9706
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    References listed on IDEAS

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    1. Sichel, Daniel E, 1993. "Business Cycle Asymmetry: A Deeper Look," Economic Inquiry, Western Economic Association International, vol. 31(2), pages 224-236, April.
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    3. Ramsey, James B & Rothman, Philip, 1996. "Time Irreversibility and Business Cycle Asymmetry," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 28(1), pages 1-21, February.
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    6. Falk, Barry, 1986. "Further Evidence on the Asymmetric Behavior of Economic Time Series over the Business Cycle," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1096-1109, October.
    7. Arthur F. Burns & Wesley C. Mitchell, 1946. "Measuring Business Cycles," NBER Books, National Bureau of Economic Research, Inc, number burn46-1, June.
    8. Melvin J. Hinich, 1982. "Testing For Gaussianity And Linearity Of A Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(3), pages 169-176, May.
    9. Neftci, Salih N, 1984. "Are Economic Time Series Asymmetric over the Business Cycle?," Journal of Political Economy, University of Chicago Press, vol. 92(2), pages 307-328, April.
    10. Marc Hallin & Claude Lefèvre & Madan Lal Puri, 1988. "On time-reversibility and the uniqueness of moving average representations for non-Gaussian stationary time series," ULB Institutional Repository 2013/2017, ULB -- Universite Libre de Bruxelles.
    11. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September.
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    Cited by:

    1. Denisa Roberts & Douglas Patterson, 2018. "A Second Order Cumulant Spectrum Test That a Stochastic Process is Strictly Stationary and a Step Toward a Test for Graph Signal Strict Stationarity," Papers 1801.06727, arXiv.org, revised Mar 2020.
    2. Yi-Ting Chen & Chung-Ming Kuan, 2002. "Time irreversibility and EGARCH effects in US stock index returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 565-578.
    3. Chen, Yi-Ting & Chou, Ray Y. & Kuan, Chung-Ming, 2000. "Testing time reversibility without moment restrictions," Journal of Econometrics, Elsevier, vol. 95(1), pages 199-218, March.
    4. Steven Cook & Alan Speight, 2006. "International Business Cycle Asymmetry and Time Irreversible Nonlinearities," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(10), pages 1051-1065.
    5. Phillip Wild & John Foster, 2012. "On testing for non-linear and time irreversible probabilistic structure in high frequency ASX financial time series data," Discussion Papers Series 466, School of Economics, University of Queensland, Australia.
    6. Randal J. Verbrugge, 1998. "A cross-country investigation of macroeconomic asymmetries," Macroeconomics 9809017, University Library of Munich, Germany, revised 30 Sep 1998.
    7. Amado Peiro, 2004. "Are business cycles asymmetric? Some European evidence," Applied Economics, Taylor & Francis Journals, vol. 36(4), pages 335-342.
    8. Coakley, Jerry & Fuertes, Ana-Maria, 2006. "Testing for sign and amplitude asymmetries using threshold autoregressions," Journal of Economic Dynamics and Control, Elsevier, vol. 30(4), pages 623-654, April.
    9. Karapanagiotidis, Paul, 2013. "Empirical evidence for nonlinearity and irreversibility of commodity futures prices," MPRA Paper 56801, University Library of Munich, Germany.
    10. McCausland, William J., 2007. "Time reversibility of stationary regular finite-state Markov chains," Journal of Econometrics, Elsevier, vol. 136(1), pages 303-318, January.
    11. Beare, Brendan K. & Seo, Juwon, 2014. "Time Irreversible Copula-Based Markov Models," Econometric Theory, Cambridge University Press, vol. 30(5), pages 923-960, October.
    12. Hinich, Melvin J. & Foster, John & Wild, Phillip, 2006. "Structural change in macroeconomic time series: A complex systems perspective," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 136-150, March.
    13. Panagiotidis, Theodore & Pelloni, Gianluigi, 2007. "Nonlinearity In The Canadian And U.S. Labor Markets: Univariate And Multivariate Evidence From A Battery Of Tests," Macroeconomic Dynamics, Cambridge University Press, vol. 11(5), pages 613-637, November.
    14. Fong, Wai Mun, 2003. "Time reversibility tests of volume-volatility dynamics for stock returns," Economics Letters, Elsevier, vol. 81(1), pages 39-45, October.
    15. Barry E. Jones & Travis D. Nesmith, 1999. "Tests for non-linear dynamics in systems of non-stationary economic time series: the case of short-term US interest rates," Finance and Economics Discussion Series 1999-55, Board of Governors of the Federal Reserve System (U.S.), revised 1999.
    16. Zacharias Psaradakis, 2008. "Assessing Time‐Reversibility Under Minimal Assumptions," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 881-905, September.
    17. Nesmith Travis D & Jones Barry E, 2008. "Linear Cointegration of Nonlinear Time Series with an Application to Interest Rate Dynamics," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(1), pages 1-18, March.
    18. Miguel Artiach, 2011. "Second-order moments of frequency asymmetric cycles," Working Papers. Serie AD 2011-27, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    19. Iglói, E. & Terdik, Gy., 2014. "When the bispectrum is real-valued," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 1-5.

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