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Testing Time-Series Stationarity Against An Alternative Whose Mean Is Periodic

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  • Hinich, Melvin A.
  • Wild, Phillip

Abstract

We develop a test of the null hypothesis that an observed time series is a realization of a strictly stationary random process. Our test is based on the result that the kth value of the discrete Fourier transform of a sample frame has a zero mean under the null hypothesis. The test that we develop will have considerable power against an important form of nonstationarity hitherto not considered in the mainstream econometric time-series literature, that is, where the mean of a time series is periodic with random variation in its periodic structure. The size and power properties of the test are investigated and its applicability to real-world problems is demonstrated by application to three economic data sets.

Suggested Citation

  • Hinich, Melvin A. & Wild, Phillip, 2001. "Testing Time-Series Stationarity Against An Alternative Whose Mean Is Periodic," Macroeconomic Dynamics, Cambridge University Press, vol. 5(3), pages 380-412, June.
    • Handle: RePEc:cup:macdyn:v:5:y:2001:i:03:p:380-412_02
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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. Wild, Phillip & Hinich, Melvin J. & Foster, John, 2010. "Are daily and weekly load and spot price dynamics in Australia's National Electricity Market governed by episodic nonlinearity?," Energy Economics, Elsevier, vol. 32(5), pages 1082-1091, September.
    3. Phillip Wild & Melvin J. Hinich & John Foster, 2008. "The Use of Trimming to Improve the Performance of Tests for Nonlinear Serial Dependence with Application to the Australian National Electricity Market," Discussion Papers Series 367, School of Economics, University of Queensland, Australia.
    4. Melvin Hinich & Apostolos Serletis, 2007. "Randomly Modulated Periodic Signals in Alberta's Electricity Market," World Scientific Book Chapters, in: Quantitative And Empirical Analysis Of Energy Markets, chapter 19, pages 256-267, World Scientific Publishing Co. Pte. Ltd..
    5. 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.).
    6. 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.
    7. Hinich, Melvin J. & Serletis, Apostolos, 2008. "Randomly modulated periodicity in the US stock market," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 654-659.

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