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Stationarity Tests Under Time-Varying Second Moments

  • Cavaliere, Giuseppe
  • Taylor, A.M. Robert

in this paper we analyze the effects of a very general class of time-varying variances on well-known stationarity tests of the i(0) null hypothesis. our setup allows, among other things, for both single and multiple breaks in variance, smooth transition variance breaks, and (piecewise-) linear trending variances. we derive representations for the limiting distributions of the test statistics under variance breaks in the errors of i(0), i(1), and near-i(1) data generating processes, demonstrating the dependence of these representations on the precise pattern followed by the variance processes. monte carlo methods are used to quantify the effects of fixed and smooth transition single breaks and trending variances on the size and power properties of the tests. finally, bootstrap versions of the tests are proposed that provide a solution to the inference problem.we are grateful to peter phillips, a co-editor, and two anonymous referees whose comments on an earlier draft have led to a considerable improvement in the paper.

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Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 21 (2005)
Issue (Month): 06 (December)
Pages: 1112-1129

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Handle: RePEc:cup:etheor:v:21:y:2005:i:06:p:1112-1129_05
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  1. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-313, September.
  2. 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?," Papers 8905, Michigan State - Econometrics and Economic Theory.
  3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  4. de Jong, Robert M., 2000. "A Strong Consistency Proof For Heteroskedasticity And Autocorrelation Consistent Covariance Matrix Estimators," Econometric Theory, Cambridge University Press, vol. 16(02), pages 262-268, April.
  5. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
  6. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March.
  7. Busetti, Fabio & Taylor, A M Robert, 2003. "Variance Shifts, Structural Breaks, and Stationarity Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 510-31, October.
  8. Hamori, Shigeyuki & Tokihisa, Akira, 1997. "Testing for a unit root in the presence of a variance shift1," Economics Letters, Elsevier, vol. 57(3), pages 245-253, December.
  9. Phillips, Peter C B & Xiao, Zhijie, 1998. " A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-69, December.
  10. Kim, Tae-Hwan & Leybourne, Stephen & Newbold, Paul, 2002. "Unit root tests with a break in innovation variance," Journal of Econometrics, Elsevier, vol. 109(2), pages 365-387, August.
  11. Shin, Yongcheol, 1994. "A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration," Econometric Theory, Cambridge University Press, vol. 10(01), pages 91-115, March.
  12. Cavaliere, Giuseppe, 2004. "Testing stationarity under a permanent variance shift," Economics Letters, Elsevier, vol. 82(3), pages 403-408, March.
  13. repec:bot:quadip:89 is not listed on IDEAS
  14. Giuseppe Cavaliere, 2005. "Unit Root Tests under Time-Varying Variances," Econometric Reviews, Taylor & Francis Journals, vol. 23(3), pages 259-292.
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