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Asymptotics of the Variance Ratio Test for MA Unit Root Processes

  • Lee, Jin (Department of Economics, Ewha Womans University)
  • Received : 20100100
  • Accepted : 20100200
  • Published : 2010.03.31

Abstract

We consider the asymptotic results of the variance ratio statistic when the underlying processes have moving average(MA) unit roots. This degenerate situation of zero spectral density near the origin cause the limit of the variance ratio to become zero. Its asymptotic behaviors are different from non-degenerating case, where the convergence rate of the variance ratio statistic is formally derived.

Keywords

References

  1. Andrews, D. W. K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation, Econometrica, 59, 817-858. https://doi.org/10.2307/2938229
  2. Campbell, J., Lo, A. and MacKinlay, A. (1997). The Econometrics of Financial Markets, Princeton University Press.
  3. Cochrane, J. (1988). How big is the random walk in GNP? Journal of Econometrics, 96, 893-920.
  4. Lee, J. (2010). Long-run variance estimation for linear processes under possible degeneracy, Journal of Economic Theory and Econometrics, 21, 1-22.
  5. Leybourne, S., McCabe, B. and Tremayne, A. (1996). Can economic time series be differenced to stationarity? Journal of Business and Econnomic statistics, 14, 435-446. https://doi.org/10.2307/1392252
  6. Lo, A. W. and MacKinlay, A. C. (1988). Stock market prices do not follow random walks: Evidence form a simple specification test, Review of Financial Studies, 1, 41-66. https://doi.org/10.1093/rfs/1.1.41
  7. Newey, W. and West, K. (1994). Automatic lag selection in covariance matrix estimation, Review of Economic Studies, 61, 631-653. https://doi.org/10.2307/2297912
  8. Phillips, P. C. B. and Solo, V. (1992). Asymptotics for linear processes, Annals of Statistics, 20, 971-1001. https://doi.org/10.1214/aos/1176348666
  9. Priestley, M. B. (1981). Spectral Analysis and Time Series, Academic Press, New York.
  10. Saikkonen, P. and Lukkonen, R. (1993). Testing for a moving average unit root in autoregressive integrated moving average models, Journal of the american Statistical Association, 88, 596-601. https://doi.org/10.1080/01621459.1993.10476312
  11. Velasco, C. and Robinson, P. M. (2001). Edgeworth expansions for spectral density estimates and studentized sample mean, Econometric Theroy, 17, 497-539. https://doi.org/10.1017/S0266466601173019