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Assessing Persistence In Discrete Nonstationary Time-Series Models


  • B. P. M. McCabe
  • G. M. Martin
  • A. R. Tremayne


The aim of this paper is to examine the application of measures of persistence in a range of time-series models nested in the framework of Cramer (1961). This framework is a generalization of the Wold (1938) decomposition for stationary time-series which, in addition to accommodating the standard I(0) and I(1) models, caters for a broad range of alternative processes. Two measures of persistence are considered in some detail, namely the long-run impulse-response and variance-ratio functions. Particular emphasis is given to the behaviour of these measures in a range of non-stationary models specified in discrete time. We document the conflict that arises between different measures, applied to the same model, as well as conflict arising from the use of a given measure in different models. Precisely which persistence measures are time dependent and which are not, is highlighted. The nature of the general representation used also helps to clarify which shock the impulse-response function refers to in the case of models where more than one random disturbance impinges on the time series. Copyright 2005 Blackwell Publishing Ltd.

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  • B. P. M. McCabe & G. M. Martin & A. R. Tremayne, 2005. "Assessing Persistence In Discrete Nonstationary Time-Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(2), pages 305-317, March.
  • Handle: RePEc:bla:jtsera:v:26:y:2005:i:2:p:305-317

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    References listed on IDEAS

    1. Hassler, U. & Marmol, F. & Velasco, C., 2006. "Residual log-periodogram inference for long-run relationships," Journal of Econometrics, Elsevier, vol. 130(1), pages 165-207, January.
    2. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    3. Tsay, Wen-Jen & Chung, Ching-Fan, 2000. "The spurious regression of fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 96(1), pages 155-182, May.
    4. Lobato, I. & Robinson, P. M., 1996. "Averaged periodogram estimation of long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 303-324, July.
    5. Lobato, Ignacio N., 1999. "A semiparametric two-step estimator in a multivariate long memory model," Journal of Econometrics, Elsevier, vol. 90(1), pages 129-153, May.
    6. Hannan, E. J., 1979. "The central limit theorem for time series regression," Stochastic Processes and their Applications, Elsevier, vol. 9(3), pages 281-289, December.
    7. Carlos Velasco, 2003. "Gaussian Semi-parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 345-378, May.
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