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Persistence and Nonstationary Models

Author

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

Abstract

The aim of this paper is to examine the measurement 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 alternative nonstationary processes. Three measures of persistence are considered, namely the long-run impulse response, variance ratio and autocorrelation functions. Particular emphasis is given to the behaviour of these measures in a range of nonstationary models. We document 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 clarify what shock the impulse response function refers to in the case of models where more than one random disturbance impinges on the time series.

Suggested Citation

  • B.P.M. McCabe & G.M. Martin & A.R. Tremayne, 2003. "Persistence and Nonstationary Models," Monash Econometrics and Business Statistics Working Papers 16/03, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2003-16
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2003/wp16-03.pdf
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    References listed on IDEAS

    as
    1. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
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    1. 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.

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    More about this item

    Keywords

    Cramer Representation; Stochastic Unit Root Model; Stochastic Integration; Impulse Response; Variance Ratio; Autocorrelation Function; Long Memory.;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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