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The variance of an integrated process need not diverge to infinity


  • Hannes Leeb

    (Dept. of Statistics, Univ. Vienna)

  • Benedikt Poetscher

    (Dept. of Statistics, Univ. Vienna)


For a process with stationary first differences necessary and sufficient conditions for the variance of the process to be unbounded are given. An example shows that the variance of an integrated process -- while being unbounded -- need not diverge to infinity. Sufficient conditions for the variance of an integrated process to diverge to infinity are provided.

Suggested Citation

  • Hannes Leeb & Benedikt Poetscher, 1999. "The variance of an integrated process need not diverge to infinity," Econometrics 9907001, EconWPA.
  • Handle: RePEc:wpa:wuwpem:9907001
    Note: Type of Document - Postscript; prepared on IBM PC/Linux; to print on Postscript; pages: 11; figures: none

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    References listed on IDEAS

    1. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
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    Cited by:

    1. Dietmar Bauer & Martin Wagner, 2002. "A Canonical Form for Unit Root Processes in the State Space Framework," Diskussionsschriften dp0204, Universitaet Bern, Departement Volkswirtschaft.
    2. Paulauskas, Vygantas, 2007. "On unit roots for spatial autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 209-226, January.
    3. Dietmar Bauer & Martin Wagner, 2003. "On Polynomial Cointegration in the State Space Framework," Diskussionsschriften dp0313, Universitaet Bern, Departement Volkswirtschaft.

    More about this item


    integrated process; unit root; difference stationarity; spectral density; long-memory; unbounded variance.;

    JEL classification:

    • 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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