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Temporal aggregation in a periodically integrated autoregressive process

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  • Franses, Philip Hans
  • Boswijk, H. Peter

Abstract

A periodically integrated autoregressive process for a time series which is observed S times per year assumes the presence of S - 1 cointegration relations between the annual series containing the seasonal observations, with the additional feature that these relations are different across the seasons. This means that there is a single unit root in the vector autoregression for these annual series. In this paper it is shown that temporally aggregating such a process does not affect the presence of this unit root, i.e. the aggregated series is also periodically integrated.

Suggested Citation

  • Franses, Philip Hans & Boswijk, H. Peter, 1996. "Temporal aggregation in a periodically integrated autoregressive process," Statistics & Probability Letters, Elsevier, vol. 30(3), pages 235-240, October.
    • Handle: RePEc:eee:stapro:v:30:y:1996:i:3:p:235-240
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    References listed on IDEAS

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    1. Herings, P.J.J., 1992. "On the structure of constrained equilibria," Research Memorandum FEW 587, Tilburg University, School of Economics and Management.
    2. Osborn, Denise R., 1991. "The implications of periodically varying coefficients for seasonal time-series processes," Journal of Econometrics, Elsevier, vol. 48(3), pages 373-384, June.
    3. Franses, Philip Hans, 1994. "A multivariate approach to modeling univariate seasonal time series," Journal of Econometrics, Elsevier, vol. 63(1), pages 133-151, July.
    4. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    5. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
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    Cited by:

    1. Tilak Abeysinghe & Gulasekaran Rajaguru, 2004. "Temporal aggregation, causality distortions and a sign rule," Econometric Society 2004 Australasian Meetings 73, Econometric Society.
    2. Łukasz Lenart, 2017. "Examination of Seasonal Volatility in HICP for Baltic Region Countries: Non-Parametric Test versus Forecasting Experiment," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 9(1), pages 29-67, March.
    3. Rotger, Gabriel Pons, "undated". "Testing for Seasonal Unit Roots with Temporally Aggregated Time Series," Economics Working Papers 2003-16, Department of Economics and Business Economics, Aarhus University.
    4. Łukasz Lenart & Mateusz Pipień, 2015. "Empirical Properties of the Credit and Equity Cycle within Almost Periodically Correlated Stochastic Processes - the Case of Poland, UK and USA," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 7(3), pages 169-186, September.

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