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Temporal aggregation in a periodically integrated autoregressive process


  • Franses, P.H.
  • Boswijk, H.P.

    (Tilburg University, Faculty of Economics)


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.
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Suggested Citation

  • Franses, P.H. & Boswijk, H.P., 1993. "Temporal aggregation in a periodically integrated autoregressive process," Research Memorandum 2ef3689d-9fa6-419a-850e-5, Tilburg University, School of Economics and Management.
  • Handle: RePEc:tiu:tiurem:2ef3689d-9fa6-419a-850e-52babdf875b5

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    References listed on IDEAS

    1. 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.
    2. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    3. 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.
    4. Franses, Philip Hans, 1994. "A multivariate approach to modeling univariate seasonal time series," Journal of Econometrics, Elsevier, vol. 63(1), pages 133-151, July.
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    Cited by:

    1. Tilak Abeysinghe & Gulasekaran Rajaguru, 2003. "Temporal Aggregation, Causality Distortions, and a Sign Rule," Departmental Working Papers wp0406, National University of Singapore, Department of Economics.
    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, CEJEME, vol. 9(1), pages 29-67, March.
    3. 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, CEJEME, vol. 7(3), pages 169-186, September.

    More about this item


    Time Series; Aggregation; statistics;


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