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Testing periodically integrated autoregressive models

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  • Franses, Philip Hans
  • McAleer, Michael

Abstract

Periodically integrated time series require a periodic differencing filter to remove the stochastic trend. A non-periodic integrated time series needs the first-difference filter for similar reasons. When the changing seasonal fluctuations for the non-periodic integrated series can be described by seasonal dummy variables for which the corresponding parameters are not constant within the sample, such a series may not be easily distinguished from a periodically integrated time series. In this paper, testing procedures developed by Franses and McAleer [4] are used to distinguish between these two alternative stochastic and non-stochastic seasonal processes when there is a single known structural break in the seasonal dummy parameters. Two empirical examples, namely, the logarithms of quarterly real GNP series for Austria and Germany, are used to illustrate the approach.

Suggested Citation

  • Franses, Philip Hans & McAleer, Michael, 1997. "Testing periodically integrated autoregressive models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(3), pages 457-465.
    • Handle: RePEc:eee:matcom:v:43:y:1997:i:3:p:457-465
    DOI: 10.1016/S0378-4754(97)00032-3
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    References listed on IDEAS

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    1. Davidson, Russell & MacKinnon, James G, 1981. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Econometrica, Econometric Society, vol. 49(3), pages 781-793, May.
    2. Franses, P.H. & McAleer, M., 1995. "Testing Nested and Non-Nested Periodically Integrated Autoregressive Models," Discussion Paper 1995-10, Tilburg University, Center for Economic Research.
    3. Philip Hans Franses & Richard Paap, 1994. "Model Selection In Periodic Autoregressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 56(4), pages 421-439, November.
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