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Testing for Non-Linear Dependence in Univariate Time Series: An Empirical Investigation of the Austrian Unemployment Rate

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  • Manfred M. Fischer

    ()

  • Wolfgang Koller

    ()

Abstract

The modelling of univariate time series is a subject of great importance in a variety of fields, in regional science and economics, and beyond. Time series modelling involves three major stages:model identification, model%0D estimation and diagnostic checking. This current paper focuses its attention on the model identification stage in general and on the issue of testing for non-linear dependence in particular. If the null hypothesis of independence is rejected, then the alternative hypothesis implies the existence of linear or non-linear dependence. The test of this hypothesis is of crucial importance. If the data are linearly dependent, the linear time series models have to be specified (generally within the SARIMA methodology). If the data are non-linearly dependent, then non-linear time series modelling (such as ARCH, GARCH and autoregressive neural network models) must be employed. Several tests have recently been developed for this purpose. In this paper we make a modest attempt to investigate the power of five competing tests (McLeod-Li-test, Hsieh-test, BDS-test, Terävirta''''s neural network test) in a real world application domain of unemployment rate prediction in order to determine what kind of non-linear specification they have good power against, and which not. The results obtained indicate that that all the tests reject the hypothesis of mere linear dependence in our application. But if interest is focused on predicting the conditional mean of the series, the neural network test is most informative for model identification and its use is therefore highly%0D recommended.

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Bibliographic Info

Paper provided by European Regional Science Association in its series ERSA conference papers with number ersa01p233.

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Date of creation: Aug 2001
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Handle: RePEc:wiw:wiwrsa:ersa01p233

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  1. Robin L. Lumsdaine & Serena Ng, 1998. "Testing for ARCH in the Presence of a Possibly Misspecified Conditional Mean," Boston College Working Papers in Economics, Boston College Department of Economics 370, Boston College Department of Economics.
  2. D. A. Peel & A. E. H. Speight, 1998. "The nonlinear time series properties of unemployment rates: some further evidence," Applied Economics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 30(2), pages 287-294, February.
  3. Brock, William A. & Sayers, Chera L., 1988. "Is the business cycle characterized by deterministic chaos?," Journal of Monetary Economics, Elsevier, Elsevier, vol. 22(1), pages 71-90, July.
  4. Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993. "Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests," Journal of Econometrics, Elsevier, Elsevier, vol. 56(3), pages 269-290, April.
  5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  6. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, Econometric Society, vol. 55(2), pages 391-407, March.
  7. Barnett, William A. & Gallant, A. Ronald & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1997. "A single-blind controlled competition among tests for nonlinearity and chaos," Journal of Econometrics, Elsevier, Elsevier, vol. 82(1), pages 157-192.
  8. Burgess, Simon M, 1992. "Asymmetric Employment Cycles in Britain: Evidence and an Explanation," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 102(411), pages 279-90, March.
  9. Brock, W.A. & Dechert, W.D. & LeBaron, B. & Scheinkman, J.A., 1995. "A Test for Independence Based on the Correlation Dimension," Working papers, Wisconsin Madison - Social Systems 9520, Wisconsin Madison - Social Systems.
  10. Sentana, Enrique, 1995. "Quadratic ARCH Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 62(4), pages 639-61, October.
  11. Granger, Clive W J, 1991. " Developments in the Nonlinear Analysis of Economic Series," Scandinavian Journal of Economics, Wiley Blackwell, Wiley Blackwell, vol. 93(2), pages 263-76.
  12. Hsieh, David A, 1989. "Testing for Nonlinear Dependence in Daily Foreign Exchange Rates," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 62(3), pages 339-68, July.
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