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Testing for Predictability in a Noninvertible ARMA Model

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Author Info

  • Markku Lanne

    ()
    (Department of Political and Economic Studies, University of Helsinki)

  • Mika Meitz

    ()
    (Department of Economics, Koç University)

  • Pentti Saikkonen

    ()
    (Department of Mathematics and Statistics, University of Helsinki)

Abstract

We develop likelihood-based tests for autocorrelation and predictability in a first order non-Gaussian and noninvertible ARMA model. Tests based on a special case of the general model, referred to as an all-pass model, are also obtained. Data generated by an all-pass process are uncorrelated but, in the non-Gaussian case, dependent and nonlinearly predictable. Therefore, in addition to autocorrelation the proposed tests can also be used to test for nonlinear predictability. This makes our tests different from their previous counterparts based on conventional invertible ARMA models. Unlike in the invertible case, our tests can also be derived by standard methods that lead to chi-squared or standard normal limiting distributions. A further convenience of the noninvertible ARMA model is that, to some extent, it can allow for conditional heteroskedasticity in the data which is useful when testing for predictability in economic and financial data. This is also illustrated by our empirical application to U.S. stock returns, where our tests indicate the presence of nonlinear predictability.

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Bibliographic Info

Paper provided by Koc University-TUSIAD Economic Research Forum in its series Koç University-TUSIAD Economic Research Forum Working Papers with number 1225.

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Length: 33 pages
Date of creation: Sep 2012
Date of revision:
Handle: RePEc:koc:wpaper:1225

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Keywords: Non-Gaussian time series; noninvertible ARMA model; all-pass process.;

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  1. Nankervis, John C. & Savin, N. E., 2010. "Testing for Serial Correlation: Generalized Andrews–Ploberger Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 246-255.
  2. Lanne, Markku & Saikkonen, Pentti, 2010. "Noncausal autoregressions for economic time series," MPRA Paper 32943, University Library of Munich, Germany.
  3. Meitz, Mika & Saikkonen, Pentti, 2013. "Maximum likelihood estimation of a noninvertible ARMA model with autoregressive conditional heteroskedasticity," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 227-255.
  4. Breid, F. Jay & Davis, Richard A. & Lh, Keh-Shin & Rosenblatt, Murray, 1991. "Maximum likelihood estimation for noncausal autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 36(2), pages 175-198, February.
  5. Rongning Wu & Richard A. Davis, 2010. "Least absolute deviation estimation for general autoregressive moving average time-series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 98-112, 03.
  6. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
  7. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
  8. Andrews, Beth & Davis, Richard A. & Jay Breidt, F., 2006. "Maximum likelihood estimation for all-pass time series models," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1638-1659, August.
  9. Taylor, Stephen J., 1982. "Tests of the Random Walk Hypothesis Against a Price-Trend Hypothesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(01), pages 37-61, March.
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