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Testing for predictability in a noninvertible ARMA model

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  • Lanne, Markku
  • Meitz, Mika
  • Saikkonen, Pentti

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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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 37151.

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Date of creation: 2012
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Handle: RePEc:pra:mprapa:37151

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Keywords: Non-Gaussian time series; noninvertible ARMA model; all-pass process; predictability of asset returns;

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  1. Taylor, Stephen J., 1982. "Tests of the Random Walk Hypothesis Against a Price-Trend Hypothesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 17(01), pages 37-61, March.
  2. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, Elsevier, vol. 22(1), pages 27-59, October.
  3. Lanne Markku & Saikkonen Pentti, 2011. "Noncausal Autoregressions for Economic Time Series," Journal of Time Series Econometrics, De Gruyter, De Gruyter, vol. 3(3), pages 1-32, October.
  4. Andrews, Beth & Davis, Richard A. & Jay Breidt, F., 2006. "Maximum likelihood estimation for all-pass time series models," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 97(7), pages 1638-1659, August.
  5. Nankervis, John C. & Savin, N. E., 2010. "Testing for Serial Correlation: Generalized Andrews–Ploberger Tests," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 28(2), pages 246-255.
  6. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, Biometrika Trust, vol. 89(2), pages 484-489, June.
  7. Breid, F. Jay & Davis, Richard A. & Lh, Keh-Shin & Rosenblatt, Murray, 1991. "Maximum likelihood estimation for noncausal autoregressive processes," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 36(2), pages 175-198, February.
  8. Mika Meitz & Pentti Saikkonen, 2012. "Maximum Likelihood Estimation of a Noninvertible ARMA Model with Autoregressive Conditional Heteroskedasticity," Koç University-TUSIAD Economic Research Forum Working Papers, Koc University-TUSIAD Economic Research Forum 1226, Koc University-TUSIAD Economic Research Forum.
  9. 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.
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