Testing for predictability in a noninvertible ARMA model
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.
|Date of creation:||2012|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Nankervis, John C. & Savin, N. E., 2010. "Testing for Serial Correlation: Generalized Andrewsâ€“Ploberger Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 246-255.
- 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.
- 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 1226, Koc University-TUSIAD Economic Research Forum.
- 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, March.
- Lanne Markku & Saikkonen Pentti, 2011.
"Noncausal Autoregressions for Economic Time Series,"
Journal of Time Series Econometrics,
De Gruyter, vol. 3(3), pages 1-32, October.
- Lanne, Markku & Saikkonen, Pentti, 2010. "Noncausal autoregressions for economic time series," MPRA Paper 32943, University Library of Munich, Germany.
- 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.
- 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.
- 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.
- 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.
- James M. Poterba & Lawrence H. Summers, 1987. "Mean Reversion in Stock Prices: Evidence and Implications," NBER Working Papers 2343, National Bureau of Economic Research, Inc.
- 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. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:37151. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)
If references are entirely missing, you can add them using this form.