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:||Sep 2012|
|Date of revision:|
|Contact details of provider:|| Postal: Rumelifeneri Yolu, Sarıyer, 34450 İstanbul|
Web page: http://erf.ku.edu.tr
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.:
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Lanne, Markku & Saikkonen, Pentti, 2010.
"Noncausal autoregressions for economic time series,"
32943, University Library of Munich, Germany.
- 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.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:koc:wpaper:1225. 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: (Sumru Oz)
If references are entirely missing, you can add them using this form.