Lanne, Markku and Meitz, Mika and Saikkonen, Pentti (2012): Testing for predictability in a noninvertible ARMA model.
Download (208kB) | Preview
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.
|Item Type:||MPRA Paper|
|Original Title:||Testing for predictability in a noninvertible ARMA model|
|Keywords:||Non-Gaussian time series; noninvertible ARMA model; all-pass process; predictability of asset returns|
|Subjects:||C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods; Simulation Methods
G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing; Trading volume; Bond Interest Rates
C - Mathematical and Quantitative Methods > C2 - Single Equation Models; Single Variables > C22 - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
|Depositing User:||Markku Lanne|
|Date Deposited:||07. Mar 2012 12:55|
|Last Modified:||13. Feb 2013 08:43|
Andrews, B., Davis, R. A., and Breidt, F. J. (2006). Maximum likelihood estimation for all-pass time series models. Journal of Multivariate Analysis 97, 1638-1659.
Andrews, B., Davis, R. A., and Breidt, F. J. (2007). Rank-based estimation for all-pass time series models. Annals of Statistics 35, 844-869.
Andrews, D. W. K., and Ploberger, W. (1996). Testing for serial correlation against an ARMA(1,1) process. Journal of the American Statistical Association 91, 1331-1342.
Breidt, J., R.A. Davis, K.S. Lii, and M. Rosenblatt (1991). Maximum likelihood estimation for noncausal autoregressive processes. Journal of Multivariate Analysis 36, 175-198.
Breidt, F. J., Davis, R. A., and Trindade, A. A. (2001). Least absolute deviation estimation for all-pass time series models. Annals of Statistics 29, 919-946.
Brockwell, P. J., and Davis, R. A. (1991). Time Series: Theory and Methods, 2nd edn. Springer- Verlag. New York.
Davies, R. B. (1977). Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 64, 247-254.
Lanne, M., and Saikkonen, P. (2011). Noncausal autoregressions for economic time series. Jour- nal of Time Series Econometrics, Vol. 3, Iss. 3, Article 2.
Lii, K.-S., and Rosenblatt, M. (1996). Maximum likelihood estimation for nonGaussian non- minimum phase ARMA sequences. Statistica Sinica 6, 1ñ22.
Meitz, M., and Saikkonen, P. (2011). Maximum likelihood estimation of a noninvertible ARMA model with autoregressive conditional heteroskedasticity. Unpublished manuscript.
Nankervis, J. C., and Savin, N. E. (2010). Testing for serial correlation: Generalized Andrews- Ploberger tests. Jounal of Business and Economic Statistics 28, 246-255.
Poterba, J. M., and Summers, L. H. (1988). Mean reversion in stock prices: evidence and implications. Journal of Financial Economics 22, 27-59.
Rosenblatt, M. (2000). Gaussian and Non-Gaussian Linear Time Series and Random Fields. Springer-Verlag, New York.
Singleton, K. J. (2006). Empirical Dynamic Asset Pricing. Princeton University Press, Princeton, NJ.
Taylor, S. J. (1982). Tests of the random walk hypothesis against a price-trend hypothesis. Journal of Financial and Quantitative Analysis 17, 37-61.
Wu, R., and Davis, R. A. (2010). Least absolute deviation estimation for general autoregressive moving average time-series models. Journal of Time Series Analysis 31, 98-112.