Testing for predictability in a noninvertible ARMA model

Lanne, Markku and Meitz, Mika and Saikkonen, Pentti (2012): Testing for predictability in a noninvertible ARMA model.

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.

• Item Type: MPRA Paper
• Language: English
• 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 ; Diffusion Processes

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