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A New Test for Superior Predictive Ability

This paper provides a new methodology to test the superior predictive ability (SPA) of technical trading rules relative to the benchmark without potential data snooping bias. Unlike other previous methods, we explicitly approximate the covariance matrix through certain decomposition, which decreases the number of elements needed to be estimated. With the help of covariance matrix, we are able to exploit more information contained in the diagonal and off-diagonal terms and as a result, so that we improve the effectiveness of testing result. Due to the nuisance parameter in composite hypothesis, we choose the generalized likelihood ratio (GLR) test which is of uniform most power, to alleviate such problem and at the same time, to provide a pivotal distribution. Bootstrap procedure is employed in our simulation to obtain the power of the test. The result shows that the GLR test dominates the SPA test proposed by Hansen (2005) in terms of power and our GLR test is sensitive to the inclusion of superior models. Therefore, it increases the power faster than that of SPA test. The result also suggests that the GLR test is less conservative than SPA test.

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Keywords: Covariance matrix estimation; Data snooping; Generalized likelihood Ratio test; Reality check; SPA test; Technical trading rules.

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