Panel Stochastic Dominance Test and Panel Informational Efficiency LR Test

Abstract

This paper propose a new panel stochastic dominance (SD) test-PDD test, the asymptotic properties are derived, which extends Davidson and Duclos (DD) SD test to a panel context. The PDD test also contributes to settle one of the demerits while working with financial derivatives time series: that the standard individual tests for Stochastic Dominance in time series are unsatisfactory in terms of power when the sample size is too small, and typically the financial derivatives have a limited life, in particular, stock options and covered warrants. This is because the pairwise SD tests are nonparametric, and nonparametric tests require large sample size, in this case, the individual tests for financial derivative time series may not distinguish between the null and the alternative hypotheses for each series, and lead to retain the null hypothesis, even if the alternative is true. Hence the PDD test would improve the power of individual SD tests: a panel test gathers all the information of all the series, and then increases the power compared to its corresponding individual test. This paper also extends the classical likelihood ratio (LR) information efficiency test to a panel framework to get more powerful new tests. A bootstrap methodology is developed to correct the size distortion of the LR test.