Statistical Tests for Weak-Form Market Efficiency

Over the years, I received numerous email enquiries on topics related to market efficiency. My survey article in Journal of Economic Surveys provides a useful guide, as the paper reviews all the statistical tests for weak-form market efficiency.

If readers ask me which tools I would recommend, the variance ratio tests come first. This is because the existence of return autocorrelations has strong theoretical justifications, especially in the context of market reactions (or mis-reactions) to information. Moreover, the market efficiency literature has shifted from testing absolute efficiency to measuring relative efficiency. The latter objective can be  achieved by using absolute variance ratio minus one.

The survey article by Charles and Darne (2009) provides an extensive review of the existing variance ratio tests. Jae Kim (my PhD supervisor) generously shares the R-codes for a battery of efficiency tests (click here). Among all the available statistical tests, my recommendation would be the wild bootstrap automatic variance ratio (WBAVR) test proposed by Kim (2009). The greatest appeal of this test is that the optimal value of lag order or holding period is selected automatically using a data-driven selection rule. Moreover, Monte Carlo simulations (see also Charles et al., 2011) show that the test possesses good small sample properties, and is robust to conditional heteroskedasticity that typically characterizes most financial time series. Applications of the WBAVR test include Kim et al. (2011), Lim and Kim (2011), Charles et al. (2012) and Lim et al. (2013).

If readers are bothered by the possible existence of nonlinear serial dependence in the returns series, I would then recommend the generalized spectral martingale test proposed by Escanciano and Velasco (2006). The selling point of this test can be found in my recent article in Applied Economics Letters.