Some curious power properties of long-horizon tests

Long‐run predictability tests are even worse than you thought

“…For instance, we omit power results for Valkanov's (2003) test. As documented previously in Hjalmarsson (2011Hjalmarsson ( , 2012), Valkanov's test has very similar power properties to those of Hjalmarsson's (2011) √ q-scaled t-statistic in the exogenous regressor case, and tends to be dominated by Hjalmarsson's Bonferroni test in the endogenous regressor case. We also do not show results for the test in Rossi (2007), which uses a long-run coefficient inferred from the short-run estimate (q = 1); the method is based on a near unit-root assumption and shows some improvement in power compared to Valkanov's (2003) test.…”

“…However, while this might seem a reasonable intuitive justification for long‐horizon regressions, econometric specifications where this intuition actually bears fruit have proven fairly elusive. Attempts to design econometric models under the alternative of return predictability, which lead to power gains for long‐horizon tests over short‐horizon tests, have met with at most limited success (Hjalmarsson, 2012; Maynard & Ren, 2014; 2019). Related studies on the relationship between long‐ and short‐run results (e.g., Boudoukh et al, 2008; Hjalmarsson, 2008; McLoughlin,, 2019) also highlight that there seems to be little to be learned from the long run, given the short run.…”