The Review of Financial Studies /v 12n 2 1999 As mentioned before,the purpose of statistical model selection criteria is to avoid overfitting.The model specification that fits the data best(minimum in-sample forecast error)is not necessarily chosen.In contrast,the retained model will have maximum external validity.In our context of return pre- diction,this means that the preferred model will have best out-of-sample forecasting performance. We decided to verify the external validity of formal model selection whenever k*>1.All models with index(k)larger than one contain at least one nontrivial forecasting variable.When one of them is chosen,the model selection criterion clearly supports predictability.To assess the external validity of such a conclusion,we ran a test on a sample that postdated the sample on which we based the model choice.To avoid confusion we will refer to the original sample on which model choice was based as the training sample.The sample that was used to check for external validity will be called the testing sample.The latter has size n,and its elements are indexed tT+1,...,T+n. External validation is investigated by projecting the market's excess re- turn,r,onto our forecast,-1.-1 is obtained from model k*,as follows: -1=1x二 (2) where is the OLSestimate of,based on the pairs ()observed over r =1....t-1.We estimate the slope coefficient in =Q+Bz1-I+, (3) from the observations indexed tT+1,...,T+n.We use the OLS estimate of B to compute a standard t-ratio,and refer to the standard normal distribution to determine p-levels.External validity is confirmed if p-levels are low,say,below 0.05. Notice that we did not adjust the t-ratio for error in the estimation of the parameters of the prediction model.Asymptotically,such an adjustment is not necessary,because we force the precision of the parameter estimates to increase as we advance through the testing sample.See also West(1996). Unfortunately,small-sample corrections are not available and would be complicated by the unit-root nature of some of the predictors. 3.The Data We investigated the predictability of the 1-month local-currency excess stock return for 14 countries.3 Our forecasts of the market's excess return is based on (a subset of)the following predictors:a January dummy;the Results can be expected to be different if excess stock returns are converted to a common currency.in which case retums from speculation in the foreign exchange market determine the outcome as well.See, for example,Ferson and Harvey (1993). 410