[We propose a new hypothesis-testing method for multipredictor regressions in small samples, where the dependent variable is regressed on lagged variables that are autoregressive. The new test is based on the augmented regression method (Amihud and Hurvich, 2004), which produces reduced-bias coefficients and is easy to implement. The method's usefulness is demonstrated by simulations and by testing a model where stock returns are predicted by two variables, income-to-consumption and dividend yield.]

Standard predictive regressions produce biased coefficient estimates in small samples when the regressors are Gaussian first-order autoregressive with errors that are correlated with the error series of the dependent variable. See Stambaugh (1999) for the single regressor model. This paper proposes a direct and convenient method to obtain reduced-bias estimators for single and multiple regressor models by employing an augmented regression, adding a proxy for the errors in the autoregressive model. We derive bias expressions for both the ordinary least-squares and our reduced-bias estimated coefficients. For the standard errors of the estimated predictive coefficients, we develop a heuristic estimator that performs well in simulations, for both the single predictor model and an important specification of the multiple predictor model. The effectiveness of our method is demonstrated by simulations and empirical estimates of common predictive models in finance. Our empirical results show that some of the predictive variables that were significant under ordinary least squares become insignificant under our estimation procedure.

We consider semiparametric estimation of the memory parameter in a model that includes as special cases both long-memory stochastic volatility and fractionally integrated exponential GARCH (FIEGARCH) models. Under our general model the logarithms of the squared returns can be decomposed into the sum of a long-memory signal and a white noise. We consider periodogram-based estimators using a local Whittle criterion function. We allow the optional inclusion of an additional term to account for possible correlation between the signal and noise processes, as would occur in the FIEGARCH model. We also allow for potential nonstationarity in volatility by allowing the signal process to have a memory parameter d*1/2. We show that the local Whittle estimator is consistent for d*∈(0,1). We also show that the local Whittle estimator is asymptotically normal for d*∈(0,3/4) and essentially recovers the optimal semiparametric rate of convergence for this problem. In particular, if the spectral density of the short-memory component of the signal is sufficiently smooth, a convergence rate of n2/5−δ for d*∈(0,3/4) can be attained, where n is the sample size and δ>0 is arbitrarily small. This represents a strong improvement over the performance of existing semiparametric estimators of persistence in volatility. We also prove that the standard Gaussian semiparametric estimator is asymptotically normal if d*=0. This yields a test for long memory in volatility.

We propose a new hypothesis-testing method for multipredictor regressions in small samples, where the dependent variable is regressed on lagged variables that are autoregressive. The new test is based on the augmented regression method (Amihud and Hurvich, 2004), which produces reduced-bias coefficients and is easy to implement. The method's usefulness is demonstrated by simulations and by testing a model where stock returns are predicted by two variables, income-to-consumption and dividend yield.