This paper considers a class of statistics that can be written as the ratio of the sample variance of a filtered time series to the sample variance of the original series. Any such statistic is shown to be optimal under normality for testing a null of white noise against some class of serially dependent alternatives. A simple characterization of the alternative class is provided. The results are used to show that a variance ratio test for mean reversion is an optimal test and to illustrate the forms of mean reversion it is best at detecting. Copyright 1992 by The Econometric Society.

Monetary theory

It is well known that augmenting a standard linear regression model with variables that are correlated with the error term but uncorrelated with the original regressors will increase the asymptotic efficiency of the original coefficients. We argue that in the context of predicting excess returns, valid augmenting variables exist and are likely to yield substantial gains in estimation efficiency and, hence, predictive accuracy. The proposed augmenting variables are ex post measures of an unforecastable component of excess returns: ex post errors from macroeconomic survey forecasts, the surprise components of asset price movements around macroeconomic news announcements, or even the weather. These “surprises” cannot be used directly in forecasting—they are not observed at the time that the forecast is made—but can nonetheless improve forecasting accuracy by reducing parameter estimation uncertainty. We derive formal results about the benefits and limits of this approach and apply it to standard examples of forecasting excess bond and equity returns. We find substantial improvements in out-of-sample forecast accuracy for standard excess bond return regressions; gains for forecasting excess stock returns are much smaller.

Abstract Employing a large number of financial indicators, we use Bayesian model averaging (BMA) to forecast real-time measures of economic activity. The indicators include credit spreads based on portfolios, constructed directly from the secondary market prices of outstanding bonds, sorted by maturity and credit risk. Relative to an autoregressive benchmark, BMA yields consistent improvements in the prediction of the cyclically sensitive measures of economic activity at horizons from the current quarter out to four quarters hence. The gains in forecast accuracy are statistically significant and economically important and owe almost exclusively to the inclusion of credit spreads in the set of predictors.