Macroeconomists are increasingly working with large Vector Autoregressions (VARs) where the number of parameters vastly exceeds the number of observations. Existing approaches either involve prior shrinkage or the use of factor methods. In this paper, we develop an alternative based on ideas from the compressed regression literature. It involves randomly compressing the explanatory variables prior to analysis. A huge dimensional problem is thus turned into a much smaller, more computationally tractable one. Bayesian model averaging can be done over various compressions, attaching greater weight to compressions which forecast well. In a macroeconomic application involving up to 129 variables, we find compressed VAR methods to forecast better than either factor methods or large VAR methods involving prior shrinkage.

We propose a new approach to imposing economic constraints on time-series forecasts of the equity premium. Economic constraints are used to modify the posterior distribution of the parameters of the predictive return regression in a way that better allows the model to learn from the data. We consider two types of constraints: Non-negative equity premia and bounds on the conditional Sharpe ratio, the latter of which incorporates timevarying volatility in the predictive regression framework. Empirically, we …nd that economic constraints systematically reduce uncertainty about model parameters, reduce the risk of selecting a poor forecasting model, and improve both statistical and economic measures of out-of-sample forecast performance. The Sharpe ratio constraint, in particular, results in considerable economic gains. for helpful comments and suggestions. Xia Meng provided excellent research assistance. We are grateful to John Campbell and David Rapach for making their codes available.

We propose a new approach to imposing economic constraints on time-series forecasts of the equity premium. Economic constraints are used to modify the posterior distribution of the parameters of the predictive return regression in a way that better allows the model to learn from the data. We consider two types of constraints: Non-negative equity premia and bounds on the conditional Sharpe ratio, the latter of which incorporates timevarying volatility in the predictive regression framework. Empirically, we …nd that economic constraints systematically reduce uncertainty about model parameters, reduce the risk of selecting a poor forecasting model, and improve both statistical and economic measures of out-of-sample forecast performance. The Sharpe ratio constraint, in particular, results in considerable economic gains.

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Studies of bond return predictability find a puzzling disparity between strong statistical evidence of return predictability and the failure to convert return forecasts into economic gains. We show that resolving this puzzle requires accounting for important features of bond return models such as volatility dynamics and unspanned macro factors. A three-factor model comprising the Fama and Bliss (1987) forward spread, the Cochrane and Piazzesi ( 2005) combination of forward rates and the Ludvigson and Ng ( 2009) macro factor generates notable gains in out-of-sample forecast accuracy compared with a model based on the expectations hypothesis. Such gains in predictive accuracy translate into higher risk-adjusted portfolio returns after accounting for estimation error and model uncertainty. Consistent with models featuring unspanned macro factors, our forecasts of future bond excess returns are strongly negatively correlated with survey forecasts of short rates.