Model Averaging in Predictive Regressions

Abstract

This paper considers forecast combination in a predictive regression. We construct the point forecast by combining predictions from all possible linear regression models given a set of potentially relevant predictors. We propose a frequentist model averaging criterion, an asymptotically unbiased estimator of the mean squared forecast error (MSFE), to select forecast weights. In contrast to the existing literature, we derive the MSFE in a local asymptotic framework without the i.i.d. normal assumption. This result allows us to decompose the MSFE into the bias and variance components and also to account for the correlations between candidate models. Monte Carlo simulations show that our averaging estimator has much lower MSFE than alternative methods such as weighted AIC, weighted BIC, Mallows model averaging, and jackknife model averaging. We apply the proposed method to stock return predictions.JEL Classification: C52, C53

Focused information criterion for locally misspecified vector autoregressive models

“…Such an extension would complement: (1) the predictive static regression setup discussed in Liu and Kuo (2016), and (2) the prediction focused model selection of autoregressive models in Claeskens et al (2007). Forecasts for autoregressive models o en start from the assumption that estimation and prediction are applied to two independent processes with the same stochastic structure.…”

“…DiTraglia (2016) provides results for generalized method of moments estimation. Liu and Kuo (2016) consider predictive regressions.…”

Estimating the variance of a combined forecast: Bootstrap-based approach

“…In this paper we use bootstrap to consistently estimate the variance of a combined forecast and the asymptotic covariance matrix of a weighted average of an estimated parameter vector using alternative models with xed weights. Our theoretical framework follows Hansen (2014) and Liu and Kuo (2016) in generating forecasts by using weighted average of the predictions from a set of candidate models that vary by the choice of auxiliary regressors adopted by forecasters. Thus, there is a panel of forecasting models with dierent sets of predictors.…”

When and when not to use optimal model averaging

“…The construction of Hansen's estimator corresponds to motivation (b) outlined above. It is no surprise that other authors then also developed optimal model averaging estimators -based on the same idea, but in the context of different model classes, different loss/risk functions, different model sets, and so on -see Cheng et al, 2015;Gao et al, 2016;Hansen, 2008;Hansen and Racine, 2012;Liang et al, 2011;Liu and Kuo, 2016;Zhang et al, 2014;Zhang et al, 2015;Zhang et al, 2016b and the references therein. The interesting part is that the authors of these papers, with few exceptions (e.g.…”