Combining simple multivariate HAR-like models for portfolio construction

Forecasts of the covariance matrix of returns is a crucial input into portfolio construction. In recent years multivariate version of the Heterogenous AutoRegressive (HAR) models have been designed to utilise realised measures of the covariance matrix to generate forecasts. This paper shows that combining forecasts from simple HAR-like models provide more coefficients estimates, stable forecasts and lower portfolio turnover. The economic benefits of the combination approach become crucial when transactions costs are taken into account. This combination approach also provides benefits in the context of direct forecasts of the portfolio weights. Economic benefits are observed at both 1-day and 1-week ahead forecast horizons

Global combinations of expert forecasts

Expert forecast combination -- the aggregation of individual forecasts from multiple subject-matter experts -- is a proven approach to economic forecasting. To date, research in this area has exclusively concentrated on local combination methods, which handle separate but related forecasting tasks in isolation. Yet, it has been known for over two decades in the machine learning community that global methods, which exploit task-relatedness, can improve on local methods that ignore it. Motivated by the possibility for improvement, this paper introduces a framework for globally combining expert forecasts. Through our framework, we develop global versions of several existing forecast combinations. To evaluate the efficacy of these new global forecast combinations, we conduct extensive comparisons using synthetic and real data. Our real data comparisons, which involve expert forecasts of core economic indicators in the Eurozone, are the first empirical evidence that the accuracy of global combinations of expert forecasts can surpass local combinations

The role of data and priors in estimating climate sensitivity

In Bayesian theory, the data together with the prior produce a posterior. We show that it is also possible to follow the opposite route, that is, to use data and posterior information (both of which are observable) to reveal the prior (which is not observable). We then apply the theory to equilibrium climate sensitivity as reported by the Intergovernmental Panel on Climate Change in an attempt to get some insight into the prior beliefs of the IPCC scientists. It appears that the data contain much less information than one might think, due to the presence of correlation. We conclude that the prior in the fifth IPCC report was too low, and in the sixth report too high

Sensitivity of GLS Estimators in Random Effects Models

Summary This paper studies the sensitivity of random effects estimators in the one-way error component regression model. Maddala and Mount (1973) give simulation evidence that in random effects models the properties of the feasible GLS estimator β are not affected by the choice of the first-step estimator ¯ θ used for the covariance matrix. Taylor (1980) gives a theoretical example of this effect. This paper provides a reason for this in terms of sensitivity. The properties of ¯ θ are transferred via an uncorrelated (and independent under normality) link, called sensitivity. The sensitivity statistic counteracts the improvement in ¯ θ. A Monte Carlo experiment illustrates the theoretical findings. Keywords

A Combination Method for Averaging OLS and GLS Estimators

To avoid the risk of misspecification between homoscedastic and heteroscedastic models, we propose a combination method based on ordinary least-squares (OLS) and generalized least-squares (GLS) model-averaging estimators. To select optimal weights for the combination, we suggest two information criteria and propose feasible versions that work even when the variance-covariance matrix is unknown. The optimality of the method is proven under some regularity conditions. The results of a Monte Carlo simulation demonstrate that the method is adaptive in the sense that it achieves almost the same estimation accuracy as if the homoscedasticity or heteroscedasticity of the error term were known

On the uncertainty of a combined forecast:The critical role of correlation

The purpose of this paper is to show that the effect of the zero-correlation assumption in combining forecasts can be huge, and that ignoring (positive) correlation can lead to confidence bands around the forecast combination that are much too narrow. In the typical case where three or more forecasts are combined, the estimated variance increases without bound when correlation increases. Intuitively, this is because similar forecasts provide little information if we know that they are highly correlated. Although we concentrate on forecast combinations and confidence bands, our theory applies to any statistic where the observations are linearly combined. We apply our theoretical results to explain why forecasts by central banks (in our case, the Bank of Japan and the European Central Bank) are so frequently misleadingly precise. In most cases ignoring correlation is harmful, and an estimated historical correlation or an imposed fixed correlation larger than 0.7 is required to produce credible confidence bands.</p

Global combinations of expert forecasts

Expert forecast combination—the aggregation of individual forecasts from multiple subjectmatter experts— is a proven approach to economic forecasting. To date, research in this area has exclusively concentrated on local combination methods, which handle separate but related forecasting tasks in isolation. Yet, it has been known for over two decades in the machine learning community that global methods, which exploit taskrelatedness, can improve on local methods that ignore it. Motivated by the possibility for improvement, this paper introduces a framework for globally combining expert forecasts. Through our framework, we develop global versions of several existing forecast combinations. To evaluate the efficacy of these new global forecast combinations, we conduct extensive comparisons using synthetic and real data. Our real data comparisons, which involve expert forecasts of core economic indicators in the Eurozone, are the first empirical evidence that the accuracy of global combinations of expert forecasts can surpass local combinations