Bayesian consensus forecasts of macroeconomic variables

Economists, like other forecasters, share knowledge, data and theories in common. Consequently, their forecast errors are likely to be highly dependent. This paper reports on an empirical study of 16 macroeconomic forecasters. Composite forecasts are computed using a sequential weighting scheme that takes dependence into account; these are compared to a simple average and median forecasts. A within-sample composite is also calculated. Both these methods perform significantly better than the average or median of the forecasts. This improvement in accuracy is apparently because the dependence between the forecasters' errors is so high that the optimal composite forecasts sometimes lie outside the range of the individual forecasts.     

To combine or not to combine? issues of combining forecasts

This paper addresses issues such as: Does it always pay to combine individual forecasts of a variable? Should one combine an unbiased forecast with one that is heavily biased? Should one use optimal weights as suggested by Bates and Granger over twenty years ago? A simple model which accounts for the main features of individual forecasts is put forward. Bayesian analysis of the model using noninformative and informative prior probability densities is provided which extends and generalizes results obtained by Winkler (1981) and compared with non-Bayesian methods of combining forecasts relying explicitly on a statistical model for the individual forecasts. It is shown that in some instances it is sensible to use a simple average of individual forecasts instead of using Bates and Granger type weights. Finally, model uncertainty is considered and the issue of combining different models for individual forecasts is addressed.     

Linear combination of forecasts with an intercept: A bayesian approach

The standard approach to combining n expert forecasts involves taking a weighted average. Granger and Ramanathan proposed introducing an intercept term and unnormalized weights. This paper deduces their proposal from Bayesian principles. We find that their formula is equivalent to taking a weighted average of the n expert forecasts plus the decision-maker's prior forecast.     

Unbiasedness,efficiency and the combination of economic forecasts

This paper considers the problem of determining whether forecasts are unbiased and examines the implications this has for combining different forecasts. The practical issues of how economic forecasts might be combined are discussed. There is an empirical illustration of the procedures in which the properties of UK forecasts from the London Business School, the National Institute, the Henley Centre for Forecasting, Phillips and Drew and the OECD are examined.     

A non-linear combination of experts' forecasts: A Bayesian approach

A general Bayesian approach to combining n expert forecasts is developed. Under some moderate assumptions on the distributions of the expert errors, it leads to a consistent, monotonic, quasi-linear average formula. This generalizes Bordley's results.     

Linear combination of forecasts: A general Bayesian model

We provide a general Bayesian model for combining forecasts from experts (or forecasting models) who might be biased and correlated with each other. The combination procedure involves debiasing and then combining unbiased forecasts. We also provide a sequential method for learning about the forecasters' biases in the process of combining information from them.     

Composite model building for foreign exchange rates

It has been shown in recent economic and statistical studies that composite forecasts may produce more accurate forecasts than individual ones. The purpose of this study is to develop composite forecasting models that may produce forecasts superior to the individual forecast implicit in forward exchange rates. In an efficient market one would expect to find little improvement with the composite models relative to the forward exchange rate.     

The combining of forecasts using recursive techniques with non-stationary weights

This paper evaluates six optimal and four ad hoc recursive combination methods on five actual data sets. The performance of all methods is compared to the mean and recursive least squares. A modification to one method is proposed and evaluated. The recursive methods were found to be very effective from start-up on two of the data sets. Where the optimal methods worked well so did the ad hoc ones, suggesting that often combination methods allowing ‘local bias’ adjustment may be preferable to the mean forecast and comparable to the optimal methods.     

Beyond heuristics and biases: A contingency model of judgemental forecasting

The conflicting viewpoints about the quality of judgemental forecasts are examined and a model is proposed that attempts to resolve the conflict. The model sees forecasts as contingent upon the repertory of forecasting strategies that the forecaster brings to the forecasting task, the strategy that he or she selects as a function of the characteristics of the task, and the rigour with which he or she applies the strategy as a function of the motivating characteristics of the environment in which the task is encountered. The implications of differences in subjects' and experimenters' assumptions about which strategies are appropriate in experimental studies are examined, as are the implications of the differences between the motivating aspects of experimental and applied settings on both performance and on the generatizability of the results of experiments to applied judgemental forecasting.     

Forecasting the Term Structure of Interest Rates Using Integrated Nested Laplace Approximations

This article discusses the use of Bayesian methods for inference and forecasting in dynamic term structure models through integrated nested Laplace approximations (INLA). This method of analytical approximation allows accurate inferences for latent factors, parameters and forecasts in dynamic models with reduced computational cost. In the estimation of dynamic term structure models it also avoids some simplifications in the inference procedures, such as the inefficient two‐step ordinary least squares (OLS) estimation. The results obtained in the estimation of the dynamic Nelson–Siegel model indicate that this method performs more accurate out‐of‐sample forecasts compared to the methods of two‐stage estimation by OLS and also Bayesian estimation methods using Markov chain Monte Carlo (MCMC). These analytical approaches also allow efficient calculation of measures of model selection such as generalized cross‐validation and marginal likelihood, which may be computationally prohibitive in MCMC estimations. Copyright © 2014 John Wiley & Sons, Ltd.     

Forecasting and trading strategies based on a price trend model

In this paper, we consider the price trend model in which it is assumed that the time series of a security's prices contain a stochastic trend component which remains constant on each of a sequence of time intervals, with each interval having random duration. A quasi‐maximum likelihood method is used to estimate the model parameters. Optimal one‐step‐ahead forecasts of returns are derived. The trading rule based on these forecasts is constructed and is found to bear similarity to a popular trading rule based on moving averages. When applying the methods to forecast the returns of the Hang Seng Index Futures in Hong Kong, we find that the performance of the newly developed trading rule is satisfactory. Copyright © 2000 John Wiley & Sons, Ltd.     

Forecasting with many predictors using Bayesian additive regression trees

Forecasting with many predictors provides the opportunity to exploit a much richer base of information. However, macroeconomic time series are typically rather short, raising problems for conventional econometric models. This paper explores the use of Bayesian additive regression trees (Bart) from the machine learning literature to forecast macroeconomic time series in a predictor‐rich environment. The interest lies in forecasting nine key macroeconomic variables of interest for government budget planning, central bank policy making and business decisions. It turns out that Bart is a valuable addition to existing methods for handling high dimensional data sets in a macroeconomic context.     

Forecasting with growth curves: the effect of error structure

"The main theme of this paper is an investigation into the importance of error structure as a determinant of the forecasting accuracy of the logistic model. The relationship between the variance of the disturbance term and forecasting accuracy is examined empirically. A general local logistic model is developed as a vehicle to be used in this investigation. Some brief comments are made on the assumptions about error structure, implicit or explicit, in the literature." The results suggest that "the variance of the disturbance term, when using the logistic to forecast human populations, is proportional to at least the square of population size."     

Forecasting time series with increasing seasonal variation

Four options for modeling and forecasting time series data containing increasing seasonal variation are discussed, including data transformations, double seasonal difference models and two kinds of transfer function-type ARIMA models employing seasonal dummy variables. An explanation is given for the typical ARIMA model identification analysis failing to identify double seasonal difference models for this kind of data. A logical process of selecting one option for a particular case is outlined, focusing on issues of linear versus non-linear increasing seasonal variation, and the level of stochastic versus deterministic behavior in a time series. Example models for the various options are presented for six time series, with point forecast and interval forecast comparisons. Interval forecasts from data-transformation models are found to generally be too wide and sometimes illogical in the dependence of their width on the point forecast level. Suspicion that maximum likelihood estimation of ARIMA models leads to excessive indications of unit roots in seasonal moving-average operators is reported.     

A bayesian forecasting model for sequential bidding

In this paper we consider the problem facing a company in selecting the values of bids to submit on a sequence of contracts put out to tender. A simple-to-implement Bayesian forecasting model is presented, based on a steady Dirichlet process whose states are indexed by the possible bid decisions open to the company. The model gives an explicit algorithm for calculating the state probabilities, needing only data on the lowest bid made by the company's competitors. The flexibility of the basic model makes it a potentially powerful forecasting system for use by companies bidding for contracts.