Comparing ex-ante forecasts from a sem and var model: An application to the italian economy

The predictive performance of a large-scale structural econometric model (SEM) of the Italian economy the Prometeia model is compared in this paper with a vector autoregressive (VAR) model estimated for a selection of six main variables of interest. The paper concentrates on the quarterly ex-ante forecasts of GDP growth rate and the annual forecasts of GDP growth and inflation rate, over the period 1980-85. It concludes that no forecaster is systematically better than the other. In particular, the VAR model outperforms the SEM in short-run forecasts, suggesting that, for the latter, more careful attention should be addressed to questions of dynamic specification. On the other hand, for longer intervals, the SEM forecasts are more accurate than the VAR forecasts, in that they can benefit from the judgemental interventions of the model users and the model can pick up the non-linearities of the economy which cannot be captured by the VAR. Given the different kinds of information that can be extracted from the two approaches, it seems more reasonable to consider them as complementary rather than alternative tools for modelling and forecasting. Therefore, rather than attempting to establish the superiority of one type of model over the other, this kind of comparisons should be seen as a useful diagnostic tool for detecting types of model misspecification.     

Reducing uncertainty in short-term projections: Linkage of monthly and quarterly models

This paper shows how monthly data and forecasts can be used in a systematic way to improve the predictive accuracy of a quarterly macroeconometric model. The problem is formulated as a model pooling procedure (equivalent to non-recursive Kalman filtering) where a baseline quarterly model forecast is modified through ‘add-factors’ or ‘constant adjustments’. The procedure ‘automatically’ constructs these adjustments in a covariance-minimizing fashion to reflect the revised expectation of the quarterly model's forecast errors, conditional on the monthly information set. Results obtained using Federal Reserve Board models indicate the potential for significant reduction in forecast error variance through application of these procedures.     

Time series forecasts and extra-model information

Often a forecaster has supplementary information (e.g. field reports or forecasts from another source) that cannot be included directly in a time series model. Especially interesting are cases where this information is given at time intervals that are different from those of the time series model forecasts. Previous authors have considered a numerical and a model-based statistical method for combining extra-model information of this type with ARIMA model forecasts. This paper extends both methods to vector ARMA model forecasts and dynamic regression (transfer function) model forecasts. It is also shown that a Lagrange multiplier numerical procedure arises as a special case of the model-based procedure. An empirical example is given.     

An evaluation of quarterly national institute forecasts

This paper examines the quarterly forecasts by the U.K. National Institute of Economic and Social Research of the rate of inflation and the change in real gross domestic product and its components for horizons of one to four quarters ahead in the U.K. The forecasts are tested to see if they satisfy three implications of the rational expectations hypothesis: unbiasedness, efficiency and consistency. Explicit consideration is given to the information set available when the forecasts are made. In general, the data are consistent with the rational expectations hypothesis and our results provide encouragement for the view that aggregate expectations will meet the ex post requirements of rationality.     

Experience in combining subjective and quantitative forecasts of open market rates

This paper presents a method of combining subjective information from open-market operators with results from a time-series forecasting model. Empirical results of forecasts for interest rates of bank reserves are presented.     

N-step combinations of forecasts

While there is general agreement that a linear combination of forecasts can outperform the individual forecasts, there is controversy about the appropriateness of the combination method to be used in a given situation. Hence, in any given application it may be more beneficial to combine different sets of combined forecasts rather than picking one of them. This paper introduces the concept of N-step combinations of forecasts which involves combining the combined forecasts obtained from different combination procedures used at the preceding step. Using quarterly GNP data, evidence supporting the increase in the accuracy of the one-period-ahead ex-ante forecasts as the combination step increases is provided. The MSE, MAE, MAPE and their corresponding standard deviations are used to evaluate the accuracy of the forecasts obtained.     

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.     

Testing for unreliable estimators and insignificant forecasts in combined forecasts

The reliability and precision of the weights used in combining individual forecasts, irrespective of the method of combination, is important in evaluating a combined forecast. The objective of this study is not to suggest the ‘best’ method of combining individual forecasts, but rather to propose exploratory procedures, that make use of all available sample information contained in the covariance matrix of individual forecast errors, to (1) detect if the weights used in combining forecasts are ‘reliable’ (and ‘stable’ if it is known that the covariance matrix of forecast errors is stationary over time) and (2) test for ‘insignificant’ individual forecasts used in forming a combined forecast. We present empirical applications using two-year sales and individual forecast data provided by a major consumer durables manufacturer to illustrate the feasibility of our proposed procedures.     

The combination of macroeconomic forecasts

The paper examines combined forecasts based on two components: forecasts produced by Chase Econometrics and those produced using the Box-Jenkins ARIMA technique. Six series of quarterly ex ante and simulated ex ante forecasts are used over 37 time periods and ten horizons. The forecasts are combined using seven different methods. The best combined forecasts, judged by average relative root-mean-square error, are superior to the Chase forecasts for three variables and inferior for two, though averaged over all six variables the Chase forecasts are slightly better. A two-step procedure produces forecasts for the last half of the sample which, on average, are slightly better than the Chase forecasts.     

Professional economic forecasts: Are they worth their costs?

Most economic forecast evaluations dating back 20 years show that professional forecasters add little to the forecasts generated by the simplest of models. Using various types of forecast error criteria, these evaluations usually conclude that the professional forecasts are little better than the no-change or ARIM A type forecast. It is our contention that this conclusion is mistaken because the conventional error criteria may not capture why forecasts are ma& or how they are used. Using forecast directional accuracy, the criterion which has been found to be highly correlated with profits in an interest rate setting, we find that professional GNP forecasts dominate the cheaper alternatives. Moreover, there appears to be no systematic relationship between this preferred criterion and the error measures used in previous studies.     

Optimal conditional ARIMA forecasts

An optimal univariate forecast, based on historical and additional information about the future, is obtained in this paper. Its statistical properties, as well as some inferential procedures derived from it, are indicated. Two main situations are considered explicitly: (1) when the additional information imposes a constraint to be fulfilled exactly by the forecasts and (2) when the information is only a conjecture about the future values of the series or a forecast from an alternative model. Theoretical and empirical illustrations are provided, and a unification of the existing methods is also attempted.     

Subjective versus objective combining of forecasts: An experiment

The paper reports results of an experiment conducted to evaluate subjective versus objective combination of forecasts. The subjects were undergraduate students at Texas A&M. The students forecasted two different types of time series. The results found show that the subjective combination of forecasts improves their accuracy as compared with individual efforts. Four ex-ante weighting methods were also used to combine the forecasts. They all improve the accuracy of the forecasts. The best results, though, were from the subjective combination of forecasts.     

Sources of error in forecasts and expectations: U.K. economic models, 1984–8

This paper presents a comparative analysis of the sources of error in forecasts for the UK economy published over a recent four-year period by four independent groups. This analysis rests on the archiving at the ESRC Macroeconomic Modelling Bureau of the original forecasts together with all their accompanying assumptions and adjustments. A method of decomposing observed forecast errors so as to distinguish the contributions of forecaster and model is set out; the impact of future expectations treated in a ‘model-consistent’ or ‘rational’ manner is specifically considered. The results show that the forecaster's adjustments make a substantial contribution to forecast performance, a good part of which comes from adjustments that bring the model on track at the start of the forecast period. The published ex-ante forecasts are usually superior to pure model-based ex-post forecasts, whose performance indicates some misspecification of the underlying models.     

Combining ordinal forecasts with an application in a financial market

The literature on combining forecasts has almost exclusively focused on combining point forecasts. The issues and methods of combining ordinal forecasts have not yet been fully explored, even though ordinal forecasting has many practical applications in business and social research. In this paper, we consider the case of forecasting the movement of the stock market which has three possible states (bullish, bearish and sluggish). Given the sample of states predicted by different forecasters, several statistical and operation research methods can be applied to determine the optimal weight assigned to each forecaster in combining the ordinal forecasts. The performance of these methods is examined using Hong Kong stock market forecasting data, and their accuracies are found to be better than the consensus method and individual forecasts.     

The uses and abuses of ‘consensus’ forecasts

Clemen's (1989) review of the forecast-combining literature amply illustrates both the interest in and the importance of this subject. This article stresses the tautological properties of various consensus measures that assure their success relative to most individual forecasts. It confirms the finding of earlier studies that for each specific macroeconomic variable roughly one-third of individual forecasters are more accurate than a consensus. However, each individual does relatively poorly for some variable while the consensus, in contrast, necessarily never fails relative to most individuals. These results, like most previous studies, describe consensus measures that are synthetic constructs derived from a pre-existing set of individual forecasts. Strictly speaking, this contemporaneous consensus is not available to individual forecasters when their forecasts are made. A prior consensus measure, which is in their information sets, was relatively much less accurate than the contemporaneous measure. Nevertheless, a small subset of individual forecasters were generally inferior to the known, prior consensus forecast.     

Forecasting contemporaneous aggregates and the combination of forecasts: The case of the U.K. monetary aggregates

A number of papers in recent years have investigated the problems of forecasting contemporaneously aggregated time series and of combining alternative forecasts of a time series. This paper considers the integration of both approaches within the example of assessing the forecasting performance of models for two of the U.K. monetary aggregates, £M3 and MO. It is found that forecasts from a time series model for aggregate £M3 are superior to aggregated forecasts from individual models fitted to either the components or counterparts of £M3 and that an even better forecast is obtained by forming a linear combination of the three alternatives. For MO, however, aggregated forecasts from its components prove superior to either the forecast from the aggregate itself or from a linear combination of the two.     

A comparative evaluation of objective and subjective weather forecasts in the united states

This paper is concerned primarily with the evaluation and comparison of objective and subjective weather forecasts. Operational forecasts of three weather elements are considered: (1) probability forecasts of precipitation occurrence, (2) categorical (i.e. non-probabilistic) forecasts of maximum and minimum temperatures and (3) categorical forecasts of cloud amount. The objective forecasts are prepared by numerical-statistical procedures, whereas the subjective forecasts are based on the judgements of individual forecasters. In formulating the latter, the forecasters consult information from a variety of sources, including the objective forecasts themselves. The precipitation probability forecasts are found to be both reliable and skilful, and evaluation of the temperature/cloud amount forecasts reveals that they are quite accurate/skilful. Comparison of the objective and subjective forecasts of precipitation occurrence indicates that the latter are generally more skilful than the former for shorter lead times (e.g. 12–24 hours), whereas the two types of forecasts are of approximately equal skill for longer lead times (e.g. 36–48 hours). Similar results are obtained for the maximum and minimum temperature forecasts. Objective cloud amount forecasts are more skilful than subjective cloud amount forecasts for all lead times. Examination of trends in performance over the last decade reveals that both types of forecasts for all three elements increased in skill (or accuracy) over the period, with improvements in objective forecasts equalling or exceeding improvements in subjective forecasts. The role and impact of the objective forecasts in the subjective weather forecasting process are discussed in some detail. The need to conduct controlled experiments and other studies of this process, with particular reference to the assimilation of information from different sources, is emphasized. Important characteristics of the forecasting system in meteorology are identified, and they are used to describe similarities and differences between weather forecasting and forecasting in other fields. Acquisition of some of these characteristics may be beneficial to other forecasting systems.     

Estimating the strength of expert judgement: The case of US mortality forecasts

The use of expert judgement is an important part of demographic forecasting. However, because judgement enters into the forecasting process in an informal way, it has been very difficult to assess its role relative to the analysis of past data. The use of targets in demographic forecasts permits us to embed the subjective forecasting process into a simple time-series regression model, in which expert judgement is incorporated via mixed estimation. The strength of expert judgement is denned, and estimated using the official forecasts of cause-specific mortality in the United States. We show that the weight given to judgement varies in an improbable manner by age. Overall, the weight given to judgement appears too high. An alternative approach to combining expert judgement and past data is suggested.     

Combining exchange rate forecasts: What is the optimal consensus measure?

In this paper a high-quality disaggregate database is utilized to examine whether individual forecasters produce efficient exchange rate predictions and also if the properties of the forecasts change when they are combined. The paper links a number of themes in the exchange rate literature and examines various methods of forecast combination. It is demonstrated, inter alia, that some forecasters are better than others, but that most are not as good as a naive no-change prediction. Combining forecasts adds to the accuracy of the predictions, but the gains mainly reflect the removal of systematic and unstable bias.     

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.