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.     

Method and situational factors in sales forecast accuracy

In this study the interaction of forecasting method (econometric versus exponential smoothing) and two situational factors are evaluated for their effects upon accuracy. Data from two independent sets of ex ante quarterly forecasts for 19 classes of mail were used to test hypotheses. Counter to expectations, the findings revealed that forecasting method did not interact with the forecast time horizon (short versus long term). However, as hypothesized, forecasting method interacted significantly with product/market definition (First Class versus other mail), an indicator of buyer sensitivity to marketing/environmental changes. Results are discussed in the context of future research on forecast accuracy.     

System-based weights versus series-specific weights in the combination of forecasts

System-based combination weights for series r/step-length h incorporate relative accuracy information from other forecast step-lengths for r and from other series for step-length h. Such weights are examined utilizing the West and Fullerton (1996) data set-4275 ex ante employment forecasts from structural simultaneous equation econometric models for 19 metropolitan areas at 10 quarterly step-lengths and a parallel set of 4275 ARIMA forecasts. The system-based weights yielded combined forecasts of higher average accuracy and lower risk of large inaccuracy than seven alternative strategies: (1) averaging; (2) relative MSE weights; (3) outperformance (per cent best) weights; (4) Bates and Granger (1969) optimal weights with a convexity constraint imposed; (5) unconstrained optimal weights; (6) select a ‘best’ method (ex ante) by series and; (7) experiment in the Bischoff (1989) sense and select either method (2) or (6) based on the outcome of e experiment. Accuracy gains of the system-based combination were concentrated at step-lengths two to five. Although alternative (5) was generally outperformed, none of the six other alternatives was systematically most accurate when evaluated relative to each other. This contrasts with Bischoff's (1989) results that held promise for an empirically applicable guideline to determine whether or not to combine.     

Regional econometric income forecast accuracy

Econometric prediction accuracy for personal income forecasts is examined for a region of the United States. Previously published regional structural equation model (RSEM) forecasts exist ex ante for the state of New Mexico and its three largest metropolitan statistical areas: Albuquerque, Las Cruces and Santa Fe. Quarterly data between 1983 and 2000 are utilized at the state level. For Albuquerque, annual data from 1983 through 1999 are used. For Las Cruces and Santa Fe, annual data from 1990 through 1999 are employed. Univariate time series, vector autoregressions and random walks are used as the comparison criteria against structural equation simulations. Results indicate that ex ante RSEM forecasts achieved higher accuracy than those simulations associated with univariate ARIMA and random walk benchmarks for the state of New Mexico. The track records of the structural econometric models for Albuquerque, Las Cruces and Santa Fe are less impressive. In some cases, VAR benchmarks prove more reliable than RSEM income forecasts. In other cases, the RSEM forecasts are less accurate than random walk alternatives. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

Ex post and ex ante analysis of provisional data

In this paper we suggest a framework to assess the degree of reliability of provisional estimates as forecasts of final data, and we re‐examine the question of the most appropriate way in which available data should be used for ex ante forecasting in the presence of a data‐revision process. Various desirable properties for provisional data are suggested, as well as procedures for testing them, taking into account the possible non‐stationarity of economic variables. For illustration, the methodology is applied to assess the quality of the US M1 data production process and to derive a conditional model whose performance in forecasting is then tested against other alternatives based on simple transformations of provisional data or of past final data. Copyright © 1999 John Wiley & Sons, Ltd.     

Assessing the historical accuracy of regional economic forecasts

This study addresses for the first time systematic evaluation of a widely used class of forecasts, regional economic forecasts. Ex ante regional structural equation model forecasts are analysed for 19 metropolitan areas. One- to ten-quarter-ahead forecasts are considered and the seven-year sample spans a complete business cycle. Counter to previous speculation in the literature, (1) dependency on macroeconomic forecasting model inputs does not substantially erode accuracy relative to univariate extrapolative methodologies and (2) stochastic time series models do not on average, yield more accurate regional economic predictions than structural models. Similar to findings in other studies, clear preferences among extrapolative methodologies do not emerge. Most general conclusions, however, are subject to caveats based on step-length effects and region-specific effects.     

Judgemental revision of sales forecasts: The relative performance of judgementally revised versus non-revised forecasts

The judgemental revision of sales forecasts is an issue which is receiving increasing attention in the forecasting literature. This paper compares the performance of forecasts after revision by managers with that of the forecasts which were accepted by them without revision. The data set consists of sales forecasting data from an industrial company, spanning six quarterly periods and relating to some 900 individual products. The findings show that, in general, the improvements made by managers bring the forecast errors of revised forecasts more into line with non-revised forecasts, but the change is often marginal, and the best result is equivalence between revised and non-revised forecasts.     

An empirical investigation of combinations of economic forecasts

This paper examines the effects of combining three econometric and three times-series forecasts of growth and inflation in the U.K. If forecasts are unbiased then a combination exploiting this fact will be more efficient than an unrestricted combination. Ex post econometric forecasts may be biased but ex ante they are unbiased. The results of the study are that a restricted linear combination of the econometric forecasts is superior to an unrestricted combination and also to the unweighted mean of the forecasts. However, it is not preferred to the best of the individual forecasts.     

On the Predictive Content of Autoregression Residuals: A Semiparametric,Copula‐Based Approach to Time Series Prediction

This paper proposes an adjustment of linear autoregressive conditional mean forecasts that exploits the predictive content of uncorrelated model residuals. The adjustment is motivated by non‐Gaussian characteristics of model residuals, and implemented in a semiparametric fashion by means of conditional moments of simulated bivariate distributions. A pseudo ex ante forecasting comparison is conducted for a set of 494 macroeconomic time series recently collected by Dees et al. (Journal of Applied Econometrics 2007; 22: 1–38). In total, 10,374 time series realizations are contrasted against competing short‐, medium‐ and longer‐term purely autoregressive and adjusted predictors. With regard to all forecast horizons, the adjusted predictions consistently outperform conditionally Gaussian forecasts according to cross‐sectional mean group evaluation of absolute forecast errors and directional accuracy. Copyright © 2012 John Wiley & Sons, Ltd.     

Forecasting the economic recession in the U.K. 1979-1982: A comparison of model-based ex ante Forecasts

This paper compares the forecasts of recession and recovery made by five non-government U.K. teams modelling the economy (Cambridge Econometrics, the London Business School, the National Institute of Economic and Social Research, the Cambridge Economic Policy Group and the Liverpool Research Group). The paper concentrates on annual ex ante projections as published over the period 1978-1982, i.e. forecasts made, before the event, of the onset, length, depth and character of the economic recession in the U.K. which began in 1979. The comparison is in terms of year by year changes in production, unemployment, prices and other variables. It concludes that no group was systematically better or worse than other groups (confirming U.S. experience) and that the groups tended to perform better in their chosen areas of specialization, e.g. medium-term groups did better at forecasting the medium-term outcome.     

Assessing time series models for forecasting international migration: Lessons from the United Kingdom

Migration is one of the most unpredictable demographic processes. The aim of this article is to provide a blueprint for assessing various possible forecasting approaches in order to help safeguard producers and users of official migration statistics against misguided forecasts. To achieve that, we first evaluate the various existing approaches to modelling and forecasting of international migration flows. Subsequently, we present an empirical comparison of ex post performance of various forecasting methods, applied to international migration to and from the United Kingdom. The overarching goal is to assess the uncertainty of forecasts produced by using different forecasting methods, both in terms of their errors (biases) and calibration of uncertainty. The empirical assessment, comparing the results of various forecasting models against past migration estimates, confirms the intuition about weak predictability of migration, but also highlights varying levels of forecast errors for different migration streams. There is no single forecasting approach that would be well suited for different flows. We therefore recommend adopting a tailored approach to forecasts, and applying a risk management framework to their results, taking into account the levels of uncertainty of the individual flows, as well as the differences in their potential societal impact.     

Co-integration,error correction and improved medium-term regional VAR forecasting

This study investigates possible improvements in medium-term VAR forecasting of state retail sales and personal income when the two series are co-integrated and represent an error-correction system. For each of North Carolina and New York, three regional vector autoregression (VAR) models are specified; an unrestricted two-equation model consisting of the two state variables, a five-equation unrestricted model with three national variables added and a Bayesian (BVAR) version of the second model. For each state, the co-integration and error-correction relationship of the two state variables is verified and an error-correction version of each model specified. Twelve successive ex ante five-year forecasts are then generated for each of the state models. The results show that including an error-correction mechanism when statistically significant improves medium-term forecasting accuracy in every case.     

Short‐term forecasts of economic activity: Are fortnightly factors useful?

A short‐term mixed‐frequency model is proposed to estimate and forecast Italian economic activity fortnightly. We introduce a dynamic one‐factor model with three frequencies (quarterly, monthly, and fortnightly) by selecting indicators that show significant coincident and leading properties and are representative of both demand and supply. We conduct an out‐of‐sample forecasting exercise and compare the prediction errors of our model with those of alternative models that do not include fortnightly indicators. We find that high‐frequency indicators significantly improve the real‐time forecasts of Italian gross domestic product (GDP); this result suggests that models exploiting the information available at different lags and frequencies provide forecasting gains beyond those based on monthly variables alone. Moreover, the model provides a new fortnightly indicator of GDP, consistent with the official quarterly series.     

Choosing among competing econometric forecasts: Regression‐based forecast combination using model selection

Forecast combination based on a model selection approach is discussed and evaluated. In addition, a combination approach based on ex ante predictive ability is outlined. The model selection approach which we examine is based on the use of Schwarz (SIC) or the Akaike (AIC) Information Criteria. Monte Carlo experiments based on combination forecasts constructed using possibly (misspecified) models suggest that the SIC offers a potentially useful combination approach, and that further investigation is warranted. For example, combination forecasts from a simple averaging approach MSE‐dominate SIC combination forecasts less than 25% of the time in most cases, while other ‘standard’ combination approaches fare even worse. Alternative combination approaches are also compared by conducting forecasting experiments using nine US macroeconomic variables. In particular, artificial neural networks (ANN), linear models, and professional forecasts are used to form real‐time forecasts of the variables, and it is shown via a series of experiments that SIC, t‐statistic, and averaging combination approaches dominate various other combination approaches. An additional finding is that while ANN models may not MSE‐dominate simpler linear models, combinations of forecasts from these two models outperform either individual forecast, for a subset of the economic variables examined. Copyright © 2001 John Wiley & Sons, Ltd.     

Ex post and ex ante prediction of unobserved multivariate time series: a structural‐model based approach

A methodology for estimating high‐frequency values of an unobserved multivariate time series from low‐frequency values of and related information to it is presented in this paper. This is an optimal solution, in the multivariate setting, to the problem of ex post prediction, disaggregation, benchmarking or signal extraction of an unobservable stochastic process. Also, the problem of extrapolation or ex ante prediction is optimally solved and, in this context, statistical tests are developed for checking online the ocurrence of extreme values of the unobserved time series and consistency of future benchmarks with the present and past observed information. The procedure is based on structural or unobserved component models, whose assumptions and specification are validated with the data alone. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

Model specification and forecasting foreign exchange rates with vector autoregressions

This study examines the forecasting accuracy of alternative vector autoregressive models each in a seven‐variable system that comprises in turn of daily, weekly and monthly foreign exchange (FX) spot rates. The vector autoregressions (VARs) are in non‐stationary, stationary and error‐correction forms and are estimated using OLS. The imposition of Bayesian priors in the OLS estimations also allowed us to obtain another set of results. We find that there is some tendency for the Bayesian estimation method to generate superior forecast measures relatively to the OLS method. This result holds whether or not the data sets contain outliers. Also, the best forecasts under the non‐stationary specification outperformed those of the stationary and error‐correction specifications, particularly at long forecast horizons, while the best forecasts under the stationary and error‐correction specifications are generally similar. The findings for the OLS forecasts are consistent with recent simulation results. The predictive ability of the VARs is very weak. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

Forecasting with balanced state space representations of multivariate distributed lag models

A procedure for estimating state space models for multivariate distributed lag processes is described. It involves singular value decomposition techniques and yields an internally balanced state space representation which has attractive properties. Following the specifications of a forecasting competition, the approach is applied to generate ex-post forecasts for US real GNP growth rates. The forecasts of the estimated state space model are compared to those of twelve econometric models and an ARIMA model.