Forecasts and expectations: Some evidence for the U.K.

Forecasts from econometric models have been given a lot of publicity in the U.K. This paper examines the performance of five major models in forecasting inflation and the rate of growth. Two types of forecast are considered: the annual pre-budget ones and a quarterly series. It is suggested that public forecasts provide a cheap method of implementing economically rational expectations.     

Merging monthly and quarterly forecasts: Experience with mqem

Forecasts from quarterly econometric models are typically revised on a monthly basis to reflect the information in current economic data. The revision process usually involves setting targets for the quarterly values of endogenous variables for which monthly observations are available and then altering the intercept terms in the quarterly forecasting model to achieve the target values. A formal statistical approach to the use of monthly data to update quarterly forecasts is described and the procedure is applied to the Michigan Quarterly Econometric Model of the US Economy. The procedure is evaluated in terms of both ex post and ex ante forecasting performance. The ex ante results for 1986 and 1987 indicate that the method is quite promising. With a few notable exceptions, the formal procedure produces forecasts of GNP growth that are very close to the published ex ante forecasts.     

Judgemental revision of sales forecasts: Effectiveness of forecast selection

When managers make revisions to sales forecasts initially generated by a rational quantitative model it is important that the particular forecasts selected for adjustment are those which would benefit most from the adjustment process (i.e. realize high errors). This study reports an empirical investigation on this issue, spanning six quarterly forecasting periods and incorporating forecasting data on over 850 products. The results show that the errors of the forecasts chosen for revision are, in general, higher than those which were not chosen. In addition, it is shown that managesrs tend to revise forecasts which are initially low, hence possibily introducing some degree of bias into the overall forecasts.     

Diagnostic tracking and model specification in combined forecasts of U.K. inflation

Combinations of several forecasts are now quite commonly used as inputs into business planning models. For example, capital budgeting generally involves a synthesis of several sources of economic forecasts. In such cases, where uncertainty and risk are also being explicitly considered, the statistical specification of the combined forecasts becomes particularly important. An investigation of the monthly forecasts of annual inflation from nine leading U.K. economic models was undertaken to examine the circumstances under which well-specified and efficient combined forecasts could be produced. This has helped to refine the general guidelines for the practical use of combinations in planning models.     

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.     

Seasonal adjustment and kalman filtering: Extension to periodic variances

This paper reviews the relations between the methods of seasonal adjustment used by official statistical agencies and the ‘model-based’ methods that postulate explicit stochastic models for the unobserved components of a time series and apply optimal signal extraction theory to obtain a seasonally adjusted series. The Kalman filter implementation of the model-based methods is described and some recent results on its properties are reviewed. The model-based methods employ homogeneous or time-invariant models that assume in particular that the autocovariance structure does not vary with the season. Relaxing this leads to the class of models known as periodic models, and an example of a seasonally heterosceclastic unobserved-components ARIMA (SHUCARIMA) model is presented. The calculation of the standard error of a seasonally adjusted series via the Kalman filter is extended to this periodic model and illustrated for a monthly rainfall series.     

Forecasting the federal budget with time-series models

The stochastic properties of conventionally denned federal expenditures and revenues are examined, and cointegration is found. Alternative time-series models-univariate ARIMA models, vector autoregressions in levels and differences, and an error correction model-are specified and estimated using quarterly data from 1955:1 through 1979:4. Updated forecasts for up to three years beyond the sample period are evaluated against actual expenditures, revenues and the deficit. The vector autoregression in levels shows evidence of nonstationarity, which leads to strong biases in the forecasts. The remaining models produce forecasts that are satisfactory by the mean squared error criterion, and the magnitudes of biases at the longer horizons are significantly smaller than those of the official forecasts.     

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.     

The Effects of Disaggregation on Forecasting Nonstationary Time Series

This paper focuses on the effects of disaggregation on forecast accuracy for nonstationary time series using dynamic factor models. We compare the forecasts obtained directly from the aggregated series based on its univariate model with the aggregation of the forecasts obtained for each component of the aggregate. Within this framework (first obtain the forecasts for the component series and then aggregate the forecasts), we try two different approaches: (i) generate forecasts from the multivariate dynamic factor model and (ii) generate the forecasts from univariate models for each component of the aggregate. In this regard, we provide analytical conditions for the equality of forecasts. The results are applied to quarterly gross domestic product (GDP) data of several European countries of the euro area and to their aggregated GDP. This will be compared to the prediction obtained directly from modeling and forecasting the aggregate GDP of these European countries. In particular, we would like to check whether long‐run relationships between the levels of the components are useful for improving the forecasting accuracy of the aggregate growth rate. We will make forecasts at the country level and then pool them to obtain the forecast of the aggregate. The empirical analysis suggests that forecasts built by aggregating the country‐specific models are more accurate than forecasts constructed using the aggregated data. Copyright © 2014 John Wiley & Sons, Ltd.     

Combining expert‐adjusted forecasts

It is well known that a combination of model‐based forecasts can improve upon each of the individual constituent forecasts. Most forecasts available in practice are, however, not purely based on econometric models but entail adjustments, where experts with domain‐specific knowledge modify the original model forecasts. There is much evidence that expert‐adjusted forecasts do not necessarily improve the pure model‐based forecasts. In this paper we show, however, that combined expert‐adjusted model forecasts can improve on combined model forecasts, in the case when the individual expert‐adjusted forecasts are not better than their associated model‐based forecasts. We discuss various implications of this finding.     

Forecasting for business planning: A case study of IBM product sales

This is a case study of a closely managed product. Its purpose is to determine whether time-series methods can be appropriate for business planning. By appropriate, we mean two things: whether these methods can model and estimate the special events or features that are often present in sales data; and whether they can forecast accurately enough one, two and four quarters ahead to be useful for business planning. We use two time-series methods, Box-Jenkins modeling and Holt-Winters adaptive forecasting, to obtain forecasts of shipments of a closely managed product. We show how Box-Jenkins transfer-function models can account for the special events in the data. We develop criteria for choosing a final model which differ from the usual methods and are specifically directed towards maximizing the accuracy of next-quarter, next-half-year and next-full-year forecasts. We find that the best Box-Jenkins models give forecasts which are clearly better than those obtained from Holt-Winters forecast functions, and are also better than the judgmental forecasts of IBM's own planners. In conclusion, we judge that Box-Jenkins models can be appropriate for business planning, in particular for determining at the end of the year baseline business-as-usual annual and monthly forecasts for the next year, and in mid-year for resetting the remaining monthly forecasts.     

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.     

Predicting Recessions with Factor Linear Dynamic Harmonic Regressions

We propose a new framework for building composite leading indicators for the Spanish economy using monthly targeted predictors and small‐scale dynamic factor models. Our leading indicator index, based on the low‐frequency components of four monthly economic variables, is able to predict the onset of the Spanish recessions as well as the gross domestic product (GDP) growth cycles and classical industrial production cycles, both historically and in real time. Also, our leading indicator provides substantial aid in forecasting annual and quarterly GDP growth rates. Using only real data available at the beginning of each forecast period, our indicator one‐step‐ahead forecasts shows substantial improvements over other alternatives. Copyright © 2013 John Wiley & Sons, Ltd.     

Modeling and forecasting aggregate stock market volatility in unstable environments using mixture innovation regressions

We perform Bayesian model averaging across different regressions selected from a set of predictors that includes lags of realized volatility, financial and macroeconomic variables. In our model average, we entertain different channels of instability by either incorporating breaks in the regression coefficients of each individual model within our model average, breaks in the conditional error variance, or both. Changes in these parameters are driven by mixture distributions for state innovations (MIA) of linear Gaussian state‐space models. This framework allows us to compare models that assume small and frequent as well as models that assume large but rare changes in the conditional mean and variance parameters. Results using S&P 500 monthly and quarterly realized volatility data from 1960 to 2014 suggest that Bayesian model averaging in combination with breaks in the regression coefficients and the error variance through MIA dynamics generates statistically significantly more accurate forecasts than the benchmark autoregressive model. However, compared to a MIA autoregression with breaks in the regression coefficients and the error variance, we fail to provide any drastic improvements.     

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.     

ARMA Models and the Box–Jenkins Methodology

The purpose of this paper is to apply the Box–Jenkins methodology to ARIMA models and determine the reasons why in empirical tests it is found that the post-sample forecasting the accuracy of such models is generally worse than much simpler time series methods. The paper concludes that the major problem is the way of making the series stationary in its mean (i.e. the method of differencing) that has been proposed by Box and Jenkins. If alternative approaches are utilized to remove and extrapolate the trend in the data, ARMA models outperform the models selected through Box–Jenkins methodology. In addition, it is shown that using ARMA models to seasonally adjusted data slightly improves post-sample accuracies while simplifying the use of ARMA models. It is also confirmed that transformations slightly improve post-sample forecasting accuracy, particularly for long forecasting horizons. Finally, it is demonstrated that AR(1), AR(2) and ARMA(1,1) models can produce more accurate post-sample forecasts than those found through the application of Box–Jenkins methodology.© 1997 John Wiley & Sons, Ltd.     

Quarterly liverpool model with current partial information: An exercise in forecasting

This paper applies an algorithm for the solution of partial current information in rational expectation models to the quarterly Liverpool macroeconomic model of the U.K. The algorithm is shown to produce marginally superior results in forecasts both in ex-post and ex-ante forecasts and can be viewed as an additional tool for the forecaster's kit-bag.     

Can out‐of‐sample forecast comparisons help prevent overfitting?

This paper shows that out‐of‐sample forecast comparisons can help prevent data mining‐induced overfitting. The basic results are drawn from simulations of a simple Monte Carlo design and a real data‐based design similar to those used in some previous studies. In each simulation, a general‐to‐specific procedure is used to arrive at a model. If the selected specification includes any of the candidate explanatory variables, forecasts from the model are compared to forecasts from a benchmark model that is nested within the selected model. In particular, the competing forecasts are tested for equal MSE and encompassing. The simulations indicate most of the post‐sample tests are roughly correctly sized. Moreover, the tests have relatively good power, although some are consistently more powerful than others. The paper concludes with an application, modelling quarterly US inflation. Copyright © 2004 John Wiley & Sons, Ltd.     

On seasonal error correction when the processes include different numbers of unit roots

We propose a seasonal cointegration model (SECM) for quarterly data which includes variables with different numbers of unit roots and thus needs to be transformed in different ways in order to yield stationarity. A Monte Carlo simulation is carried out to investigate the consequences of specifying a SECM with all variables in annual diffrerences in this situation. The SECM in annual differences is compared to the correctly specified model. Pre‐testing for unit roots using two different approaches, and where the models are specified according to the unit root test results, is also considered. The forecast mean squared error criterion and certain parameter estimation results indicate that, in practice, a cointegration model where all variables are transformed with the annual difference filter is more robust than one obtained by pre‐testing for a smaller number of unit roots. The second‐best choice when the true model is not known and when the aim is to forecast, is an ordinary VAR model also in annual differences. Copyright © 2003 John Wiley & Sons, Ltd.     

Selection and estimation of component models for seasonal time series

We present a method for investigating the evolution of trend and seasonality in an observed time series. A general model is fitted to a residual spectrum, using components to represent the seasonality. We show graphically how well the fitted spectrum captures the evidence for evolving seasonality associated with the different seasonal frequencies. We apply the method to model two time series and illustrate the resulting forecasts and seasonal adjustment for one series. Copyright © 2000 John Wiley & Sons, Ltd.