Forecasting the Italian industrial production index in real time

Daily electricity consumption data, available almost in real time, can be used in Italy to estimate the level of industrial production in any given month before the month is over. We present a number of procedures that do this using electricity consumption in the first 14 days of the month. (This is an extension of a previous model that used monthly electricity data.) We show that, with a number of adjustments, a model using half-monthly electricity data generates acceptable estimates of the monthly production index. More precisely, these estimates are more accurate than univariate forecasts but less accurate than estimates based on monthly electricity data. A further improvement can be obtained by combining ‘half-monthly’ electricity-based estimates with univariate forecasts. We also present quarterly estimates and discuss confidence intervals for various types of forecasts.     

Seasonality in large-scale macroeconometric models

Macroeconomic indicators are typically appraised in seasonally adjusted form, and forecasts are often presented in a similar way (as annual changes, for example). Moreover, the quarterly macroeconomic models used in forecasting are commonly estimated from seasonally adjusted data. Nevertheless, these models can generate forecasts with seasonal patterns, and this paper assesses the cause and cure of this phenomenon. It is found that forecast seasonality is induced by seasonality in the various inputs: exogenous variables, residual adjustments, the dynamic specification of certain equations, and annual changes in policy variables. Series changing annually but observed quarterly are termed ‘intercalated series’, and are simple examples of periodic processes. Forecast seasonality can be removed by appropriate adjustment of all these inputs. Models containing explicit future expectations variables solved in a model-consistent manner are also considered: numerical sensitivity to the terminal quarter may result from terminal conditions that require adjustment when seasonality is present.     

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.     

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.     

On Forecasting Conflict in the Sudan: 2009–2012

This paper considers univariate and multivariate models to forecast monthly conflict events in the Sudan over the out‐of‐sample period 2009–2012. The models used to generate these forecasts were based on a specification from a machine learning algorithm fit to 2000–2008 monthly data. The model that includes previous month's wheat price performs better than a similar model which does not include past wheat prices (the univariate model). Both models did not perform well in forecasting conflict in a neighborhood of the 2012 ‘Heglig crisis’. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Forecasting Monetary Policy Decisions in Australia: A Forecast Combinations Approach

This paper applies a triple‐choice ordered probit model, corrected for nonstationarity to forecast monetary decisions of the Reserve Bank of Australia. The forecast models incorporate a mix of monthly and quarterly macroeconomic time series. Forecast combination is used as an alternative to one multivariate model to improve accuracy of out‐of‐sample forecasts. This accuracy is evaluated with scoring functions, which are also used to construct adaptive weights for combining probability forecasts. This paper finds that combined forecasts outperform multivariable models. These results are robust to different sample sizes and estimation windows. Copyright © 2011 John Wiley & Sons, Ltd.     

Nowcasting quarterly GDP growth in a monthly coincident indicator model

This paper presents an extension of the Stock and Watson coincident indicator model that allows one to include variables available at different frequencies while taking care of missing observations at any time period. The proposed procedure provides estimates of the unobserved common coincident component, of the unobserved monthly series underlying any included quarterly indicator, and of any missing values in the series. An application to a coincident indicator model for the Portuguese economy is presented. We use monthly indicators from business surveys whose results are published with a very short delay. By using the available data for the monthly indicators and for quarterly real GDP, it becomes possible to produce simultaneously a monthly composite index of coincident indicators and an estimate of the latest quarter real GDP growth well ahead of the release of the first official figures. Copyright © 2005 John Wiley & Son, Ltd.     

Integrating Quarterly Data into a Dynamic Factor Model of US Monthly GDP

This paper develops and estimates a dynamic factor model in which estimates for unobserved monthly US Gross Domestic Product (GDP) are consistent with observed quarterly data. In contrast to existing approaches, the quarterly averages of our monthly estimates are exactly equal to the Bureau of Economic Analysis (BEA) quarterly estimates. The relationship between our monthly estimates and the quarterly data is therefore the same as the relationship between quarterly and annual data. The study makes use of Bayesian Markov chain Monte Carlo and data augmentation techniques to simulate values for the logarithms on monthly US GDP. The imposition of the exact linear quarterly constraint produces a non‐standard distribution, necessitating the implementation of a Metropolis simulation step in the estimation. Our methodology can be easily generalized to cases where the variable of interest is monthly GDP and in such a way that the final results incorporate the statistical uncertainty associated with the monthly GDP estimates. We provide an example by incorporating our monthly estimates into a Markov switching model of the US business cycle. Copyright © 2016 John Wiley & Sons, Ltd.     

Quarterly forecasts of the italian business cycle by means of monthly economic indicators

Recent years have witnessed a growing availability of high-frequency indicators which can be used to forecast future economic activity. This paper shows how some of the widely known monthly economic indicators at present available in Italy can be used in a systematic and coordinated manner to forecast the main variables of the National Accounts. In order to reduce as much as possible the amount of judgment in the analysis of the business cycle, a model-based approach is adopted. Thus, a pseudo macro-econometric model of the Italian economy is built, which can be used to produce forecasts one semester ahead of the last National Accounts data release. The model can be used autonomously as well as in combination with the Bank of Italy's quarterly econometric model.     

Forecast Combination and Bayesian Model Averaging: A Prior Sensitivity Analysis

In this study we evaluate the forecast performance of model‐averaged forecasts based on the predictive likelihood carrying out a prior sensitivity analysis regarding Zellner's g prior. The main results are fourfold. First, the predictive likelihood does always better than the traditionally employed ‘marginal’ likelihood in settings where the true model is not part of the model space. Secondly, forecast accuracy as measured by the root mean square error (RMSE) is maximized for the median probability model. On the other hand, model averaging excels in predicting direction of changes. Lastly, g should be set according to Laud and Ibrahim (1995: Predictive model selection. Journal of the Royal Statistical Society B 57 : 247–262) with a hold‐out sample size of 25% to minimize the RMSE (median model) and 75% to optimize direction of change forecasts (model averaging). We finally apply the aforementioned recommendations to forecast the monthly industrial production output of six countries, beating for almost all countries the AR(1) benchmark model. Copyright © 2011 John Wiley & Sons, Ltd.     

Forecasting with an econometric model: The ‘ragged edge’ problem

In practical econometric forecasting exercises, incomplete data on current and immediate past values of endogenous variables are available. This paper considers various approaches to this ‘ragged edge’ problem, including the common device of treating as ‘temporarily exogenous’ an endogenous variable whose value is known, by deleting it from the set of endogenous variables for whose forecast values the model is solved and suppressing the corresponding structural equation. It is seen that this forecast can be adjusted to coincide with the optimal forecast. The initial discussion concerns the textbook linear simultaneous equation model; extensions to non-linear dynamic models are described.     

Forecast accuracy after pretesting with an application to the stock market

In econometrics, as a rule, the same data set is used to select the model and, conditional on the selected model, to forecast. However, one typically reports the properties of the (conditional) forecast, ignoring the fact that its properties are affected by the model selection (pretesting). This is wrong, and in this paper we show that the error can be substantial. We obtain explicit expressions for this error. To illustrate the theory we consider a regression approach to stock market forecasting, and show that the standard predictions ignoring pretesting are much less robust than naive econometrics might suggest. We also propose a forecast procedure based on the ‘neutral Laplace estimator’, which leads to an improvement over standard model selection procedures. Copyright © 2004 John Wiley & Sons, Ltd.     

Monthly data and short‐term forecasting: an assessment of monthly data in a VAR model

Use of monthly data for economic forecasting purposes is typically constrained by the absence of monthly estimates of GDP. Such data can be interpolated but are then prone to measurement error. However, the variance matrix of the measurement errors is typically known. We present a technique for estimating a VAR on monthly data, making use of interpolated estimates of GDP and correcting for the impact of measurement error. We then address the question how to establish whether the model estimated from the interpolated monthly data contains information absent from the analogous quarterly VAR. The techniques are illustrated using a bivariate VAR modelling GDP growth and inflation. It is found that, using inflation data adjusted to remove seasonal effects and the impacts of changes to indirect taxes, the monthly model has little to add to a quarterly model when projecting one quarter ahead. However, the monthly model has an important role to play in building up a picture of the current quarter once one or two months' hard data becomes available. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

Prediction,diagnosis, and causal thinking in forecasting

While forecasting involves forward/predictive thinking, it depends crucially on prior diagnosis for suggesting a model of the phenomenon, for defining‘relevant’variables, and for evaluating forecast accuracy via the model. The nature of diagnostic thinking is examined with respect to these activities. We first consider the difficulties of evaluating forecast accuracy without a causal model of what generates outcomes. We then discuss the development of models by considering how attention is directed to variables via analogy and metaphor as well as by what is unusual or abnormal. The causal relevance of variables is then assessed by reference to probabilistic signs called‘cues to causality’. These are: temporal order, constant conjunction, contiguity in time and space, number of alternative explanations, similarity, predictive validity, and robustness. The probabilistic nature of the cues is emphasized by discussing the concept of spurious correlation and how causation does not necessarily imply correlation. Implications for improving forecasting are considered with respect to the above issues.     

Nonlinear identification of judgmental forecasts effects at SKU level

Prediction of demand is a key component within supply chain management. Improved accuracy in forecasts directly affects all levels of the supply chain, reducing stock costs and increasing customer satisfaction. In many application areas, demand prediction relies on statistical software which provides an initial forecast subsequently modified by the expert's judgment. This paper outlines a new methodology based on state‐dependent parameter (SDP) estimation techniques to identify the nonlinear behaviour of such managerial adjustments. This non‐parametric SDP estimate is used as a guideline to propose a nonlinear model that corrects the bias introduced by the managerial adjustments. One‐step‐ahead forecasts of stock‐keeping unit sales sampled monthly from a manufacturing company are utilized to test the proposed methodology. The results indicate that adjustments introduce a nonlinear pattern, undermining accuracy. This understanding can be used to enhance the design of the forecasting support system in order to help forecasters towards more efficient judgmental adjustments. Copyright © 2010 John Wiley & Sons, Ltd.     

Local to unity,long‐horizon forecasting thresholds for model selection in the AR(1)

This article introduces a novel framework for analysing long‐horizon forecasting of the near non‐stationary AR(1) model. Using the local to unity specification of the autoregressive parameter, I derive the asymptotic distributions of long‐horizon forecast errors both for the unrestricted AR(1), estimated using an ordinary least squares (OLS) regression, and for the random walk (RW). I then identify functions, relating local to unity ‘drift’ to forecast horizon, such that OLS and RW forecasts share the same expected square error. OLS forecasts are preferred on one side of these ‘forecasting thresholds’, while RW forecasts are preferred on the other. In addition to explaining the relative performance of forecasts from these two models, these thresholds prove useful in developing model selection criteria that help a forecaster reduce error. Copyright © 2004 John Wiley & Sons, Ltd.     

Combining forecasts based on multiple encompassing tests in a macroeconomic core system

This paper investigates whether and to what extent multiple encompassing tests may help determine weights for forecast averaging in a standard vector autoregressive setting. To this end we consider a new test‐based procedure, which assigns non‐zero weights to candidate models that add information not covered by other models. The potential benefits of this procedure are explored in extensive Monte Carlo simulations using realistic designs that are adapted to UK and to French macroeconomic data, to which trivariate vector autoregressions (VAR) are fitted. Thus simulations rely on potential data‐generating mechanisms for macroeconomic data rather than on simple but artificial designs. We run two types of forecast ‘competitions’. In the first one, one of the model classes is the trivariate VAR, such that it contains the generating mechanism. In the second specification, none of the competing models contains the true structure. The simulation results show that the performance of test‐based averaging is comparable to uniform weighting of individual models. In one of our role model economies, test‐based averaging achieves advantages in small samples. In larger samples, pure prediction models outperform forecast averages. Copyright © 2010 John Wiley & Sons, Ltd.     

Analysis of the US business cycle with a Vector‐Markov‐switching model

This paper identifies turning points for the US ‘business cycle’ using information from different time series. The model, a multivariate Markov‐switching model, assumes that each series is characterized by a mixture of two normal distributions (a high and low mean) with the switching from one to the other determined by a common Markov process. The procedure is applied to the series composing the composite coincident indicator in the USA to obtain business cycle turning points. The business cycle chronology is closer to the NBER reference cycle than the turning points obtained from the individual series using a univariate model. The model is also used to forecast the series with some encouraging results. Copyright © 2001 John Wiley & Sons, Ltd.