Forecast combination for U.S. recessions with real-time data

This paper proposes the use of forecast combination to improve predictive accuracy in forecasting the U.S. business cycle index, as published by the Business Cycle Dating Committee of the NBER. It focuses on one-step ahead out-of-sample monthly forecast utilising the well-established coincident indicators and yield curve models, allowing for dynamics and real-time data revisions. Forecast combinations use log-score and quadratic-score based weights, which change over time. This paper finds that forecast accuracy improves when combining the probability forecasts of both the coincident indicators model and the yield curve model, compared to each model's own forecasting performance.     

Data revisions to German national accounts: Are initial releases good nowcasts?

Data revisions to national accounts pose a serious challenge to policy decision making. Well-behaved revisions should be unbiased, small, and unpredictable. This article shows that revisions to German national accounts are biased, large, and predictable. Moreover, with use of filtering techniques designed to process data subject to revisions, the real-time forecasting performance of initial releases can be increased by up to 23%. For total real GDP growth, however, the initial release is an optimal forecast. Yet, given the results for disaggregated variables, the averaging out of biases and inefficiencies at the aggregate GDP level appears to be good luck rather than good forecasting.     

Real-time forecasting of German GDP based on a large factor model with monthly and quarterly data

This paper discusses a factor model for short-term forecasting of GDP growth using a large number of monthly and quarterly time series in real-time. To take into account the different periodicities of the data and missing observations at the end of the sample, the factors are estimated by applying an EM algorithm, combined with a principal components estimator. We discuss some in-sample properties of the estimator in a real-time environment and propose alternative methods for forecasting quarterly GDP with monthly factors. In the empirical application, we use a novel real-time dataset for the German economy. Employing a recursive forecast experiment, we evaluate the forecast accuracy of the factor model with respect to German GDP. Furthermore, we investigate the role of revisions in forecast accuracy and assess the contribution of timely monthly observations to the forecast performance. Finally, we compare the performance of the mixed-frequency model with that of a factor model, based on time-aggregated quarterly data.     

Predicting recessions with a composite real-time dynamic probit model

In this paper we propose a composite indicator for real-time recession forecasting based on alternative dynamic probit models. For this purpose, we use a large set of monthly macroeconomic and financial leading indicators from the German and US economies. Alternative dynamic probit regressions are specified through automated general-to-specific and specific-to-general lag selection procedures on the basis of slightly different initial sets. The resulting recession probability forecasts are then combined in order to decrease the volatility of the forecast errors and increase their forecasting accuracy. This procedure features not only good in-sample forecast statistics, but also good out-of-sample performances, as is illustrated using a real-time evaluation exercise.     

On the forecasting performance of a small-scale DSGE model

Dynamic stochastic general equilibrium (DSGE) models have recently become standard tools for policy analysis. Nevertheless, their forecasting properties have still barely been explored. In this article, we address this problem by examining the quality of forecasts of the key U.S. economic variables: the three-month Treasury bill yield, the GDP growth rate and GDP price index inflation, from a small-size DSGE model, trivariate vector autoregression (VAR) models and the Philadelphia Fed Survey of Professional Forecasters (SPF). The ex post forecast errors are evaluated on the basis of the data from the period 1994–2006. We apply the Philadelphia Fed “Real-Time Data Set for Macroeconomists” to ensure that the data used in estimating the DSGE and VAR models was comparable to the information available to the SPF.Overall, the results are mixed. When comparing the root mean squared errors for some forecast horizons, it appears that the DSGE model outperforms the other methods in forecasting the GDP growth rate. However, this characteristic turned out to be statistically insignificant. Most of the SPF's forecasts of GDP price index inflation and the short-term interest rate are better than those from the DSGE and VAR models.     

Sparse structures with LASSO through principal components: Forecasting GDP components in the short-run

This paper examines the use of sparse methods to forecast the real (in the chain-linked volume sense) expenditure components of the US and EU GDP in the short-run sooner than national statistics institutions officially release the data. We estimate current-quarter nowcasts, along with one- and two-quarter forecasts, by bridging quarterly data with available monthly information announced with a much smaller delay. We solve the high-dimensionality problem of monthly datasets by assuming sparse structures of leading indicators capable of adequately explaining the dynamics of the analyzed data. For variable selection and estimation of the forecasts, we use LASSO together with its recent modifications. We propose an adjustment that combines LASSO cases with principal components analysis to improve the forecasting performance. We evaluated the forecasting performance by conducting pseudo-real-time experiments for gross fixed capital formation, private consumption, imports, and exports over a sample from 2005–2019, compared with benchmark ARMA and factor models. The main results suggest that sparse methods can outperform the benchmarks and identify reasonable subsets of explanatory variables. The proposed combination of LASSO and principal components further improves the forecast accuracy.     

A look into the factor model black box: Publication lags and the role of hard and soft data in forecasting GDP

We derive forecast weights and uncertainty measures for assessing the roles of individual series in a dynamic factor model (DFM) for forecasting the euro area GDP from monthly indicators. The use of the Kalman smoother allows us to deal with publication lags when calculating the above measures. We find that surveys and financial data contain important information for the GDP forecasts beyond the monthly real activity measures. However, this is discovered only if their more timely publication is taken into account properly. Differences in publication lags play a very important role and should be considered in forecast evaluation.     

Professional forecasters and real-time forecasting with a DSGE model

This paper analyses the real-time forecasting performance of the New Keynesian DSGE model of Galí, Smets and Wouters (2012), estimated on euro area data. It investigates the extent to which the inclusion of forecasts of inflation, GDP growth and unemployment by professional forecasters improve the forecasting performance. We consider two approaches for conditioning on such information. Under the “noise” approach, the mean professional forecasts are assumed to be noisy indicators of the rational expectations forecasts implied by the DSGE model. Under the “news” approach, it is assumed that the forecasts reveal the presence of expected future structural shocks in line with those estimated in the past. The forecasts of the DSGE model are compared with those from a Bayesian VAR model, an AR(1) model, a sample mean and a random walk.     

FRED-SD: A real-time database for state-level data with forecasting applications

We construct a real-time dataset (FRED-SD) with vintage data for the U.S. states that can be used to forecast both state-level and national-level variables. Our dataset includes approximately 28 variables per state, including labor-market, production, and housing variables. We conduct two sets of real-time forecasting exercises. The first forecasts state-level labor-market variables using five different models and different levels of industrially disaggregated data. The second forecasts a national-level variable exploiting the cross-section of state data. The state-forecasting experiments suggest that large models with industrially disaggregated data tend to have higher predictive ability for industrially diversified states. For national-level data, we find that forecasting and aggregating state-level data can outperform a random walk but not an autoregression. We compare these real-time data experiments with forecasting experiments using final-vintage data and find very different results. Because these final-vintage results are obtained with revised data that would not have been available at the time the forecasts would have been made, we conclude that the use of real-time data is essential for drawing proper conclusions about state-level forecasting models.     

Multi-step forecasting in emerging economies: An investigation of the South African GDP

To forecast at several, say h, periods into the future, a modeller faces a choice between iterating one-step-ahead forecasts (the IMS technique), or directly modeling the relationship between observations separated by an h-period interval and using it for forecasting (DMS forecasting). It is known that structural breaks, unit-root non-stationarity and residual autocorrelation may improve DMS accuracy in finite samples, all of which occur when modelling the South African GDP over the period 1965–2000. This paper analyzes the forecasting properties of 779 multivariate and univariate models that combine different techniques of robust forecasting. We find strong evidence supporting the use of DMS and intercept correction, and attribute their superior forecasting performance to their robustness in the presence of breaks.     

Adaptive learning forecasting,with applications in forecasting agricultural prices

We introduce a new forecasting methodology, referred to as adaptive learning forecasting, that allows for both forecast averaging and forecast error learning. We analyze its theoretical properties and demonstrate that it provides a priori MSE improvements under certain conditions. The learning rate based on past forecast errors is shown to be non-linear. This methodology is of wide applicability and can provide MSE improvements even for the simplest benchmark models. We illustrate the method’s application using data on agricultural prices for several agricultural products, as well as on real GDP growth for several of the corresponding countries. The time series of agricultural prices are short and show an irregular cyclicality that can be linked to economic performance and productivity, and we consider a variety of forecasting models, both univariate and bivariate, that are linked to output and productivity. Our results support both the efficacy of the new method and the forecastability of agricultural prices.     

Forecasting the UK economy with a medium-scale Bayesian VAR

We estimate a Bayesian VAR (BVAR) for the UK economy and assess its performance in forecasting GDP growth and CPI inflation in real time relative to forecasts from COMPASS, the Bank of England’s DSGE model, and other benchmarks. We find that the BVAR outperformed COMPASS when forecasting both GDP and its expenditure components. In contrast, their performances when forecasting CPI were similar. We also find that the BVAR density forecasts outperformed those of COMPASS, despite under-predicting inflation at most forecast horizons. Both models over-predicted GDP growth at all forecast horizons, but the issue was less pronounced in the BVAR. The BVAR’s point and density forecast performances are also comparable to those of a Bank of England in-house statistical suite for both GDP and CPI inflation, as well as to the official Inflation Report projections. Our results are broadly consistent with the findings of similar studies for other advanced economies.     

Density forecasting with Bayesian Vector Autoregressive models under macroeconomic data uncertainty

Macroeconomic data are subject to data revisions. Yet, the usual way of generating real-time density forecasts from Bayesian Vector Autoregressive (BVAR) models makes no allowance for data uncertainty from future data revisions. We develop methods of allowing for data uncertainty when forecasting with BVAR models with stochastic volatility. First, the BVAR forecasting model is estimated on real-time vintages. Second, the BVAR model is jointly estimated with a model of data revisions such that forecasts are conditioned on estimates of the ‘true’ values. We find that this second method generally improves upon conventional practice for density forecasting, especially for the United States.     

Predicting ordinary and severe recessions with a three-state Markov-switching dynamic factor model: An application to the German business cycle

We estimate a Markow-switching dynamic factor model with three states based on six leading business cycle indicators for Germany, preselected from a broader set using the elastic net soft-thresholding rule. The three states represent expansions, normal recessions and severe recessions. We show that a two-state model is not sensitive enough to detect relatively mild recessions reliably when the Great Recession of 2008/2009 is included in the sample. Adding a third state helps to distinguish normal and severe recessions clearly, so that the model identifies all business cycle turning points in our sample reliably. In a real-time exercise, the model detects recessions in a timely manner. Combining the estimated factor and the recession probabilities with a simple GDP forecasting model yields an accurate nowcast for the steepest decline in GDP in 2009Q1, and a correct prediction of the timing of the Great Recession and its recovery one quarter in advance.     

Google data in bridge equation models for German GDP

Interest in the use of “big data” when it comes to forecasting macroeconomic time series such as private consumption or unemployment has increased; however, applications to the forecasting of GDP remain rather rare. This paper incorporates Google search data into a bridge equation model, a version of which usually belongs to the suite of forecasting models at central banks. We show how such big data information can be integrated, with an emphasis on the appeal of the underlying model in this respect. As the decision as to which Google search terms should be added to which equation is crucial —- both for the forecasting performance itself and for the economic consistency of the implied relationships —- we compare different (ad-hoc, factor and shrinkage) approaches in terms of their pseudo real time out-of-sample forecast performances for GDP, various GDP components and monthly activity indicators. We find that sizeable gains can indeed be obtained by using Google search data, where the best-performing Google variable selection approach varies according to the target variable. Thus, assigning the selection methods flexibly to the targets leads to the most robust outcomes overall in all layers of the system.     

A Dynamic Panel Data Approach to the Forecasting of the GDP of German Länder

Abstract

In this paper, we make multi-step forecasts of the annual growth rates of the real GDP for each of the 16 German Länder simultaneously. We apply dynamic panel models accounting for spatial dependence between regional GDP. We find that both pooling and accounting for spatial effects help to improve the forecast performance substantially. We demonstrate that the effect of accounting for spatial dependence is more pronounced for longer forecasting horizons (the forecast accuracy gain is about 9% for a 1-year horizon and exceeds 40% for a 5-year horizon). We recommend incorporating a spatial dependence structure into regional forecasting models, especially when long-term forecasts are made.     

Differing behaviours of forecasters of UK GDP growth

The literature suggests that the dispersion of agents’ forecasts of an event flows from heterogeneity of beliefs and models. Using a data set of fixed event point forecasts of UK GDP growth by a panel of independent forecasters published by HM Treasury, we investigate three questions concerning this dispersion: (a) Are agent’s beliefs randomly distributed or do agents fall into groups with similar beliefs? (b) as agents revise their forecasts, what roles are played by their previous and consensus forecasts? and (c) is an agent’s private information of persistent value? We find that agents fall into four clusters, a large majority, a few pessimists, and two idiosyncratic agents. Our proposed model of forecast revisions shows agents are influenced positively by a change in the consensus forecast and negatively influenced by the previous distance of their forecast from the consensus. We show that the forecasts of a minority of agents significantly lead the consensus.     

Forecasting GDP growth with NIPA aggregates: In search of core GDP

In addition to GDP, which is measured using expenditure data, the U.S. national income and product accounts (NIPAs) provide a variety of measures of economic activity, including gross domestic income and other aggregates that exclude one or more of the components that make up GDP. Similarly to the way in which economists have attempted to use core inflation—which excludes volatile energy and food prices—to predict headline inflation, the omission of GDP components may be useful in extracting a signal as to where GDP is going. We investigate the extent to which these NIPA aggregates constitute “core GDP.” In an out-of-sample forecasting exercise using a novel real-time dataset of NIPA aggregates, we find that consumption growth and the growth of GDP excluding inventories and trade have historically outperformed a canonical univariate benchmark for forecasting GDP growth, suggesting that these are promising measures of core GDP growth.     

A comparison of mixed frequency approaches for nowcasting Euro area macroeconomic aggregates

In this paper, we focus on the different methods which have been proposed in the literature to date for dealing with mixed-frequency and ragged-edge datasets: bridge equations, mixed-data sampling (MIDAS), and mixed-frequency VAR (MF-VAR) models. We discuss their performances for nowcasting the quarterly growth rate of the Euro area GDP and its components, using a very large set of monthly indicators. We investigate the behaviors of single indicator models, forecast combinations and factor models, in a pseudo real-time framework. MIDAS with an AR component performs quite well, and outperforms MF-VAR at most horizons. Bridge equations perform well overall. Forecast pooling is superior to most of the single indicator models overall. Pooling information using factor models gives even better results. The best results are obtained for the components for which more economically related monthly indicators are available. Nowcasts of GDP components can then be combined to obtain nowcasts for the total GDP growth.     

Stable seasonal pattern models for forecast revision: A comparative study

Many firms prepare forecasts at the beginning of each financial quarter that predict total sales over the upcoming quarter. Such forecasts may be used to make financial projections, or to plan manufacturing capacity and materials purchases. As weekly sales are recorded during the quarter, these quarterly forecasts are often revised, allowing plans and projections to be adjusted appropriately. A formal basis for these forecast revisions may be found in so-called stable seasonal pattern models, which are based on the observation that in many instances, the sales that accrue during a given period of a quarter follow a regular pattern. This paper discusses a number of stable seasonal pattern models – several from the literature, two that are novel – which have been evaluated for making forecast revisions at Sun Microsystems, Inc. Commonalities between the models are elucidated using a general theoretical framework, and a straightforward sample-based mechanism is described that affords great flexibility in the design and use of stable seasonal pattern models. The paper culminates in a detailed comparison of the performance of new and existing stable seasonal pattern models with respect to Sun's sales data.