POOLING VERSUS MODEL SELECTION FOR NOWCASTING GDP WITH MANY PREDICTORS: EMPIRICAL EVIDENCE FOR SIX INDUSTRIALIZED COUNTRIES

This paper discusses pooling versus model selection for nowcasting with large datasets in the presence of model uncertainty. In practice, nowcasting a low‐frequency variable with a large number of high‐frequency indicators should account for at least two data irregularities: (i) unbalanced data with missing observations at the end of the sample due to publication delays; and (ii) different sampling frequencies of the data. Two model classes suited in this context are factor models based on large datasets and mixed‐data sampling (MIDAS) regressions with few predictors. The specification of these models requires several choices related to, amongst other things, the factor estimation method and the number of factors, lag length and indicator selection. Thus there are many sources of misspecification when selecting a particular model, and an alternative would be pooling over a large set of different model specifications. We evaluate the relative performance of pooling and model selection for nowcasting quarterly GDP for six large industrialized countries. We find that the nowcast performance of single models varies considerably over time, in line with the forecasting literature. Model selection based on sequential application of information criteria can outperform benchmarks. However, the results highly depend on the selection method chosen. In contrast, pooling of nowcast models provides an overall very stable nowcast performance over time. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Financial nowcasts and their usefulness in macroeconomic forecasting

Financial data often contain information that is helpful for macroeconomic forecasting, while multi-step forecast accuracy benefits from incorporating good nowcasts of macroeconomic variables. This paper considers the usefulness of financial nowcasts for making conditional forecasts of macroeconomic variables with quarterly Bayesian vector autoregressions (BVARs). When nowcasting quarterly financial variables’ values, we find that taking the average of the available daily data and a daily random walk forecast to complete the quarter typically outperforms other nowcasting approaches. Using real-time data, we find gains in out-of-sample forecast accuracy from the inclusion of financial nowcasts relative to unconditional forecasts, with further gains from the incorporation of nowcasts of macroeconomic variables. Conditional forecasts from quarterly BVARs augmented with financial nowcasts rival the forecast accuracy of mixed-frequency dynamic factor models and mixed-data sampling (MIDAS) models.     

Mixed‐frequency models with moving‐average components

Temporal aggregation in general introduces a moving‐average (MA) component in the aggregated model. A similar feature emerges when not all but only a few variables are aggregated, which generates a mixed‐frequency (MF) model. The MA component is generally neglected, likely to preserve the possibility of ordinary least squares estimation, but the consequences have never been properly studied in the MF context. In this paper we show, analytically, in Monte Carlo simulations and in a forecasting application on US macroeconomic variables, the relevance of considering the MA component in MF mixed‐data sampling (MIDAS) and unrestricted MIDAS models (MIDAS–autoregressive moving average (ARMA) and UMIDAS‐ARMA). Specifically, the simulation results indicate that the short‐term forecasting performance of MIDAS‐ARMA and UMIDAS‐ARMA are better than that of, respectively, MIDAS and UMIDAS. The empirical applications on nowcasting US gross domestic product (GDP) growth, investment growth, and GDP deflator inflation confirm this ranking. Moreover, in both simulation and empirical results, MIDAS‐ARMA is better than UMIDAS‐ARMA.     

MIDAS vs. mixed-frequency VAR: Nowcasting GDP in the euro area

This paper compares the mixed-data sampling (MIDAS) and mixed-frequency VAR (MF-VAR) approaches to model specification in the presence of mixed-frequency data, e.g. monthly and quarterly series. MIDAS leads to parsimonious models which are based on exponential lag polynomials for the coefficients, whereas MF-VAR does not restrict the dynamics and can therefore suffer from the curse of dimensionality. However, if the restrictions imposed by MIDAS are too stringent, the MF-VAR can perform better. Hence, it is difficult to rank MIDAS and MF-VAR a priori, and their relative rankings are better evaluated empirically. In this paper, we compare their performances in a case which is relevant for policy making, namely nowcasting and forecasting quarterly GDP growth in the euro area on a monthly basis, using a set of about 20 monthly indicators. It turns out that the two approaches are more complements than substitutes, since MIDAS tends to perform better for horizons up to four to five months, whereas MF-VAR performs better for longer horizons, up to nine months.     

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.     

Nowcasting China’s GDP Using a Bayesian Approach

Real time nowcasting is an assessment of current-quarter GDP from timely released economic and financial series before the GDP figure is disseminated. Providing a reliable current quarter nowcast in real time based on the most recently released economic and financial monthly data is crucial for central banks to make policy decisions and longer-term forecasting exercises. In this study, we use dynamic factor models to bridge monthly information with quarterly GDP and achieve reduction in the dimensionality of the monthly data. We develop a Bayesian approach to provide a way to deal with the unbalanced features of the dataset and to estimate latent common factors. We demonstrate the validity of our approach through simulation studies, and explore the applicability of our approach through an empirical study in nowcasting the China’s GDP using 117 monthly data series of several categories in the Chinese market. The simulation studies and empirical study indicate that our Bayesian approach may be a viable option for nowcasting the China’s GDP.     

Forecasting macroeconomic variables using collapsed dynamic factor analysis

We explore a new approach to the forecasting of macroeconomic variables based on a dynamic factor state space analysis. Key economic variables are modeled jointly with principal components from a large time series panel of macroeconomic indicators using a multivariate unobserved components time series model. When the key economic variables are observed at a low frequency and the panel of macroeconomic variables is at a high frequency, we can use our approach for both nowcasting and forecasting purposes. Given a dynamic factor model as the data generation process, we provide Monte Carlo evidence of the finite-sample justification of our parsimonious and feasible approach. We also provide empirical evidence for a US macroeconomic dataset. The unbalanced panel contains quarterly and monthly variables. The forecasting accuracy is measured against a set of benchmark models. We conclude that our dynamic factor state space analysis can lead to higher levels of forecasting precision when the panel size and time series dimensions are moderate.     

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 three-frequency dynamic factor model for nowcasting Canadian provincial GDP growth

This paper estimates a three-frequency dynamic factor model for nowcasting the Canadian provincial gross domestic product (GDP). The Canadian provincial GDP at market prices is released by Statistics Canada annually with a significant lag (11 months). This necessitates a mixed-frequency approach that can process timely monthly data, the quarterly national accounts, and the annual target variable. The model is estimated on a wide set of provincial, national and international data. In a pseudo real-time exercise, we find that the model outperforms simple benchmarks and is competitive with more sophisticated mixed-frequency approaches (MIDAS models). We also find that variables from the Labour Force Survey are important predictors of real activity. This paper expands previous work that has documented the importance of foreign variables for nowcasting Canadian GDP. This paper finds that including national and foreign predictors is useful for Ontario, while worsening the nowcast performance for smaller provinces.     

Using low frequency information for predicting high frequency variables

We analyze ways of incorporating low frequency information into models for the prediction of high frequency variables. In doing so, we consider the two existing versions of the mixed frequency VAR, with a focus on the forecasts for the high frequency variables. Furthermore, we introduce new models, namely the reverse unrestricted MIDAS (RU-MIDAS) and reverse MIDAS (R-MIDAS), which can be used for producing forecasts of high frequency variables that also incorporate low frequency information. We then conduct several empirical applications for assessing the relevance of quarterly survey data for forecasting a set of monthly macroeconomic indicators. Overall, it turns out that low frequency information is important, particularly when it has just been released.     

Real-time squared: A real-time data set for real-time GDP forecasting

This paper uses real-time data to mimic real-time GDP forecasting activity. Through automatic searches for the best indicators for predicting GDP one and four steps ahead, we compare the out-of-sample forecasting performance of adaptive models using different data vintages, and produce three main findings. First, despite data revisions, the forecasting performance of models with indicators is better, but this advantage tends to vanish over longer forecasting horizons. Second, the practice of using fully updated datasets at the time the forecast is made (i.e., taking the best available measures of today's economic situation) does not appear to bring any effective improvement in forecasting ability: the first GDP release is predicted equally well by models using real-time data as by models using the latest available data. Third, although the first release is a rational forecast of GDP data after all statistical revisions have taken place, the forecast based on the latest available GDP data (i.e. the “temporarily best” measures) may be improved by combining preliminary official releases with one-step-ahead forecasts.     

Nowcasting GDP with a pool of factor models and a fast estimation algorithm

We propose a novel mixed-frequency dynamic factor model with time-varying parameters and stochastic volatility for macroeconomic nowcasting and develop a fast estimation algorithm. This enables us to generate forecast densities based on a large space of factor models. We apply our framework to nowcast US GDP growth in real time. Our results reveal that stochastic volatility seems to improve the accuracy of point forecasts the most, compared to the constant-parameter factor model. These gains are most prominent during unstable periods such as the Covid-19 pandemic. Finally, we highlight indicators driving the US GDP growth forecasts and associated downside risks in real time.     

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.     

Short-term forecasting of GDP with a DSGE model augmented by monthly indicators

DSGE models are useful tools for evaluating the impact of policy changes, but their use for (short-term) forecasting is still in its infancy. Besides theory-based restrictions, the timeliness of data is an important issue. Since DSGE models are based on quarterly data, they suffer from the publication lag of quarterly national accounts. In this paper we present a framework for the short-term forecasting of GDP based on a medium-scale DSGE model for a small open economy within a currency area. We utilize the information available in monthly indicators based on the approach proposed by Giannone et al. (2009). Using Austrian data, we find that the forecasting performance of the DSGE model can be improved considerably by incorporating monthly indicators, while still maintaining the story-telling capability of the model.     

Leading Indicators for Euro‐area Inflation and GDP Growth*

In this paper, we evaluate the role of a set of variables as leading indicators for Euro‐area inflation and GDP growth. Our leading indicators are taken from the variables in the European Central Bank's (ECB) Euro‐area‐wide model database, plus a set of similar variables for the US. We compare the forecasting performance of each indicator ex post with that of purely autoregressive models. We also analyse three different approaches to combining the information from several indicators. First, ex post, we discuss the use as indicators of the estimated factors from a dynamic factor model for all the indicators. Secondly, within an ex ante framework, an automated model selection procedure is applied to models with a large set of indicators. No future information is used, future values of the regressors are forecast, and the choice of the indicators is based on their past forecasting records. Finally, we consider the forecasting performance of groups of indicators and factors and methods of pooling the ex ante single‐indicator or factor‐based forecasts. Some sensitivity analyses are also undertaken for different forecasting horizons and weighting schemes of forecasts to assess the robustness of the results.     

Sparse Partial Least Squares in Time Series for Macroeconomic Forecasting

Factor models have been applied extensively for forecasting when high‐dimensional datasets are available. In this case, the number of variables can be very large. For instance, usual dynamic factor models in central banks handle over 100 variables. However, there is a growing body of literature indicating that more variables do not necessarily lead to estimated factors with lower uncertainty or better forecasting results. This paper investigates the usefulness of partial least squares techniques that take into account the variable to be forecast when reducing the dimension of the problem from a large number of variables to a smaller number of factors. We propose different approaches of dynamic sparse partial least squares as a means of improving forecast efficiency by simultaneously taking into account the variable forecast while forming an informative subset of predictors, instead of using all the available ones to extract the factors. We use the well‐known Stock and Watson database to check the forecasting performance of our approach. The proposed dynamic sparse models show good performance in improving efficiency compared to widely used factor methods in macroeconomic forecasting. Copyright © 2014 John Wiley & Sons, Ltd.     

High-frequency monitoring of growth at risk

Monitoring changes in financial conditions provides valuable information on the contribution of financial risks to future economic growth. For that purpose, central banks need real-time indicators to promptly adjust their policy stance. In this paper, we extend the quarterly growth-at-risk (GaR) approach of Adrian et al. (2019) by accounting for the high-frequency nature of financial conditions indicators. Specifically, we use Bayesian mixed-data sampling (MIDAS) quantile regressions to exploit the information content of both a financial stress index and a financial conditions index, leading to real-time high-frequency GaR measures for the euro area. We show that our daily GaR indicator (i) displays good GDP nowcasting properties, (ii) can provide an early signal of GDP downturns, and (iii) allows day-to-day assessment of the effects of monetary policies. During the first six months of the Covid-19 pandemic period, it has provided a timely measure of the tail risks to euro-area GDP.     

Forecasting GDP over the Business Cycle in a Multi‐Frequency and Data‐Rich Environment

This paper merges two specifications recently developed in the forecasting literature: the MS‐MIDAS model (Guérin and Marcellino, 2013) and the factor‐MIDAS model (Marcellino and Schumacher, 2010). The MS‐factor MIDAS model that we introduce incorporates the information provided by a large data set consisting of mixed frequency variables and captures regime‐switching behaviours. Monte Carlo simulations show that this specification tracks the dynamics of the process and predicts the regime switches successfully, both in‐sample and out‐of‐sample. We apply this model to US data from 1959 to 2010 and properly detect recessions by exploiting the link between GDP growth and higher frequency financial variables.