Factor MIDAS for Nowcasting and Forecasting with Ragged‐Edge Data: A Model Comparison for German GDP*

In this article, we merge two strands from the recent econometric literature. First, factor models based on large sets of macroeconomic variables for forecasting, which have generally proven useful for forecasting. However, there is some disagreement in the literature as to the appropriate method. Second, forecast methods based on mixed‐frequency data sampling (MIDAS). This regression technique can take into account unbalanced datasets that emerge from publication lags of high‐ and low‐frequency indicators, a problem practitioner have to cope with in real time. In this article, we introduce Factor MIDAS, an approach for nowcasting and forecasting low‐frequency variables like gross domestic product (GDP) exploiting information in a large set of higher‐frequency indicators. We consider three alternative MIDAS approaches (basic, smoothed and unrestricted) that provide harmonized projection methods that allow for a comparison of the alternative factor estimation methods with respect to nowcasting and forecasting. Common to all the factor estimation methods employed here is that they can handle unbalanced datasets, as typically faced in real‐time forecast applications owing to publication lags. In particular, we focus on variants of static and dynamic principal components as well as Kalman filter estimates in state‐space factor models. As an empirical illustration of the technique, we use a large monthly dataset of the German economy to nowcast and forecast quarterly GDP growth. We find that the factor estimation methods do not differ substantially, whereas the most parsimonious MIDAS projection performs best overall. Finally, quarterly models are in general outperformed by the Factor MIDAS models, which confirms the usefulness of the mixed‐frequency techniques that can exploit timely information from business cycle indicators.     

Nowcasting German GDP: Foreign factors,financial markets,and model averaging

This paper develops a nowcasting model for the German economy. The model outperforms a number of alternatives and produces forecasts not only for GDP but also for other key variables. We show that the inclusion of a foreign factor improves the model’s performance, while financial variables do not. Additionally, a comprehensive model averaging exercise reveals that factor extraction in a single model delivers slightly better results than averaging across models. Finally, we estimate a “news” index for the German economy in order to assess the overall performance of the model beyond forecast errors in GDP. The index is constructed as a weighted average of the nowcast errors related to each variable included in the model.     

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.     

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.     

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.     

Nowcasting with payments system data

We consider the potential usefulness of a large set of electronic payments data, comprising the values and numbers of both debit card transactions and cheques that clear through the banking system, for the problem of reducing the current-period forecast (‘nowcast’) loss for (the growth rates of) GDP and retail sales. The payments system variables capture a broad range of spending activity and are available on a very timely basis, making them suitable current indicators. We generate nowcasts of GDP and retail sales growth for a given month on seven different dates, over a period of two and a half months preceding the first official releases, which is the period over which nowcasts would be of interest. We find statistically significant evidence that payments system data can reduce the nowcast error for both GDP and retail sales growth. Both debit transaction and cheque clearance data are of value in reducing nowcast losses for GDP growth, although the latter are of little or no value when debit data are also included. For retail sales, cheque data appear to produce no further nowcast loss reductions, regardless of whether or not debit transactions are included in the nowcasting model.     

Nowcasting growth using Google Trends data: A Bayesian Structural Time Series model

This paper investigates the benefits of internet search data in the form of Google Trends for nowcasting real U.S. GDP growth in real time through the lens of mixed frequency Bayesian Structural Time Series (BSTS) models. We augment and enhance both model and methodology to make these better amenable to nowcasting with large number of potential covariates. Specifically, we allow shrinking state variances towards zero to avoid overfitting, extend the SSVS (spike and slab variable selection) prior to the more flexible normal-inverse-gamma prior which stays agnostic about the underlying model size, as well as adapt the horseshoe prior to the BSTS. The application to nowcasting GDP growth as well as a simulation study demonstrate that the horseshoe prior BSTS improves markedly upon the SSVS and the original BSTS model with the largest gains in dense data-generating-processes. Our application also shows that a large dimensional set of search terms is able to improve nowcasts early in a specific quarter before other macroeconomic data become available. Search terms with high inclusion probability have good economic interpretation, reflecting leading signals of economic anxiety and wealth effects.     

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.     

Measuring output gap nowcast uncertainty

We propose a methodology for gauging the uncertainty in output gap nowcasts across a large number of commonly-deployed vector autoregressive (VAR) specifications for inflation and the output gap. Our approach utilises many output gap measures to construct ensemble nowcasts for inflation using a linear opinion pool. The predictive densities for the latent output gap utilise weights based on the ability of each specification to provide accurate probabilistic forecasts of inflation. In an application based on US real-time data, nowcasting over the out-of-sample evaluation period from 1991q2 to 2010q1, we demonstrate that a system of bivariate VARs produces well-calibrated ensemble densities for inflation, in contrast to univariate autoregressive benchmarks. The implied nowcast densities for the output gap are multimodal and indicate a considerable degree of uncertainty. For example, we assess the probability of a negative output gap at around 45% between 2004 and 2007. Despite the Greenspan policy regime, there still remained a substantial risk that the nowcast for output was below potential in real time. We extend our methodology to include distinct output gap measures, based on alternative filters, and show that, in our application, the nowcast density for the output gap is sensitive to the detrending method.     

Nowcasting food inflation with a massive amount of online prices

The consensus in the literature on providing accurate inflation forecasts underlines the importance of precise nowcasts. In this paper, we focus on this issue by employing a unique, extensive dataset of online food and non-alcoholic beverages prices gathered automatically from the webpages of major online retailers in Poland since 2009. We perform a real-time nowcasting experiment by using a highly disaggregated framework among popular, simple univariate approaches. We demonstrate that pure estimates of online price changes are already effective in nowcasting food inflation, but accounting for online food prices in a simple, recursively optimized model delivers further gains in the nowcast accuracy. Our framework outperforms various other approaches, including judgmental methods, traditional benchmarks, and model combinations. After the outbreak of the COVID-19 pandemic, its nowcasting quality has improved compared to other approaches and remained comparable with judgmental nowcasts. We also show that nowcast accuracy increases with the volume of online data, but their quality and relevance are essential for providing accurate in-sample fit and out-of-sample nowcasts. We conclude that online prices can markedly aid the decision-making process at central banks.     

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.     

Daily news sentiment and monthly surveys: A mixed-frequency dynamic factor model for nowcasting consumer confidence

Policymakers, firms, and investors closely monitor traditional survey-based consumer confidence indicators and treat them as an important piece of economic information. To obtain a daily nowcast of monthly consumer confidence, we introduce a latent factor model for the vector of monthly survey-based consumer confidence and daily sentiment embedded in economic media news articles. The proposed mixed-frequency dynamic factor model uses a Toeplitz correlation matrix to account for the serial correlation in the high-frequency sentiment measurement errors. We find significant accuracy gains in nowcasting survey-based Belgian consumer confidence with economic media news sentiment.     

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.     

Nowcasting Indian GDP

Nowcasting has become a useful tool for making timely predictions of gross domestic product (GDP) in a data‐rich environment. However, in developing economies this is more challenging due to substantial revisions in GDP data and the limited availability of predictor variables. Taking India as a leading case, we use a dynamic factor model nowcasting method to analyse these two issues. Firstly, we propose to compare nowcasts of the first release of GDP to those of the final release to assess differences in their predictability. Secondly, we expand a standard set of predictors typically used for nowcasting GDP with nominal and international series, in order to proxy the variation in missing employment and service sector variables in India. We find that the factor model improves over several benchmarks, including bridge equations, but only for the final GDP release and not for the first release. Also, the nominal and international series improve predictions over and above real series. This suggests that future studies of nowcasting in developing economies which have similar issues of data revisions and availability as India should be careful in analysing first‐ vs. final‐release GDP data, and may find that predictions are improved when additional variables from more timely international data sources are included.     

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.     

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.     

Real‐Time Nowcasting of GDP: A Factor Model vs. Professional Forecasters

We perform a fully real‐time nowcasting (forecasting) exercise of US GDP growth using Giannone et al.'s (2008) factor model framework. To this end, we have constructed a real‐time database of vintages from 1997 to 2010 for a panel of variables, enabling us to reproduce, for any given day in that range, the exact information that was available to a real‐time forecaster. We track the daily evolution of the model performance along the real‐time data flow and find that the precision of the nowcasts increases with information releases and the model fares well relative to the Survey of Professional Forecasters (SPF).     

Forecast Pooling for European Macroeconomic Variables*

We compare alternative forecast pooling methods and 58 forecasts from linear, time‐varying and non‐linear models, using a very large dataset of about 500 macroeconomic variables for the countries in the European Monetary Union. On average, combination methods work well but single non‐linear models can outperform them for several series. The performance of pooled forecasts, and of non‐linear models, improves when focusing on a subset of unstable series, but the gains are minor. Finally, on average over the EMU countries, the pooled forecasts behave well for industrial production growth, unemployment and inflation, but they are often beaten by non‐linear models for each country and variable.