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.     

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.     

Forecasting Euro‐Area Macroeconomic Variables Using a Factor Model Approach for Backdating

We suggest to use a factor model based backdating procedure to construct historical Euro‐area macroeconomic time series data for the pre‐Euro period. We argue that this is a useful alternative to standard contemporaneous aggregation methods. The article investigates for a number of Euro‐area variables whether forecasts based on the factor‐backdated data are more precise than those obtained with standard area‐wide data. A recursive pseudo‐out‐of‐sample forecasting experiment using quarterly data is conducted. Our results suggest that some key variables (e.g. real GDP, inflation and long‐term interest rate) can indeed be forecasted more precisely with the factor‐backdated data.     

Predictive financial models of the euro area: A new evaluation test

This paper investigates the predictive ability of financial variables for euro area growth. Our forecasts are built from univariate autoregressive and single equation models. Euro area aggregate forecasts are constructed both by employing aggregate variables and by aggregating country-specific forecasts. The forecast evaluation is based on a recently developed test for equal predictive ability between nested models. Employing a monthly dataset from the period between January 1988 and May 2005 and setting the out-of-sample period to be from 2001 onwards, we find that the single most powerful predictor on a country basis is the stock market returns, followed by money supply growth. However, for the euro area aggregate, the set of most powerful predictors includes interest rate variables as well. The forecasts from pooling individual country models outperform those from the aggregate itself for short run forecasts, while for longer horizons this pattern is reversed. Additional benefits are obtained when combining information from a range of variables or combining model forecasts.     

Automated Model Selection in Finance: General‐to‐Specific Modelling of the Mean and Volatility Specifications*

General‐to‐Specific (GETS) modelling has witnessed major advances thanks to the automation of multi‐path GETS specification search. However, the estimation complexity associated with financial models constitutes an obstacle to automated multi‐path GETS modelling in finance. Making use of a recent result we provide and study simple but general and flexible methods that automate financial multi‐path GETS modelling. Starting from a general model where the mean specification can contain autoregressive terms and explanatory variables, and where the exponential volatility specification can include log‐ARCH terms, asymmetry terms, volatility proxies and other explanatory variables, the algorithm we propose returns parsimonious mean and volatility specifications.     

Can the random walk model be beaten in out-of-sample density forecasts? Evidence from intraday foreign exchange rates

It has been documented that random walk outperforms most economic structural and time series models in out-of-sample forecasts of the conditional mean dynamics of exchange rates. In this paper, we study whether random walk has similar dominance in out-of-sample forecasts of the conditional probability density of exchange rates given that the probability density forecasts are often needed in many applications in economics and finance. We first develop a nonparametric portmanteau test for optimal density forecasts of univariate time series models in an out-of-sample setting and provide simulation evidence on its finite sample performance. Then we conduct a comprehensive empirical analysis on the out-of-sample performances of a wide variety of nonlinear time series models in forecasting the intraday probability densities of two major exchange rates—Euro/Dollar and Yen/Dollar. It is found that some sophisticated time series models that capture time-varying higher order conditional moments, such as Markov regime-switching models, have better density forecasts for exchange rates than random walk or modified random walk with GARCH and Student-t innovations. This finding dramatically differs from that on mean forecasts and suggests that sophisticated time series models could be useful in out-of-sample applications involving the probability density.     

Bayesian Model Averaging and exchange rate forecasts

Exchange rate forecasting is hard and the seminal result of Meese and Rogoff [Meese, R., Rogoff, K., 1983. Empirical exchange rate models of the seventies: Do they fit out of sample? Journal of International Economics 14, 3–24] that the exchange rate is well approximated by a driftless random walk, at least for prediction purposes, still stands despite much effort at constructing other forecasting models. However, in several other macro and financial forecasting applications, researchers in recent years have considered methods for forecasting that effectively combine the information in a large number of time series. In this paper, I apply one such method for pooling forecasts from several different models, Bayesian Model Averaging, to the problem of pseudo out-of-sample exchange rate predictions. For most currency–horizon pairs, the Bayesian Model Averaging forecasts using a sufficiently high degree of shrinkage, give slightly smaller out-of-sample mean square prediction error than the random walk benchmark. The forecasts generated by this model averaging methodology are however very close to, but not identical to, those from the random walk forecast.     

Multivariate Small Area Estimation of Multidimensional Latent Economic Well-being Indicators

Factor analysis models are used in data dimensionality reduction problems where the variability among observed variables can be described through a smaller number of unobserved latent variables. This approach is often used to estimate the multidimensionality of well-being. We employ factor analysis models and use multivariate empirical best linear unbiased predictor (EBLUP) under a unit-level small area estimation approach to predict a vector of means of factor scores representing well-being for small areas. We compare this approach with the standard approach whereby we use small area estimation (univariate and multivariate) to estimate a dashboard of EBLUPs of the means of the original variables and then averaged. Our simulation study shows that the use of factor scores provides estimates with lower variability than weighted and simple averages of standardised multivariate EBLUPs and univariate EBLUPs. Moreover, we find that when the correlation in the observed data is taken into account before small area estimates are computed, multivariate modelling does not provide large improvements in the precision of the estimates over the univariate modelling. We close with an application using the European Union Statistics on Income and Living Conditions data.     

Evaluation of the best M4 competition methods for small area population forecasting

The ‘M4’ forecasting competition results were featured recently in a special issue of the International Journal of Forecasting and included projections for demographic time series. We sought to investigate whether the best M4 methods could improve the accuracy of small area population forecasts, which generally suffer from much higher forecast errors than regions with larger populations. The aim of this study was to apply the top ten M4 forecasting methods to produce 5- and 10-year forecasts of small area total populations using historical datasets from Australia and New Zealand. Forecasts were compared against the actual population numbers and forecasts from two simple benchmark models. The M4 methods were found to perform relatively well compared to our benchmarks. In the light of these findings, we discuss possible future directions for small area population forecasting research.     

Combining Forecasts from Nested Models*

Motivated by the common finding that linear autoregressive models often forecast better than models that incorporate additional information, this paper presents analytical, Monte Carlo and empirical evidence on the effectiveness of combining forecasts from nested models. In our analytics, the unrestricted model is true, but a subset of the coefficients is treated as being local‐to‐zero. This approach captures the practical reality that the predictive content of variables of interest is often low. We derive mean square error‐minimizing weights for combining the restricted and unrestricted forecasts. Monte Carlo and empirical analyses verify the practical effectiveness of our combination approach.     

Measuring Synchronization and Convergence of Business Cycles for the Euro area,UK and US*

This paper investigates business cycle relations among different economies in the Euro area. Cyclical dynamics are explicitly modelled as part of a time series model. We introduce mechanisms that allow for increasing or diminishing phase shifts and for time‐varying association patterns in different cycles. Standard Kalman filter techniques are used to estimate the parameters simultaneously by maximum likelihood. The empirical illustrations are based on gross domestic product (GDP) series of seven European countries that are compared with the GDP series of the Euro area and that of the US. The original integrated time series are band‐pass filtered. We find that there is an increasing resemblance between the business cycle fluctuations of the European countries analysed and those of the Euro area, although with varying patterns.     

Modelling and forecasting government bond spreads in the euro area: A GVAR model

This paper proposes an extension to Global Vector Autoregressive (GVAR) models to capture time-varying interdependence among financial variables. Government bond spreads in the euro area feature a time-varying pattern of co-movement that poses a serious challenge for econometric modelling and forecasting. This pattern of the data is not captured by the standard specification that model spreads as persistent processes reverting to a time-varying mean determined by two factors: a local factor, driven by fiscal fundamentals and growth, and a global world factor, driven by the market’s appetite for risk. This paper argues that a third factor, expectations of exchange rate devaluation, gained traction during the crises. This factor is well captured via a GVAR that models the interdependence among spreads by making each country’s spread function of global European spreads. Global spreads capture the exposure of each country’s spread to other spreads in the euro area in terms of the time-varying ‘distance’ between their fiscal fundamentals. This new specification dominates the standard one in modelling the time-varying pattern of co-movements among spreads and the response of euro area spreads to the Greek debt crisis.     

Does the Phillips curve help to forecast euro area inflation?

We find that it does, but choosing the right specification is not trivial. Based on an extensive forecast evaluation we document notable forecast instabilities for most simple Phillips curves. Euro area inflation was particularly hard to forecast in the run-up to the Economic and Monetary Union and after the sovereign debt crisis, when the trends—and, for the latter period, also the amount of slack—were harder to pin down. Yet, some specifications outperform a univariate benchmark and point to the following lessons: (i) the key type of time variation to consider is an inflation trend; (ii) a simple filter-based output gap works well, but after the Great Recession it is outperformed by endogenously estimated slack or by “institutional” estimates; (iii) external variables do not bring forecast gains; (iv) newer-generation Phillips curve models with several time-varying features are a promising avenue for forecasting; and (v) averaging over a wide range of modelling choices helps.     

Forecasting small area populations with long short-term memory networks

Local and state governments depend on small area population forecasts to make important decisions concerning the development of local infrastructure and services. Despite their importance, current methods often produce highly inaccurate forecasts. Recent years have witnessed promising developments in time series forecasting using Machine Learning across a wide range of social and economic variables. However, limited work has been undertaken to investigate the potential application of Machine Learning methods in demography, particularly for small area population forecasting. In this paper we describe the development of two Long-Short Term Memory network architectures for small area populations. We employ the Keras Tuner to select layer unit numbers, vary the window width of input data, and apply a double training and validation regime which supports work with short time series and prioritises later sequence values for forecasts. These methods are transferable and can be applied to other data sets. Retrospective small area population forecasts for Australia were created for the periods 2006–16 and 2011–16. Model performance was evaluated against actual data and two benchmark methods (LIN/EXP and CSP-VSG). We also evaluated the impact of constraining small area population forecasts to an independent national forecast. Forecast accuracy was influenced by jump-off year, constraining, area size, and remoteness. The LIN/EXP model was the best performing method for the 2011-based forecasts whilst deep learning methods performed best for the 2006-based forecasts, including significant improvements in the accuracy of 10 year forecasts. However, benchmark methods were consistently more accurate for more remote areas and for those with populations <5000.     

Forecast Encompassing and Parameter Estimation*

A desirable property of a forecast is that it encompasses competing predictions, in the sense that the accuracy of the preferred forecast cannot be improved through linear combination with a rival prediction. In this paper, we investigate the impact of the uncertainty associated with estimating model parameters in‐sample on the encompassing properties of out‐of‐sample forecasts. Specifically, using examples of non‐nested econometric models, we show that forecasts from the true (but estimated) data generating process (DGP) do not encompass forecasts from competing mis‐specified models in general, particularly when the number of in‐sample observations is small. Following this result, we also examine the scope for achieving gains in accuracy by combining the forecasts from the DGP and mis‐specified models.     

Forecasting large datasets with Bayesian reduced rank multivariate models

The paper addresses the issue of forecasting a large set of variables using multivariate models. In particular, we propose three alternative reduced rank forecasting models and compare their predictive performance for US time series with the most promising existing alternatives, namely, factor models, large‐scale Bayesian VARs, and multivariate boosting. Specifically, we focus on classical reduced rank regression, a two‐step procedure that applies, in turn, shrinkage and reduced rank restrictions, and the reduced rank Bayesian VAR of Geweke ( 1996 ). We find that using shrinkage and rank reduction in combination rather than separately improves substantially the accuracy of forecasts, both when the whole set of variables is to be forecast and for key variables such as industrial production growth, inflation, and the federal funds rate. The robustness of this finding is confirmed by a Monte Carlo experiment based on bootstrapped data. We also provide a consistency result for the reduced rank regression valid when the dimension of the system tends to infinity, which opens the way to using large‐scale reduced rank models for empirical analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

Forecasting interest rates with shifting endpoints

We consider forecasting the term structure of interest rates with the assumption that factors driving the yield curve are stationary around a slowly time‐varying mean or ‘shifting endpoint’. The shifting endpoints are captured using either (i) time series methods (exponential smoothing) or (ii) long‐range survey forecasts of either interest rates or inflation and output growth, or (iii) exponentially smoothed realizations of these macro variables. Allowing for shifting endpoints in yield curve factors provides substantial and significant gains in out‐of‐sample predictive accuracy, relative to stationary and random walk benchmarks. Forecast improvements are largest for long‐maturity interest rates and for long‐horizon forecasts. Copyright © 2013 John Wiley & Sons, Ltd.     

Periodically expanding discounted debt: a threat to fiscal policy sustainability?

This paper models the behaviour of discounted US debt using a Markov‐switching time series model. The significance of modelling fiscal policy within this framework derives from the implications it has for long‐term sustainability. The two‐regime framework used in this paper identifies periods where the present value of US Federal debt is expanding versus periods when it is collapsing. Using an updated data series from Hamilton and Flavin ( 1986 ), a test is conducted to establish if the expanding periods pose a threat to the long‐run sustainability of fiscal policy. For the USA, it is found that they do not. Copyright © 2005 John Wiley & Sons, Ltd.     

Determination of Long‐run and Short‐run Dynamics in EC‐VARMA Models via Canonical Correlations

This article studies a simple, coherent approach for identifying and estimating error‐correcting vector autoregressive moving average (EC‐VARMA) models. Canonical correlation analysis is implemented for both determining the cointegrating rank, using a strongly consistent method, and identifying the short‐run VARMA dynamics, using the scalar component methodology. Finite‐sample performance is evaluated via Monte Carlo simulations and the approach is applied to modelling and forecasting US interest rates. The results reveal that EC‐VARMA models generate significantly more accurate out‐of‐sample forecasts than vector error correction models (VECMs), especially for short horizons. Copyright © 2015 John Wiley & Sons, Ltd.     

Principal components at work: the empirical analysis of monetary policy with large data sets

The empirical analysis of monetary policy requires the construction of instruments for future expected inflation. Dynamic factor models have been applied rather successfully to inflation forecasting. In fact, two competing methods have recently been developed to estimate large‐scale dynamic factor models based, respectively, on static and dynamic principal components. This paper combines the econometric literature on dynamic principal components and the empirical analysis of monetary policy. We assess the two competing methods for extracting factors on the basis of their success in instrumenting future expected inflation in the empirical analysis of monetary policy. We use two large data sets of macroeconomic variables for the USA and for the Euro area. Our results show that estimated factors do provide a useful parsimonious summary of the information used in designing monetary policy. Copyright © 2005 John Wiley & Sons, Ltd.