https://www.robjhyndman.com/papers/ijf25.pdf

25 years of time series forecasting

In this paper, we outline a version of the New Area-Wide Model (NAWM) of the euro area designed for use in the (Broad) Macroeconomic Projection Exercises regularly undertaken by ECB/Eurosystem staff. We present estimation results for the NAWM that are obtained by employing Bayesian inference methods and document the properties of the estimated model by reporting its impulse-response functions and forecast-error-variance decompositions, by inspecting the model-based sample moments, and by examining the model's forecasting performance relative to a number of benchmarks, including a Bayesian VAR. We finally consider several applications to illustrate the potential contributions the NAWM can make to forecasting and policy analysis.

The New Area-Wide Model of the Euro Area: A Micro-Founded Open-Economy Model for Forecasting and Policy Analysis

Historically, time series forecasts of economic variables have used only a handful of predictor variables, while forecasts based on a large number of predictors have been the province of judgmental forecasts and large structural econometric models. The past decade, however, has seen considerable progress in the development of time series forecasting methods that exploit many predictors, and this chapter surveys these methods. The first group of methods considered is forecast combination (forecast pooling), in which a single forecast is produced from a panel of many forecasts. The second group of methods is based on dynamic factor models, in which the comovements among a large number of economic variables are treated as arising from a small number of unobserved sources, or factors. In a dynamic factor model, estimates of the factors (which become increasingly precise as the number of series increases) can be used to forecast individual economic variables. The third group of methods is Bayesian model averaging, in which the forecasts from very many models, which differ in their constituent variables, are averaged based on the posterior probability assigned to each model. The chapter also discusses empirical Bayes methods, in which the hyperparameters of the priors are estimated. An empirical illustration applies these different methods to the problem of forecasting the growth rate of the U.S. index of industrial production with 130 predictor variables.

Forecasting with Many Predictors

Central banks and other forecasters are increasingly interested in various aspects of density forecasts However, recent sharp changes in macroeconomic volatility, including the Great Moderation and the more recent sharp rise in volatility associated with increased variation in energy prices and the deep global recession—pose significant challenges to density forecasting Accordingly, this paper examines, with real-time data, density forecasts of US GDP growth, unemployment, inflation, and the federal funds rate from Bayesian vector autoregression (BVAR) models with stochastic volatility The results indicate that adding stochastic volatility to BVARs materially improves the real-time accuracy of density forecasts This article has supplementary material online

Real-Time Density Forecasts From Bayesian Vector Autoregressions With Stochastic Volatility

This paper estimates and tests a new Keynesian small open economy model in the tradition of Christiano, Eichenbaum, and Evans (2005) and Smets and Wouters (2003) using Bayesian estimation techniques on Swedish data. To account for the switch to an inflation targeting regime in 1993 we allow for a discrete break in the central bank's instrument rule. A key equation in the model - the uncovered interest rate parity (UIP) condition - is well known to be rejected empirically. Therefore we explore the consequences of modifying the UIP condition to allow for a negative correlation between the risk premium and the expected change in the nominal exchange rate. The results show that the modification increases the persistence and volatility in the real exchange rate and that this model has an empirical advantage compared with the standard UIP specification.

/pdf/evaluating-an-estimated-new-keynesian-small-open-economy-pw34z9oc4m.pdf

Evaluating an Estimated New Keynesian Small Open Economy Model

There are many indications that formal methods are not used to their full potential by central banks today. In this paper we demonstrate how BVAR and DSGE models can be used to shed light on questions that policy makers deal with in practice using data from Sweden. We compare the forecast performance of BVAR and DSGE models with the Riksbank's official, more subjective forecasts, both in terms of the actual forecasts and root mean square errors. We also discuss how to combine model- and judgment-based forecasts, and show that the combined forecast performs well out-of-sample. In addition, we show the advantages of structural analysis and use the models for interpreting the recent development of the inflation rate using historical decompositions. Lastly, we discuss the monetary transmission mechanism in the formal models, using impulse response functions and conditional forecasts.

/pdf/modern-forecasting-models-in-action-improving-macroeconomic-2yz83pa7ej.pdf

Modern Forecasting Models in Action: Improving Macroeconomic Analyses at Central Banks

There are many indications that formal methods are not used to their full potential by central banks today. In this paper we demonstrate how BVAR and DSGE models can be used to shed light on questions that policy makers deal with in practice using data from Sweden. We compare the forecast performance of BVAR and DSGE models with the Riksbank's official, more subjective forecasts, both in terms of the actual forecasts and root mean square errors. We also discuss how to combine model- and judgment based forecasts, and show that the combined forecast performs well out-of-sample. In addition, we show the advantages of structural analysis and use the models for interpreting the recent development of the inflation rate using historical decompositions. Lastly, we discuss the monetary transmission mechanism in the formal models, using impulse response functions and conditional forecasts.

We consider forecast combination and, indirectly, model selection for VAR models when there is uncertainty about which variables to include in the model in addition to the forecast variables. The key difference from traditional Bayesian variable selection is that we also allow for uncertainty regarding which endogenous variables to include in the model. That is, all models include the forecast variables, but may otherwise have differing sets of endogenous variables. This is a difficult problem to tackle with a traditional Bayesian approach. Our solution is to focus on the forecasting performance for the variables of interest and we construct model weights from the predictive likelihood of the forecast variables. The procedure is evaluated in a small simulation study and found to perform competitively in applications to real world data.

/pdf/bayesian-forecast-combination-for-var-models-4r30j9x4fc.pdf

Bayesian Forecast Combination for VAR Models

When generating conditional forecasts in dynamic models it is common to impose the conditions as restrictions on future structural shocks. However, these conditional forecasts often ignore that there may be uncertainty about the future development of the restricted variables. Our paper therefore proposes a generalization such that the conditions can be given as the full distribution of the restricted variables. We demonstrate, in two empirical applications, that ignoring the uncertainty about the conditions implies that the distributions of the unrestricted variables are too narrow.

https://www.econstor.eu/bitstream/10419/83026/1/767915046.pdf

Density-conditional forecasts in dynamic multivariate models

The time trend and the distribution of malignant mesothelioma in Denmark are described on the basis of all notifications of cancer cases to the Danish Cancer Registry during the period 1943-1980. The age and sex adjusted incidence rates of pleural as well as peritoneal mesothelioma are increasing with time and reached in the latest 3-year registration period 1978-1980 a remarkably high total incidence of 14.7 cases per million men and 7.0 cases per million women. Towards the end of the observation period, however, the rate of increase was stagnating and for the younger age-groups even a fall in incidence of this malignancy was noted, perhaps reflecting the introduction of compulsory hygienic precautions in the handling of asbestos in Denmark. The incidence and time trend of peritoneal mesothelioma was similar among males and females while pleural mesothelioma was three times more common among males compared with females and showed an increase in incidence 15 years previous to females. For pleural mesothelioma in men notified through the 10-year period 1968, 1977, a significant excess was associated with residence in areas with high degrees of urbanization and in ship building towns.

Michael K. Andersson

Papers

Modern Forecasting Models in Action: Improving Macroeconomic Analyses at Central Banks

Modern Forecasting Models in Action: Improving Macroeconomic Analyses at Central Banks

Bayesian Forecast Combination for VAR Models

Density-conditional forecasts in dynamic multivariate models

Trend and distribution of mesothelioma in Denmark.