Michael P. Clements

Macroeconomic Forecasting With Mixed-Frequency Data

Many macroeconomic series, such as U.S. real output growth, are sampled quarterly, although potentially useful predictors are often observed at a higher frequency. We look at whether a mixed data-frequency sampling (MIDAS) approach can improve forecasts of output growth. The MIDAS specification used in the comparison uses a novel way of including an autoregressive term. We find that the use of monthly data on the current quarter leads to significant improvement in forecasting current and next quarter output growth, and that MIDAS is an effective way to exploit monthly data compared with alternative methods.

A comparison of the forecast performance of Markov-switching and threshold autoregressive models of US GNP

While there has been a great deal of interest in the modelling of non-linearities in economic time series, there is no clear consensus regarding the forecasting abilities of non-linear time-series models. We evaluate the performance of two leading non-linear models in forecasting post-war US GNP, the self-exciting threshold autoregressive model and the Markov-switching autoregressive model. Two methods of analysis are employed: an empirical forecast accuracy comparison of the two models, and a Monte Carlo study. The latter allows us to control for factors that may otherwise undermine the performance of the non-linear models.

EVALUATING THE FORECAST DENSITIES OF LINEAR AND NON-LINEAR MODELS: APPLICATIONS TO OUTPUT GROWTH AND UNEMPLOYMENT

In economics density forecasts are rarely available, and as a result attention has traditionally focused on poit forecasts of the mean and the use of mean square error statistics to represent the loss function. We extend the methods of forecasts density evaluation in Diebold, Gunther and Tay (1997) to compare linear and non-linear model based forecasts of US out put growth and changes in the unemployment rate.

Economic Forecasting: Some Lessons from Recent Research

This paper describes some recent advances and contributions to our understanding of economic forecasting. The framework we develop helps explain the findings of forecasting competitions and the prevalence of forecast failure. It constitutes a general theoretical background against which recent results can be judged. We compare this framework to a previous formulation, which was silent on the very issues of most concern to the forecaster. We describe a number of aspects which it illuminates, and draw out the implications for model selection. Finally, we discuss the areas where research remains needed to clarify empirical findings which lack theoretical explanations.

A Monte Carlo study of the forecasting performance of empirical SETAR models

In this paper we investigate the multi-period forecast performance of a number of empirical self exciting threshold autoregressive (SETAR) models that have been proposed in the literature for modeling exchange rates and GNP, amongst other variables. An indicator of when such models are likely to forecast well is suggested based on the serial dependence of regimes, as a means of distinguishing between types of nonlinearities that can be exploited for improved fit versus those that contribute to a better (relative to linear models) out-of-sample forecast performance. In our study the indicator provides a reasonable guide to those models which embody nonlinearities that may yield improved conditional mean forecasts.

The performance of alternative forecasting methods for SETAR models

We compare a number of methods that have been proposed in the literature for obtaining h-step ahead minimum mean square error forecasts for SETAR models. These forecasts are compared to those from an AR model. The comparison of forecasting methods is made using Monte Carlo simulation. The Monte Carlo method of calculating SETAR forecasts is generally at least as good as that of the other methods we consider. An exception is when the disturbances in the SETAR model come from a highly asymmetric distribution, when a Bootstrap method is to be preferred. An empirical application calculates multi-period forecasts from a SETAR model of US GNP using a number of the forecasting methods. We find that whether there are improvements in forecast performance relative to a linear AR model depends on the historical epoch we select, and whether forecasts are evaluated conditional on the regime the process was in at the time the forecast was made.

Business Cycle Asymmetries: Characterization and Testing Based on Markov-Switching Autoregressions

Tests for business cycle asymmetries are developed for Markov-switching autoregressive models. The tests of deepness, steepness, and sharpness are Wald statistics, which have standard asymptotics. For the standard two-regime model of expansions and contractions, deepness is shown to imply sharpness (and vice versa), whereas the process is always nonsteep. Two and three-state models of U.S. GNP growth are used to illustrate the approach, along with models of U.S. investment and consumption growth. The robustness of the tests to model misspecification, and the effects of regime-dependent heteroscedasticity, are investigated.

Decision-based Evaluation

Forecasts are generally made for a purpose. If we suppose an environment whereby agents make decisions (equivalently, select actions) based on a particular forecast, then we can evaluate that forecast in terms of its expected economic value (equivalently, expected loss), where the expectation is calculated using the actual probabilities of the states of nature. Typically, we might expect users to have different economic value (or loss) functions, so that the actions and expected losses induced by two rival sets of forecasts need not be such that each user’s expected economic value is maximized by the same set of forecasts. In Section 6.2 we show following Diebold et al. (1998)1 that only when a density forecast coincides with the true conditional density will it be optimal (in the sense of maximizing economic value) for all users regardless of their loss functions. This is a compelling reason to assess how well the forecast distribution matches the actual distribution, as in Section 5.2 — a forecast density that provides a close match to the true density can be used by all with equanimity, no matter what their individual loss functions. For decision-based evaluation in general we require the whole forecast density.

Empirical analysis of macroeconomic time series: VAR and structural models

VAR and structural econometric models have complementary roles in the modelling of macroeconomic time series. A constant parameter VAR, provided it is statistically well specified, constitutes a valid basis for testing hypotheses of dynamic specification, exogeneity, and a priori structure, thus facilitating model evaluation, as well as suggesting a potentially efficient model development strategy. Deterministic (e.g. trends and regime shifts) and stochastic (e.g. integrated variables) non-stationarities are analysable within this framework, and the Johansen maximum likelihood procedure for cointegrated systems is used in an analysis of the determination of earnings, prices, productivity, and unemployment in the U.K

Forecast combination and encompassing

Forecast combination is often found to improve forecast accuracy. This chapter considers different types of forecast combination and tests of forecast encompassing. The latter indicate when a combination is more accurate than an individual forecast ex post, in a range of circumstances: when the forecasts themselves are the objects of interest; when the forecasts are derived from models with unknown parameters; and when the forecast models are nested. We consider forecast encompassing tests which are framed in terms of the model’s estimated parameters and recognize that parameter estimation uncertainty affects forecast accuracy, as well as conditonal tests of encompassing. We also look at the conditions under which forecast encompassing can be established irrespective of the form of the loss function.