Introduction

Our aim with this book is to present an overview of the theory and methods underlying forecasting as currently practiced in economics and finance, but more widely applicable to a great range of forecasting problems. We hope to provide an overview that is useful to practitioners in places such as central banks and financial institutions, academic researchers as well as graduate students seeking a point of entry into the field. The assumed econometric level of the reader is that of someone who has taken a graduate or advanced undergraduate course in econometrics.

Whenever a forecast is being constructed or evaluated, an overriding concern revolves around the practical problem that the best forecasting model is not only unknown but also unlikely to be known well enough to even correctly specify forecasting equations up to a set of unknown parameters. We view this as the only reasonable description of the forecaster’s problem. Some methods do claim to find the correct model (oracle methods) as the sample gets very large. However, in any problem with a finite sample there is always a set of models—as opposed to a single model—that are consistent with the data. Moreover, in many situations the data generating process changes over time, further emphasizing the difficulty in obtaining very large samples of observations on which to base a model. These foundations— using misspecified models to forecast outcomes generated by a process that may be evolving over time—generate many of the complications encountered in forecasting. If the true models were fully known apart from the values of the parameters, Bayesian methods could be used to construct density and point forecasts that, for a given loss function, would be difficult or impossible to beat in practice.

Without knowing the true data-generating process, the problem of constructing a good forecasting method becomes much more difficult. Oftentimes very simple (and clearly misspecified) methods provide forecasts that outperform more complicated methods that seek to exploit the data in ways we would expect to be important and advantageous. As a case in point, simple averages of forecasts from many models, even ones that on their own do not seem to be very good, are often found empirically to outperform carefully chosen model averages or the best individual models.

1.1 OUTLINE OF THE BOOK

The approach of this book is for the most part based on forecasting as a decision theoretic problem. By this we mean that the forecaster has a specific objective in mind (i.e., wishes to make a decision) and wants to base this decision on some data. Setting up this approach comprises most of the first part of the book. This part details the basic elements of the decision problem, with chapters on the decision maker’s loss function, forecasting as a decision-theoretic problem, and an overview of general approaches to forecasting employing either classical or Bayesian methods. This part of the book provides foundations for understanding how different methods fit together. We also provide details of methods that are subsequently applied to many of the issues examined in the next part of the book, e.g., model selection and forecast combination.

The second part of the book reviews various approaches to constructing forecasting models. Methods employed differ for many reasons: lack of relevant data or the existence of a great deal of potentially relevant data, as well as assumptions made on functional forms for the models. In these chapters we attempt, as far as possible, to present the methods in enough detail that they can be employed without reference to other sources.

The third part of the book examines the evaluation of forecasts, while the fourth part covers forecasting models that deal with special complications such as model instability (breaks) and highly persistent (trending) data. This part also discusses data structures of special interest to forecasters, including real-time data (revised data) and data collected at different frequencies.

Finally, the fourth part of the book presents various extensions and refinements to the forecasting methods covered in the earlier parts of the book, including forecasting under model instability, long-run forecasting, and forecasting with data that either take a non-standard form (count data and durations) or are measured at irregular intervals and are subject to revisions.