Book reviews 641

Alan Pankratz, 1991, Forecasting with Dynamic Regression Models (John Wiley and Sons, New York), ISBN O-471-61528-5, g47.50.

The title of this book is misleading. The book is about an extension of univariate Box-Jenkins models which Box and Jenkins refer to as “com- bined transfer function-disturbance” models. In these models a variable to be forecast is mod- elled as a linear function of its own lagged values and a distributed lag of one or more independent variables, plus a disturbance modelled as an ARIMA process. Pankratz chooses to call this a dynamic regression model, an unfortunate choice of terminology because it courts confusion with the autoregressive distributed lag models that characterize the modern econometric approach to time series analysis.

Even more unfortunate is the fact that Pan- kratz has chosen not to inform his readers about the existence, let alone the details, of this com- peting dynamic regression methodology. 1 can only speculate that he feels that the differences between the two methodologies are so great that describing the competition would confuse more than enlighten. I cannot agree with this; in my view an author has a moral responsibility to inform readers of the intellectual context of the methodology he is teaching. A title such as ‘Forecasting with Transfer Functions’ would have avoided this problem; with its current title, a chapter is missing from this book.

What would this missing chapter contain? The regression model, or econometric, approach to forecasting did not fare well in the 1970s when competing with Box-Jenkins ARIMA forecasts. One response to this by econometricians was to develop a synthesis of the econometric and Box- Jenkins methodologies, showing that economet- ric regression models could be viewed as Box- Jenkins models in which a priori restrictions suggested by economic theory have been im- posed on the parameters. Econometricians then claimed that their failure to match Box-Jenkins forecasts was due to the imposition of inapprop- riate constraints, not to any basic flaw in their methodology.

Economic theory has some ability to identify long-run relationships between economic vari- ables, as created by equilibrium forces, but is of little help regarding the specification of time lags

and dynamic adjustments. Viewed from this per- spective, ARIMA models were successful be- cause they were very flexible in their specifica- tion of the dynamics, but contained a potential flaw in that they ignored completely information that economic theory could offer concerning the role of long-run equilibria. Recognizing this, modern dynamic regression models of economet- ricians have allowed for a very flexible lag struc- ture by permitting the data to play a stronger role in the specification of the model’s dynamic structure, and have incorporated the role of long-run equilibria by adding an ‘error-correc- tion term’ representing the extent to which the long-run equilibrium is not met. This exploits the concept of cointegration and leads to models which mix levels and differences, impossible in an ARIMA model since stationarity is achieved by differencing all non-stationary variables, with the consequent loss of long-run information pro- vided by the levels data.

The error correction model of the econometri- cians, couched in the mold of an autoregressive distributed lag model, could be viewed as a movement from the original, discredited, econometric regression model towards the more dynamically flexible Box-Jenkins model, but without fully adopting its atheoretical character. The Pankratz dynamic regression model could be viewed as a movement away from the Box- Jenkins model by incorporating explanatory vari- ables, but in a way which retains the atheoretical flavor of the Box-Jenkins approach. But despite this movement towards each other, these two regression approaches have more differences than similarities, perhaps most dramatically illus- trated by the fact that a need to model the error term with an ARIMA structure is an integral part of the Pankratz methodology, whereas in the econometric approach it is interpreted as reflecting a specification error, requiring a re- formulation of the model.

Enough of what the Pankratz book does not do. What about what it does do? To this re- viewer, who has always found the transfer func- tion analysis of Box and Jenkins difficult, even in its alleged easy form with only one explanatory variable, Pankratz does a wonderful job of de- scribing an alternative, much clearer and more sensible way of specifying transfer functions. The transfer function model is written as an au-

toregressive rational distributed lag regression model with an ARIMA disturbance. In this for- mat, extensions such as intervention analysis, incorporation of additional explanatory vari- ables. and detection of outliers are straight- forward. and Pankratz does a good job of ex- plaining them. He succeeds because he has omit- ted technical derivations and has provided lots of detailed examples, pitching the book at the level of the student, not the professor. In this respect it is an admirable sequel to his 1983 book on univariate Box-Jenkins models.

Pankratz claims that this book could be used as a text for undergraduate students who have had only one course in statistics. With Pankratz as the instructor I do not doubt this is feasible. but I would hesitate before asking my students to work through this book without knowledge of univariate Box-Jenkins and multiple regression. Although in early chapters Pankratz provides primers on ARIMA models and on regression, I found they were sensible to me only because I already knew the material: one new thing en-

countered, the extended autocorrelation func- tion, I never did understand. Teaching from this book would require appropriate software not provided with the book; several software sources are cited in the preface.

This book is not, as its title implies, an exposi- tion of forecasting with dynamic regression mod- els; readers will learn nothing about error correc- tion models, cointegration, unit root tests, COMFAC analysis or encompassing, to name but a few features of modern econometric dy- namic regression models. What readers will find is a clear presentation, at an elementary level, of a regression-based variant of Box-Jenkins trans- fer functions, supplemented with an excellent set of worked-out examples.

Peter Kennedy Simon Fraser lJniversit)l

Burnaby, B. C., Cunuda