Time Series and Dynamic Models, CHRISTIAN GOURIEROUX AND ALAIN MONFORT, CambridgeUniversity Press, Cambridge, 1997, ISBN 0-521-41146-7 (hardbound), ISBN 0-521-42308-2 (paperback),

pp. xv � 668. Price £65.00 (hardbound), £22.95 (paperback).

This is the third volume in a relatively new series begun in 1995 called Themes in Modern Econometrics,produced by Cambridge University Press under the editorship of Peter Phillips and Adrian Pagan (with

Christian Gourieroux and Mike Wickens as advisory editors). As with the ®rst two books in the series, thisvolume is also written by Christian Gourieroux and Alain Monfort, two of France's leading econo-

metricians, and is also a translation from a French volume originally published in 1990. Although the most

recent paper in the list of references is one published in 1992, it would appear that the volume is a puretranslation with no serious updating attempted (other than for referenced papers that were subsequently

published). Giampiero Gallo was responsible for the translation (and editing), and has done a creditable

job in providing a readable translation.At what market is this book aimed? The Themes in Modern Econometrics series aims to `provide an

organised sequence of textbooks in econometrics aimed squarely at the student population . . . written at a

level accessible to students in an introductory course in econometrics behind them . . . the distinct emphasisthroughout will be on pedagogic excellence' (p. iv). However, this book widely misses the mark in terms of

the level of knowledge assumed, and also in the exposition of material. While it may be accessible to French

students who have taken an introductory econometrics course, this will certainly not be the case for moststudents in Australia, Canada, Japan, New Zealand, the UK, or the USA. In terms of pedagogy, the

emphasis on theory and presenting results as theorems is far too heavy ( for example, there are 33 theorems

in Chapter 9, and 26 in Chapter 8!), and the essential motivation of results and ideas is lacking in places. Insome cases, the reasons why some of the theorems are introduced are not obvious. While some of the

techniques are illustrated with empirical examples, even good students would often be at a loss about how

to implement some of the procedures in practice.Following an introductory chapter, the book is divided into four parts on: Traditional Methods

(3 chapters covering 98 pages); Probabilistic and Statistical Properties of Stationary Processes (5 chapters,

233 pages); Time Series Econometrics and Nonstationary Models (5 chapters, 217 pages); and State-SpaceModels (2 chapters, 62 pages). Parts 2 and 3 form the core of the volume. One slightly annoying feature of

these two parts is that, from chapter to chapter, the focus switches back and forth between univariate and

multivariate models.The ®rst chapter introduces the notion of what a time-series is, and provides some illustrations. Although

®ve sets of data are discussed, the data for only two of them, namely nine years of monthly observations on

the French consumer price index (1970±78) and eighteen years of monthly data on second-class passengertra�c on the French National Railway (1963±80), are actually displayed. This may be appropriate for a

French audience, but I doubt that it will be true more generally for an international clientele. The authorsuse this chapter to highlight some of the issues that are discussed in detail in later chapters, such as trend

removal, seasonal adjustment, detection of structural breaks, causality, and the distinction between the

short run and long run.

CCC 0883±7252/98/060681±04$17.50 Received 3 September 1998# 1998 John Wiley & Sons, Ltd.

JOURNAL OF APPLIED ECONOMETRICS

J. Appl. Econ., 13, 681±684 (1998)

The ®rst traditional method discussed in Part 1 is the use of the linear regression model for seasonal

adjustment (Chapter 2), where the assumption is that the time-series is made up of three additive compo-

nents, namely, trend component, seasonal component and a random error. It is assumed further that thetrend and seasonal components can be written as known functions, so that the models can be estimated by

ordinary least squares. Given the assumption that students have already been exposed to an introductoryeconometrics course, it is unfortunate that a review of the properties of the linear regression model, and a

demonstration that many of the well-known results introduced ( for example, Salkever's result on the use of

dummy variables for prediction) are merely special cases of more general results, is not presented. Di�erenttransformations of the dependent variable, such as log (called the multiplicative model) and the logistic

transformation are introduced, but there is no examination of how the choice between these two and the

untransformed variable might be made. The discussion of outliers suggests that, if standardized residualsare greater than two in absolute value, then an outlier has been detected, without any indication that this

may merely re¯ect a problem with the estimated model itself! Serial correlation in the form of auto-

regressions is analysed, and the Durbin±Watson test and Cochrane±Orcutt transformation are both intro-duced, with no warnings as to their use when lagged dependent variables are present. Most of this chapter

assumes a knowledge of matrix algebra, and in some places Kronecker products.

Two of the motivations for the use of moving average models for seasonal adjustment, as compared withthe regression approach, are that the former enables simple updating when new data becomes available, and

is less sensitive to structural change. Following the introduction of several moving averages, including

Spencer and Henderson averages, one of the highlights is a step-by-step explanation of what exactly thequarterly X-11 program does to a series (but there is little explanation of or motivation for why these steps

are taken). This is one of the few times I have seen such a discussion in a textbook. A second highlight is the

demonstration of what happens to a white-noise process when it is transformed by a moving averagetransformation, and the Slutzky±Yule e�ect. Extensive use is made of the lag operator and the properties of

the lag operator are assumed knowledge (surprisingly, no reference is made to Section 5.2 in Chapter 5,

which provides an introduction to the properties of lead and lag operators). A short chapter is devoted toexponential smoothing methods, including simple exponential smoothing, double exponential smoothing

and the Holt±Winters non-seasonal and seasonal methods. There are no empirical applications of these

methods. Given the brief explanation of these methods, students would probably draw the conclusion thatthey are not especially important.

Chapters 5±9 in Part 2 on Probabilistic and Statistical Properties of Stationary Processes, are devoted to

univariate and multivariate ARMA and ARIMA models. No attempt is made to link the material in thispart to that in Chapters 2±4. The material introduced in Chapter 5 is fairly predictable, with covariance

stationarity, the autocorrelation and partial autocorrelation functions, the spectral density function, andinverse autocorrelation functions all being covered in quick succession. This is followed by discussions of

pure autoregressive models, pure moving average models, and autoregressive moving average models. There

is a brief explanation of how the orders of pure models might be selected using information from theautocorrelation, partial autocorrelation and inverse autocorrelation functions. The motivation for

considering ARIMA models is the rather bold (and not necessarily correct) statement that `it is apparent

that for most economic series, the stationarity hypothesis is not appropriate' (p. 167). At this stage, someeconomic illustrations of this argument would have been useful. On page 170 in the proof of Theorem 5.18,

a reference is made to a term `asymptotically stationary', but this is not de®ned until page 234 (there is no

forward reference).Chapter 6 discusses the four steps for the Box±Jenkins forecasting method of identi®cation, estimation,

validation and forecasting, although estimation is discussed before identi®cation. Estimation methods

covered include maximum likelihood, backcasting, and two-step methods. For the two-step methodsintroduced, there is no mention of the fact that these particular two stage estimators are ine�cient, that the

standard OLS formula standard errors are not consistent estimates for the true standard errors, or how

e�cient two-step methods might be computed, as in Hannan and Rissanen (1982). Unfortunately, thediscussion of unit-root testing is left to Chapter 14 so at this stage it is suggested that the decision on

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# 1998 John Wiley & Sons, Ltd. J. Appl. Econ., 13, 681±684 (1998)

whether to di�erence the data depends on how close to unity are the estimates of the autocorrelation

function. Although there are procedures for testing between non-nested ARMA models, and Monte Carlo

results that suggest nesting of models within a larger general model is generally not the powerful testingprocedure (see McAleer et al., 1988), it is claimed that in order to carry out this comparison `it is convenient

to set up a situation where one of the models is a special case of other' (p. 194)! As a means of evaluatingthe selected model, both the Box±Pierce and the Ljung±Box tests are introduced. While the poor sample

properties of the former are noted, the relatively poor sample properties of the latter are not (see Godfrey,

1979). Despite their extensive use in practice, information criteria receive scant attention. Eight pages aredevoted to an application of the Box±Jenkins forecasting method to the French railway passenger tra�c

series, but no mention is made of the fact that for two of the twelve forecasts produced for this model, the

realized values fall outside the con®dence interval for the forecast. Seasonality in this series is handled by aseasonal di�erence, but the observant reader will wonder how this treatment relates to the methods

discussed in earlier chapters.

The focus in the next two chapters is on multivariate models. Chapter 7 is a relatively short chapterdevoted to multiple time-series, the de®nition of stationarity in a systems context, and the moving average

and autoregressive representations. There is also some emphasis on moving average models with Markov

coe�cients. Chapter 8 introduces stationary ARMA models and ARIMA processes. There is also a verybrief overview of the frequency domain approach for both univariate and multivariate models that would

have been more useful had it been earlier and more detailed.

There is another potentially confusing switch back to univariate models in Chapter 9. Despite havingdiscussed estimation and validation in the context of the Box±Jenkins methodology, Chapter 9 is devoted

to estimation and testing of stationary univariate models. This inevitably leads to some unnecessary

duplication of material. The properties of the periodogram and empirical autocovariances are described.Maximum likelihood estimation, in both the time and frequency domains, are discussed, as are the

asymptotic properties of the maximum likelihood estimates, and the three standard likelihood testing

principles. Expressions are obtained for the Lagrange Multiplier tests, but they are not su�ciently detailedto see how they can be computed easily in practice. There is a separate brief extension of maximum

likelihood methods to multivariate models. Although it can be demonstrated in a couple of lines of algebra

using Kruskal's Theorem, over two pages are spent showing that estimating an unrestricted vectorautoregression by generalized least squares and each equation by ordinary least squares will produce

identical results.

Chapters 10 and 11 revert to multivariate models. In a bivariate context, Chapter 10 covers the di�erentde®nitions of causality (such as Granger, Pierce±Haugh and Sims), measures of causality, and their

meaning in terms of multivariate autoregressive models. The careful reader will wonder what happens whenthere are three variables and whether the causality measures are changed. An empirical example relating to

German and French prices is used to illustrate measures of causality and their decompositions (with no

testing), but the data are not provided in the volume. The concepts of predeterminedness, strict exogeneityand non-causality are also related to one another. Chapter 11 treats the concepts of integration, cointegra-

tion, the Engle±Granger representation theorem, and fractional processes. Judging by the space devoted to

fractional processes, the authors obviously see this as an important area.Chapter 12 on expectations appears to be a little out of place. Following extremely brief introductions to

adaptive and naive expectations of less than a page in total, the bulk of the chapter is devoted to rational

expectations, and to methods for ®nding the solutions to dynamic rational expectations models withcurrent and/or future expectations. This chapter relies heavily on the authors' previous research in this area.

Speci®cation analysis is the subject of Chapter 13. After brief discussions of the three standard testing

principles, the idea of non-nested tests, and how to use the likelihood ratio test to choose the lag length in avector autoregression, the material in this chapter complements that in earlier chapters by discussing the

testing of non-causality, predeterminedness and exogeneity (Chapter 10), and the testing of the rational

expectations hypothesis (Chapter 12). It should be noted that the entire discussion is in terms of stationaryvariables.

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Chapter 14 on the statistical properties of non-stationary processes attempts to cover a wide range of

material in the space of a little over forty pages: the spurious regression problem, the problem of unit root

testing (including the Dickey±Fuller and Schmidt±Phillips tests), the problems raised by regressions withnon-stationary variables; and the Johansen and Engle±Granger tests for cointegration. There are also

several pages devoted to the determination of the order of integration in a fractional process to complementthe discussion in Chapter 11. The discussion of the Phillips±Perron test is all too brief, considering its

importance in the literature. Given the date of the French original, the discussion of material relating to

Johansen's (1988) procedure is essentially limited to the material in that paper. Unfortunately, there are noempirical illustrations of any of the techniques presented.

The ®nal part of the volume on state-space models consists of two chapters, the ®rst covering the

mechanics of state-space models: the measurement and updating equations, forecasting, ®xed intervalsmoothing and computation of the log-likelihood. The second chapter contains a set of applications to the

standard linear regression model to calculate recursive coe�cients and residuals, ARMA models,

unobserved components models, Harrison and Steven's structural models, the impact of missing data onlyin the context of a simple AR(1) model, and rational expectations models.

With the exception of the introductory chapter, each chapter contains a set of exercises which tend to be

theoretical in nature, and which will allow the reader to check on the understanding of the materialinvolved. Unfortunately, no solutions are provided for any of the exercises. While the book has 14 pages of

references, a lot of material is introduced without explicit reference to the literature, and many do not seem

to have been cited. For example, if a student were interested in learning more about the estimation ofautoregressive models with missing observations, the volume would be of no help. In many places, no

attribution is given for the detailed technical discussions or results. For example, in the eight pages

discussing Johansen's (1988) approach, the word Johansen appears once, and then only as a reference forwhere to ®nd the tables of critical values! Perhaps not surprisingly, there is no author index. There is a 4-

page subject index, but it is basic. Statistical tables are provided for the standard normal, t, F, Durbin±

Watson, Dickey±Fuller tests, and the Johansen tests for the rank of the cointegrating vector.Although this volume is unlikely to be competitive with the leading time series econometrics textbooks in

the market, it should have a useful place as a reference tool for researchers.

ACKNOWLEDGEMENTS

I would like to thank Michael McAleer for his detailed and extremely helpful comments and suggestions.

REFERENCES

Godfrey, L. G. (1979), `Testing the adequacy of a time series model', Biometrika, 66, 67±72.Hannan, E. J. and J. Rissanen (1982), `Recursive estimation of mixed autoregressive±moving average order',Biometrika, 69, 81±94.

Johansen, S. (1988), `Statistical analysis of cointegrating vectors', Journal of Economic Dynamics andControl, 12, 231±254.

McAleer, M., C. R. McKenzie and A. D. Hall (1988), `Testing separate time series models', Journal of TimeSeries Analysis, 9, 169±189.

COLIN MCKENZIE*

Osaka School of International Public PolicyOsaka University, 1-16 Machikaneyama

Toyonaka, Osaka 560-0043

JAPAN

* Correspondence to: Professor Colin McKenzie, Osaka School of International Public Policy, Osaka University, 1-16Machikaneyama, Toyonaka, Osaka 560-0043, Japan.

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# 1998 John Wiley & Sons, Ltd. J. Appl. Econ., 13, 681±684 (1998)