Rook reviews 271

me to what is to me the major shortcoming of

the book. Like most edited volumes. the spread of material is generally out of the control of the

editor which means inevitably patchy coverage of the financial markets. I am, however, surprised by the domination of stock-related instruments and the complete absence of the interest rate

futures markets. In 1990. both the JGB and EuroYen (the fastest growing contract in the world) futures contracts had higher volume than the Nikkei futures, and yet they were not even mentioned! Neither were the commodity mar- kets, despite Tocom being in the top 10 of futures exchanges, and Tokyo Sugar the leading soft commodity market. These quibbles aside, I welcome the book as an important and worth-

while contribution. It should be an obligatory reference for all researchers into the operations

of financial markets.

Richard Flavell Imperial College, London, UK

F.A.G. den Butter and M.M.G. Fase, Seasonal Adjustment as a Practical Problem (Elsevier, Amsterdam, 1991), pp. iv + 226, US$94.50, Df1165.00.

Seasonal adjustments as a subject of research probably has a relatively lowly status, and is sometimes unfairly regarded as a routine or mechanical exercise to be done before the seri- ous work gets done. But econometric model- builders have long been aware of the importance of seasonal adjustment when estimating dynamic econometric models. Serious biases can arise if, for example, inappropriate prior adjustment has been applied to the data before any attempt is made to identify the dynamic adjustment pro- cesses in the model.

It is still the case that all U.K. macro models are estimated with data which have been previ- ously seasonally adjusted, and it is still a com- mon practice to estimate dynamic models using prior adjusted data. The main reason for this continuing practice is that models are used to forecast seasonally adjusted variables, simply be- cause seasonally adjusted values are invariably

used in public discussions of the economy. Given this widespread use of adjusted data for model- ling, it is important to decide on the adequacy of

the adjustment method used. A further reason for paying considerable attention to seasonal ad- justment is the importance attached to monetary or other aggregates as leading indicators of short-term movements in the economy, seasonal- ly adjusted measures of which will be highly misleading if they are inappropriately adjusted. But how can we judge between alternative ad- justment techniques? It is this question which this monograph by den Butter and Fase is princi- pally about.

There are a number of distinct approaches to seasonally adjusting data, which are used to a greater or lesser extent. Of these the Bureau of Census method X-l 1 and its variants are prob- ably most familiar and widely used. Apart from the general problem of the best way to adjust a single series, other important issues about ad- justment procedures arise when more than one series is being considered for adjustment. This introduces the fundamental problem of seasonal- ly adjusting when data are subject to ‘balancing’ constraints, i.e. they are components which satis- fy an aggregate, such as the counterparts to the broad money definition. Finally, different meth- ods arc affected to a greater or lesser extent by additional data. What this book so excellently achieves is a clear presentation of these three elements: the methodology of adjustment proce- dures, the problems that arise in applying these to single and multiple series, and the evaluation of procedures as new data arise.

To be more specific about these problems, consider the general decomposition of a series Y,,; Y!, (i = months, j = year)

Y, = T, + St, + 4, 3

where T is the trend-cycle component, S the seasonal and I the irregular component.

Following den Butter and Fase, we may dis- tinguish seasonal adjustment methods according to whether they are mechanical, which apply a fixed procedure to each series being considered, and those methods which do not, and hence arc non-mechanical.

The most famous of what den Butter and Fase describe as mechanical method is X-l 1. which

has been in use since the 1960s. But as anyone who uses it will know, there arc a number of options to the standardiscd form of the method which are applied in practice, including whether to treat the seasonal as additive on multiplica- tive, and how to treat outliers.

X-l 1 is an interactive procedure which first computes an approximation to T,, by using a centred 12-term moving average. The deviations of Y from this are the first estimate of the combined seasonal and irregular component. For each month a five-term moving average, the first estimate of the seasonal index for that month, is derived by averaging. Then by adjusting the basic Y series by the estimated seasonal. the process of trend extraction and estimation of seasonal factors is repeated to get the final esti- mate of the scasonality series.

The X-l 1 method may be criticised because it is not based on an underlying statistical model. This is not true in the sense that it may be shown to conform with an underlying statistical model. It can be shown, for example, that X-11 can be approximated by a high-order ARIMA model dcpendcnt on a normally distributed (0, w’) error. This point, however. has to be treated with cart, since it does not mean that mechanical procedures are therefore equivalent to a statisti- cal one. A different, and more practical, criti- cism of this method (as with all methods based on computing moving averages) is that informa- tion is lost, and the procedure will tend to under- estimate the seasonal pattern at the beginning and at the end of a series. However, extensions to the method, most notably by Da&urn, are important attempts to overcome this [set Da&urn (1978)).

In the non-mechanical class, each series is adjusted using a time series model appropriate to the series concerned, unlike the previous section where a11 series are adjusted by a procedure with fixed characteristics. The most familiar procc- durc here is the ARIMA (autoregressive intc- grated moving average) model, advocated by Box and Jenkins. The general form of model for the variable y, is determined by Box-Jenkins identification procedures based on the time series properties of the data giving an ARIMA (11, d, q) 21; (P. D. Q) model. where d is the level of diffcrencing required to induce stationarity, and the order of the polynomial in the model is

given by p and q. In turn, the seasonal factors are given by L> - the order of seasonal dif- ferencing - and P and Q, which are the degrees of seasonal autoregression and moving average, respectively.

As already noted, an important variant of the X-l 1 procedure is the X-l 1 ARIMA developed by Da&urn, which attempts to deal with the sensitivity of X-l 1 estimates at the end of the sample data. Since the problem arises from the use of asymmetric weights in the moving aver- ages at the end (and the beginning) of the data, the X-11 ARIMA extrapolates the series by ARIMA forecasts (back casts) so that symmetric weighting can be used.

Burman’s MSX (minimum signal extraction) method is another important variant, this time of ARIMA modelling. where the decomposition of the series uses spectral analysis. Since this de- composition is not unique. the method is con- strained so that the adjustment takes out as little variation in the series as possible. (Hence it is called minimum signal extraction.)

A final example of non-mechanical modelling, and one which the book emphasises is structural time series models (STMs) which directly de- scribe the stochastic structure of the trend, sea- sonal and irregular component. Thus in terms of the decomposition above ( l), a general form of the STM model is

T, = T, , + T, + u, , (2)

7, = 7,-, + 14, 1 (3)

i.e. T is a function of a stochastic variable, as is the seasonal factor. Thus the stochastic variables u, and 14, and the irregular variable I, are the sources of stochastic variation in this model.

Estimation of STM models uses maximum likelihood methods, after first putting the model into a state-space form. Estimation of the SYS-

tern’s hyperparameters (essentially the ratios of variances of u, and II,) uses a prediction error decomposition and the Kalman Filter, and pro- cedures for estimating models such as these have been extensively described by Harvey [Harvey (1981, lW)].

Estimating seasonal factors in a single series is one matter. But in many cases data obey adding- up constraints, so the seasonally adjusted series needs to satisfy constraints too.

273

This problem arises once seasonal adjustment is applied to a set of variables, and is particularly relevant to monetary data. Balancing constraints arise in two ways. One concerns definitional constraints. For example, the counterparts of M4 is an example of an accounting definition which must apply before and after adjustment.

A further way in which adding-up constraints arise is due to the need to ensure that temporal constraints hold, e.g. that the yearly total is equal to the sum of the quarterly amounts of a variable.

would have resulted in the unrestricted cast as compared with the restricted one. The important question which this prompts is how to judge the cost of applying these constraints. judging this either in general analytical, or in empirical casc- study terms. This brings us to the general prob- lem of evaluating seasonal adjustment proce- dures: either in terms of judging between different methods of seasonal adjustment, or in assessing their robustness when, for example, applied to a balanced set of data.

The problem as it affects seasonal adjustment procedures is then easy to state. The constraint that the seasonally adjusted component series must equal the seasonally adjusted total has to apply. What methods can be used to achieve this? A variety of more or less demanding tech- niques are available, as we now describe.

(i) Ad hoc distribution of the residual entry. In adjusting a set of data, this is operationally the easiest thing to do, though from a technical point of view the least satisfactory. Briefly. an ‘unimportant’ residual variable is used to ensure that the adding-up constraint holds. The draw- back is obvious. The residual series may then behave in a way which is difficult to interpret. If the series is judged unimportant this may be acceptable, but is nonetheless a drawback.

Having noted at least some of the principal ways in which seasonal adjustment can be under- taken, are there ways of judging between them? “Simulated series apart, true seasonality remains a theoretical concept and is, hence, unobservable (den Butter and Fase).” Practical procedures abound, as illustrated in this book. In a com-

parative exercise, the effect of different procc- dures can be judged using, for example, Thcil inequality coefficients calculated pairwise using seasonal components estimated by different ad- justment procedures. Similarly as a check on the changes in seasonal patterns which different methods identify, avcragc changes of the scason- al components can bc useful.

(ii) Linear adjustment methods. If the meth- od of seasonal adjustment is linear. then this ensures that definitional constraints automatical- ly hold. Thus,

Although comparisons arc guided not by theoretical principles, but rather by empirical judgements, nonetheless there are a number of properties which are agreed to be desirable in an adjustment procedure. A standard set of prop- erties would include l orthogonality, l idempotency,

A(Y, + ~2) = A(Y,) + A 3 l residual seasonality and residual trend/cycle

where A is the linear method of seasonal adjust- ment, and y, and y2 are the two series consid- ered. This means that where the seasonal adjust- ment procedure is, for example, the simple fixed additive method, balancing is automatically achieved. Similarly, adding up constraints can be automatically met if STM procedures are used by restricting the structural model to be the same for each series. This means that the relative hyperparameters for each series are the same, so that in this sense the stochastic properties of the underlying model are constant across the differ- ent series.

movement, l stability.

Orthogonality is fairly straightforward and rc- quires that the estimated seasonal and trend/ cycle are orthogonal. Clearly. failure to meet this test means the estimated model is misspccified. Idempotency entails that repeated application of the adjustment procedure yields the same adjus- ted series as the first. It is not. however. the cast that all procedures meet this requirement. A fixed additive model does. but den Butter and Fase give illustrations where, for example, the Burman method does not.

In this latter case. the application of the re- striction is not without its costs-namely what

Residual seasonality is akin to the first test. and tests whether the irregular series retain any seasonal effects. Failure to satisfy this test again

clearly providing evidence that the adjustment procedure is inadequate. A test of the independ-

ence of the irregular component is usually used for this. A related test on the trend/cycle com- ponent can also signify model misspecification. Finally, the stability of the estimated seasonal model when new data are encountered is an important practical test. Estimated seasonal ef- fects over different, but overlapping, sample periods, using summary measures of stability- such as the average change in seasonal effects over a given interval-are an important guide to the properties of a given adjustment procedure.

Conclusions

Den Butter and Fase have written a thorough and readable account of the many issues of modelling, evaluating. and using seasonal mod- els. Throughout there is a wealth of applications which makes the book especially useful. The brief summary contained here does not do jus- tice to the altcrnativc methods they cover, and only a selection of the principal ones have been noted here. Also. there is an admirable concen- tration upon actual empirical examples. mainly drawn from monetary data which arc liberally used to illustrate the properties of the different methods.

As the authors themselves note, “seasonal adjustment will often form part of policy diag- nosis, and will therefore frequently involve some degree of subjectivity”. They go on, *‘this mono- graph. offers the reader some guidance in forming his own judgement in this technical sub- ject”. It is my judgement that the authors have achieved this objective admirably. They have written a short book which manages to cover the main elements of the subject in a lucid and objective way.

Brian Henry Bank of England. UK

References

Dagum, E.D.. 1978, “Modelling. forecasting and aeasonnlly adjusting timeserie< with the X-l I ARIMA method”. 771e S/ari,sticictrl. 27. ‘K-2 16.

H:irvey, A.C.. 1981, Tim-Swim Modds (Philip Allen. Oxford).

Frank W. Elwell, The Evolution of the Future (Praeger Publishers, New York, NY, 1991), pp. 144. $37.95.

This is, for me. a disappointing book, one that does not deliver on the promise of its first chap- ter. Elwell starts out in fine style, attacking most futurists for their reliance on trend cxtrapola- tion, the absence of any explicit theory, and their lack of any sense of history. As a result, he charges, futurists have failed to live up to the promise that ‘foresight will allow us to change society either to achieve a potential out- come .,. or to avoid it. .‘. To make up for these deficiencies’. Elwell introduces us to cultural materialism with its emphasis on two key asser- tions:

(1) ‘The various parts of society are inter- related,’ and

(2) ‘The entire structure of the sociocultural system rests on the way a society exploits its environment to meet the biopsychological needs of its population.’

Perhaps naively, and with my innate bias to- ward scenario planning as the preferred tool for defining alternative possible futures. I had hoped (and expected) that Elwell would use the theoretical base of cultural materialism as a framework for exploring ways in which the fu- ture might evolve. Instead, I found myself con- fronted (as early as the second chapter) with what seemed to me to be virtually an ‘iron law’ of social evolution paraphrased below:

Under the modern idea of progress, there is an inevitable intensification of production and reproduction, leading to bureaucratization, rationalization and the growth of secondary groups [governments, corporations, media, labor organizations, etc.] at the expense of primary groups [family, community, friend- ships, etc.], with resultant increases in aliena- tion and powerlessness as individuals become victims of their own institutions.