Non-linear time series: Howell Tong, (Clarendon Press, Oxford, UK, 1990), pp. 564, £50.00.
1
Book reviews 249 make agricultural economists aware a the vast range of techniques available to the empirical in- vestigator. However, it does not provide agricult- ural economics students with a substitute for a more comprehensive econometrics text. A final point. There is no mention of cointegration or of the associated literature on the implications of nonstationarity in econometric estimation. This may reflect writing and publication lags or a slow take-up of new ideas in the agricultural literature but, given that this is a book about the economet- ric analysis of time series data, the omission may be increasingly seen as important. David Byers, University College of Wales Aberystwyth, Wales, UK Howell Tong, Non-linear Time Series (Clarendon Press, Oxford, UK, 1990) pp. 564, E50.00. Most forecasting methods are based on linear models, such as the class of ARIMA processes. However some time series exhibit behaviour which cannot satisfactorily be described by a linear model. For example the infamous lynx data shows a regular cyclic effect where the ascent part of the cycle is generally much longer than the descent part. In recent years, statisticians have devoted much attention to various classes of non-linear time series models, such as threshold autoregres- sive, bilinear, ARCH and exponential autoregressive models. The mathematics involved can be fascinating to those that like such things and there are interesting connections via such topics as limit cycles and difference equations with another major area of current research interest, namely chaos theory. It is stimulating to find, for example, that an apparently random time series may be gener- ated by a non-linear but strictly deterministic equation. This book, by an acknowledged expert in the field, may well become the standard reference source on non-linear time series models for some time to come. The author has a clear, attractive writing style which is lightened with humour and Chinese proverbs. Generally speaking there is a nice balance between theory and practice. The author suggests some suitable of the book, called ‘set meals’, for particular groups of readers, such as ‘fast food’ (for applied statisticians in a hurry), or ‘gourmet food’ (for those looking for research problems). The book also advertises a P.C. package, called STAR, which will test for non-linearity, fit threshold autoregressive models, and calculate multi-step non-linear forecasts. After an introductory chapter, Chapter 2 re- views some fundamental ideas in dynamical sys- tems, focussing on the quest for a deeper under- standing of cyclical phenomena. Chapter 3 de- scribes a variety of non-linear models, while Chapter 4 discusses the probabilistic aspects of such models including stability, stationarity, time reversibility, and invertibility. Some catastrophe theory is also included. Chapter 5 discusses how to fit non-linear models, and Chapter 6 discusses non-linear least-squares prediction. Chapter 7 (over 90 pages) describes some case studies in detail. Appendix 3 (67 pages) lists many specimen data sets, and there is an extensive list of refer- ences. Despite the obvious importance of this book for time-series analysts, the forecaster may find much less of direct interest, as evidenced by the brevity (12 pages) of Chapter 6. One problem is that it can be difficult to evaluate conditional expectations for non-linear models for more than one step ahead. Furthermore, forecasts often have unexpected properties when compared with linear forecasts. For example, the width of prediction intervals does not necessarily increase with the lead time. Perhaps the most alarming effect (il- lustrated in Figure 6.1) is that a predictive distri- bution need not be unimodal misleading, and the author recommends looking at the whole predic- tive (i.e. conditional) distribution of a forecast value whenever this is computationally possible. In summary, this is an excellent timely book on non-linear time series models, which I would thor- oughly recommend to time-series analysts, but which is probably only of marginal interest to specialist forecasters. Chris Chatfield University of Bath, UK
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Transcript of Non-linear time series: Howell Tong, (Clarendon Press, Oxford, UK, 1990), pp. 564, £50.00.
Book reviews 249
make agricultural economists aware a the vast range of techniques available to the empirical in- vestigator. However, it does not provide agricult- ural economics students with a substitute for a more comprehensive econometrics text. A final point. There is no mention of cointegration or of the associated literature on the implications of nonstationarity in econometric estimation. This may reflect writing and publication lags or a slow take-up of new ideas in the agricultural literature but, given that this is a book about the economet- ric analysis of time series data, the omission may be increasingly seen as important.
David Byers, University College of Wales
Aberystwyth, Wales, UK
Howell Tong, Non-linear Time Series (Clarendon Press, Oxford, UK, 1990) pp. 564, E50.00.
Most forecasting methods are based on linear models, such as the class of ARIMA processes. However some time series exhibit behaviour which cannot satisfactorily be described by a linear model. For example the infamous lynx data shows a regular cyclic effect where the ascent part of the cycle is generally much longer than the descent part. In recent years, statisticians have devoted much attention to various classes of non-linear
time series models, such as threshold autoregres- sive, bilinear, ARCH and exponential autoregressive models. The mathematics involved can be fascinating to those that like such things and there are interesting connections via such topics as limit
cycles and difference equations with another major area of current research interest, namely chaos theory. It is stimulating to find, for example, that an apparently random time series may be gener- ated by a non-linear but strictly deterministic equation.
This book, by an acknowledged expert in the field, may well become the standard reference source on non-linear time series models for some time to come. The author has a clear, attractive writing style which is lightened with humour and Chinese proverbs. Generally speaking there is a
nice balance between theory and practice. The author suggests some suitable of the book, called ‘set meals’, for particular groups of readers, such as ‘fast food’ (for applied statisticians in a hurry), or ‘gourmet food’ (for those looking for research problems). The book also advertises a P.C. package, called STAR, which will test for non-linearity, fit threshold autoregressive models, and calculate multi-step non-linear forecasts.
After an introductory chapter, Chapter 2 re- views some fundamental ideas in dynamical sys- tems, focussing on the quest for a deeper under- standing of cyclical phenomena. Chapter 3 de- scribes a variety of non-linear models, while Chapter 4 discusses the probabilistic aspects of such models including stability, stationarity, time reversibility, and invertibility. Some catastrophe theory is also included. Chapter 5 discusses how to fit non-linear models, and Chapter 6 discusses non-linear least-squares prediction. Chapter 7 (over 90 pages) describes some case studies in detail. Appendix 3 (67 pages) lists many specimen data sets, and there is an extensive list of refer- ences.
Despite the obvious importance of this book for time-series analysts, the forecaster may find much less of direct interest, as evidenced by the brevity (12 pages) of Chapter 6. One problem is that it can be difficult to evaluate conditional expectations for non-linear models for more than one step ahead. Furthermore, forecasts often have unexpected properties when compared with linear forecasts. For example, the width of prediction intervals does not necessarily increase with the lead time. Perhaps the most alarming effect (il- lustrated in Figure 6.1) is that a predictive distri- bution need not be unimodal misleading, and the author recommends looking at the whole predic- tive (i.e. conditional) distribution of a forecast value whenever this is computationally possible.
In summary, this is an excellent timely book on non-linear time series models, which I would thor- oughly recommend to time-series analysts, but which is probably only of marginal interest to specialist forecasters.
Chris Chatfield University of Bath, UK
