Measuring business cycles in economic time series.

*(English)*Zbl 0958.91059
Lecture Notes in Statistics. 154. New York, NY: Springer. viii, 189 p. (2001).

This monograph studies measurement of economic cycles in (macroeconomic) time series. The central theme of the book is the Hodrick-Prescott filter, its usefulness, advantages and limitations. It is shown that straightforward modifications based on ARIMA modelling methodology lead to significant improvements in the end result.

Chapter 1 provides an introduction and a brief overview. Chapter 2 introduces basic concepts of time series analysis with particular stress on the spectrum and linear filters. Chapter 3 is devoted to ARIMA models, their identification, estimation, diagnostic checking. Space is given to issues concerning preprocessing of time series. The usage of ARIMA models for signal extraction and time series decomposition is introduced in this chapter as well.

Chapter 4 presents various formulations of the Hodrick-Prescott filter and a discussion of its properties. The latter is continued in Chapter 5 with a study of the resulting cycle component, its weakness at the end points of the time series, the possibility for spurious results, noisiness of the filtered signal. Engineers and mathematicians will be especially pleased to find out that the Hodrick-Prescott filter is a Butterworth filter and can be formulated also as a Wiener-Kolmogorov filter. On the technical side, systematic usage of autocovariance generating functions makes transparent the relation between time domain and spectral domain properties of filters.

Chapters 6 and 7 present in detail the proposed improvements to the Hodrick-Prescott filter. First, its performance at the end points of the series can be significantly enhanced by extending the series with forecasts and backcasts from a model built for the particular series. Secondly, the seasonal adjustment can be done using ARIMA model decomposition. Evidence for significant improvement is shown both in terms of theoretical properties and in practical interpretation, such as determining turning points in the business cycle.

This is a very comprehensive book on a contemporary approach to the extraction of components from time series.

Chapter 1 provides an introduction and a brief overview. Chapter 2 introduces basic concepts of time series analysis with particular stress on the spectrum and linear filters. Chapter 3 is devoted to ARIMA models, their identification, estimation, diagnostic checking. Space is given to issues concerning preprocessing of time series. The usage of ARIMA models for signal extraction and time series decomposition is introduced in this chapter as well.

Chapter 4 presents various formulations of the Hodrick-Prescott filter and a discussion of its properties. The latter is continued in Chapter 5 with a study of the resulting cycle component, its weakness at the end points of the time series, the possibility for spurious results, noisiness of the filtered signal. Engineers and mathematicians will be especially pleased to find out that the Hodrick-Prescott filter is a Butterworth filter and can be formulated also as a Wiener-Kolmogorov filter. On the technical side, systematic usage of autocovariance generating functions makes transparent the relation between time domain and spectral domain properties of filters.

Chapters 6 and 7 present in detail the proposed improvements to the Hodrick-Prescott filter. First, its performance at the end points of the series can be significantly enhanced by extending the series with forecasts and backcasts from a model built for the particular series. Secondly, the seasonal adjustment can be done using ARIMA model decomposition. Evidence for significant improvement is shown both in terms of theoretical properties and in practical interpretation, such as determining turning points in the business cycle.

This is a very comprehensive book on a contemporary approach to the extraction of components from time series.

Reviewer: Georgi Boshnakov (Manchester /UK)