Measuring Business Cycles in Economic Time Series

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November 2000



This book outlines and demonstrates problems with the use of the HP filter, and proposes an alternative strategy for inferring cyclical behavior from a time series featuring seasonal, trend, cyclical and noise components. The main innovation of the alternative strategy involves augmenting the series forecasts and back-casts obtained from an ARIMA model, and then applying the HP filter to the augmented series. Comparisons presented using artificial and actual data demonstrate the superiority of the alternative strategy.


1 Introduction and Brief Summary.
2 A Brief Review of Applied Time Series Analysis.
2.1 Some Basic Concepts.
2.2 Stochastic Processes and Stationarity.
2.3 Differencing.
2.4 Linear Stationary Process, Wold Representation. and Auto-correlation Function.
2.5 The Spectrum.
2.6 Linear Filters and Their Squared Gain.
3 ARIMA Models and Signal Extraction.
3.1 ARIMA Models.
3.2 Modeling Strategy, Diagnostics and Inference.
3.2.1 Identification.
3.2.2 Estimation and Diagnostics.
3.2.3 Inference.
3.2.4 A Particular Class of Models.
3.3 Preadjustment.
3.4 Unobserved Components and Signal Extraction.
3.5 ARIMA-Model-Based Decomposition of a Time Series.
3.6 Short-Term and Long-Term Trends.
4 Detrending and the Hodrick-Prescott Filter.
4.1 The Hodrick-Prescott Filter: Equivalent Representations.
4.2 Basic Characteristics of the Hodrick-Prescott Filter.
4.3 Some Criticisms and Discussion of the Hodrick-Prescott Filter.
4.4 The Hodrick-Prescott Filter as a Wiener-Kolmogorov Filter.
4.4.1 An Alternative Representation.
4.4.2 Derivation of the Filter.
4.4.3 The Algorithm.
4.4.4 A Note on Computation.
5 Some Basic Limitations of the Hodrick-Prescott Filter.
5.1 Endpoint Estimation and Revisions.
5.1.1 Preliminary Estimation and Revisions.
5.1.2 An Example.
5.2 Spurious Results.
5.2.1 Spurious Crosscorrelation.
5.2.2 Spurious Autocorrelation; Calibration.
5.2.3 Spurious Periodic Cycle.
5.3 Noisy Cyclical Signal.
6 Improving the Hodrick-Prescott Filter.
6.1 Reducing Revisions.
6.2 Improving the Cyclical Signal.
7 Hodrick-Prescott Filtering Within a Model-Based Approach.
7.1 A Simple Model-Based Algorithm.
7.2 A Complete Model-Based Method; Spuriousness Reconsidered.
7.3 Some Comments on Model-Based Diagnostics and Inference.
7.4 MMSE Estimation of the Cycle: A Paradox.
Author Index.


From the reviews:
"Altogether this book is more on the mathematical side, it is well written following the same idea throughout and contains many exercises which complete the different topics. The text concentrates on the approach of the authors...I enjoyed reading this nicely written book which can certainly be recommended to all mathematically oriented statisticians interested in the subject."
EAN: 9780387951126
ISBN: 0387951121
Untertitel: 'Lecture Notes in Statistics'. Softcover reprint of the original 1st ed. 2001. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: November 2000
Seitenanzahl: 204 Seiten
Format: kartoniert
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