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Journal ArticleDOI

Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series

01 Nov 1999-The Review of Economics and Statistics (MIT press journals)-Vol. 81, Iss: 4, pp 575-593
TL;DR: The authors developed a set of approximate band-pass filters and illustrates their application to measuring the business-cycle component of macroeconomic activity, and compared them with several alternative filters commonly used for extracting business cycle components.
Abstract: Band-pass filters are useful in a wide range of economic contexts. This paper develops a set of approximate band-pass filters and illustrates their application to measuring the business-cycle component of macroeconomic activity. Detailed comparisons are made with several alternative filters commonly used for extracting business-cycle components.

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Journal ArticleDOI
TL;DR: The paper revisits the inflation forecasting problem posed by Stock and Watson (1999), and compute the model confidence set (MCS) for their set of inflation forecasts, and compares a number of Taylor rule regressions to determine the MCS of the best in terms of in-sample likelihood criteria.
Abstract: This paper introduces the model confidence set (MCS) and applies it to the selection of models. A MCS is a set of models that is constructed such that it will contain the best model with a given level of confidence. The MCS is in this sense analogous to a confidence interval for a parameter. The MCS acknowledges the limitations of the data, such that uninformative data yield a MCS with many models, whereas informative data yield a MCS with only a few models. The MCS procedure does not assume that a particular model is the true model; in fact, the MCS procedure can be used to compare more general objects, beyond the comparison of models. We apply the MCS procedure to two empirical problems. First, we revisit the inflation forecasting problem posed by Stock and Watson (1999), and compute the MCS for their set of inflation forecasts. Second, we compare a number of Taylor rule regressions and determine the MCS of the best regression in terms of in-sample likelihood criteria.

1,460 citations

Journal ArticleDOI
TL;DR: In this paper, the authors developed optimal finite-sample approximations for the band pass filter, based on the generally false assumption that the data are generated by a random walk.
Abstract: We develop optimal finite-sample approximations for the band pass filter. These approximations include one-sided filters that can be used in real time. Optimal approximations depend upon the details of the time series representation that generates the data. Fortunately, for U.S. macroeconomic data, getting the details exactly right is not crucial. A simple approach, based on the generally false assumption that the data are generated by a random walk, is nearly optimal. We use the tools discussed here to document a new fact: There has been a significant shift in the money–inflation relationship before and after 1960.

1,225 citations

Journal ArticleDOI
TL;DR: In this article, the authors explore how the introduction of habit preferences into the simple intertemporal consumption-based capital asset pricing model "solves" the equity premium and risk-free rate puzzles.

1,030 citations

References
More filters
Journal ArticleDOI
TL;DR: In this article, the authors reviewed recent developments in business cycle theory and found that the growth model, which was developed to account for the secular patterns in important economic aggregates, displays the business cycle phenomena once it incorporates the observed randomness in the rate of technological advance.

1,883 citations

Book
01 Jan 1981

1,167 citations

Journal ArticleDOI
TL;DR: This paper argued that the reporting of facts in light of theory fosters the development of theory and argued that dynamic neoclassical macro theory guided the selection of facts to report, and that these facts will foster the further development of this theory.
Abstract: This paper argues that the reporting of facts in light of theory fosters the development of theory Dynamic neoclassical macro theory guided the selection of facts to report The hope is that these facts will foster the further development of this theory A finding is that the price level is countercyclical in the post-Korean War period This finding debunks the myths that the price level is procyclical, with the postwar period being no exception

896 citations

Book
01 Jan 1974
TL;DR: In this article, the distribution theory of Spectral Estimators with applications to Statistical Inference has been studied in the context of time series and Spectral models for continuous-time processes.
Abstract: Preliminaries: Time Series and Spectra, Summary of Vector Space Geometry, Some Probability Notations and Properties. Models for Spectral Analysis - The Univariate Case: The Wiener Theory of Spectral Analysis, Stationary and Weakly Stationary Stochastic Processes, The Spectral Representation for Weakly Stationary Stochastic Processes - A Special Case, The General Spectral Representation for Weakly Stationary Processes, The Discrete and Continuous Components of the Process, Physical Realizations of the Different Kinds of Spectra, The Real Spectral Representation, Ergodicity and the Connection between the Wiener and Stationary Process Theories, Statistical Estimation of the Autocovariance and the Mean Ergodic Theorem. Sampling, Aliasing, and Discrete-Time Models: Sampling and the Aliasing Problem, The Spectral Model for Discrete-Time Series Linear Filters - General Properties with Applications to Continuous-Time Processes: Linear Filters, Combining Linear Filters, Inverting Linear Filters, Nonstationary Processes Generated by Time Varying Linear Filters. Multivariate Spectral Models and Their Applications: The Spectrum of a Multivariate Time Series-Wiener Theory, Multivariate Weakly Stationary Stochastic Processes, Linear Filters for Multivariate Time Series, The Bivariate Spectral Parameters, Their Interpretations and Uses. The Multivariate Spectral Parameters, Their Interpretations and Uses Digital Filters: General Properties of Digital Filters, The Effect of Finite Data Length, Digital Filters with Finitely Many Nonzero Weights, Digital Filters Obtained by Combining Simple Filters, Filters with Gapped Weights and Results Concerning the Filtering of Series with Polynomial Trends. Finite Parameter Models, Linear Prediction and Real-Time Filtering: Moving Averages, Autoregressive Processes, The Linear Prediction Problem, Mixed Autoregressive-Moving Average Processes and Recursive Prediction, Linear Filtering in Real Time. The Distribution Theory of Spectral Estimates with Applications to Statistical Inference: Distribution of the Finite Fourier Transform and the Periodogram. Distribution Theory for Univariate Spectral Estimators, Distribution Theory for Multivariate Spectral Estimators with Applications to Statistical Inference. Sampling Properties of Spectral Estimates, Experimental Design and Spectral Computations, Properties of Spectral Estimators and the Selection of Spectral Windows, Experimental Design, Methods for Computing Spectral Estimators, Data Processing Problems and Techniques.

871 citations