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Simultaneous Statistical Inference in Dynamic Factor Models

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Time Series Analysis and Forecasting

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Abstract

Based on the theory of multiple statistical hypotheses testing, we elaborate likelihood-based simultaneous statistical inference methods in dynamic factor models (DFMs). To this end, we work up and extend the methodology of Geweke and Singleton (Int Econ Rev 22:37–54, 1981) by proving a multivariate central limit theorem for empirical Fourier transforms of the observable time series. In an asymptotic regime with observation horizon tending to infinity, we employ structural properties of multivariate chi-square distributions in order to construct asymptotic critical regions for a vector of Wald statistics in DFMs, assuming that the model is identified and model restrictions are testable. A model-based bootstrap procedure is proposed for approximating the joint distribution of such a vector for finite sample sizes. Examples of important multiple test problems in DFMs demonstrate the relevance of the proposed methods for practical applications.

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Acknowledgements

The authors are grateful to Prof. Manfred Deistler for valuable comments regarding Problem 1. Special thanks are due to the organizers of the International work-conference on Time Series (ITISE 2015) for the successful meeting.

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Authors and Affiliations

  1. Institute for Statistics, University of Bremen, 330 440, 28344, Bremen, Germany

    Thorsten Dickhaus

  2. Institute of Statistics, University of Ulm, Helmholtzstr. 20, 89081, Ulm, Germany

    Markus Pauly

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  1. Thorsten Dickhaus
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  2. Markus Pauly
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Correspondence to Thorsten Dickhaus .

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Editors and Affiliations

  1. CITIC-UGR, University of Granada, Granada, Spain

    Ignacio Rojas

  2. CITIC-UGR, University of Granada, Granada, Spain

    Héctor Pomares

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Dickhaus, T., Pauly, M. (2016). Simultaneous Statistical Inference in Dynamic Factor Models. In: Rojas, I., Pomares, H. (eds) Time Series Analysis and Forecasting. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-28725-6_3

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