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pp 1-7 | Cite as

A Bootstrap Approach to Testing for Time-Variability of AR Process Coefficients in Regression Time Series with t-Distributed White Noise Components

  • Hamza AlkhatibEmail author
  • Mohammad Omidalizarandi
  • Boris Kargoll
Chapter
Part of the International Association of Geodesy Symposia book series

Abstract

In this paper, we intend to test whether the random deviations of an observed regression time series with unknown regression coefficients can be described by a covariance-stationary autoregressive (AR) process, or whether an AR process with time-variable (say, linearly changing) coefficients should be set up. To account for possibly present multiple outliers, the white noise components of the AR process are assumed to follow a scaled (Student) t-distribution with unknown scale factor and degree of freedom. As a consequence of this distributional assumption and the nonlinearity of the estimator, the distribution of the test statistic is analytically intractable. To solve this challenging testing problem, we propose a Monte Carlo (MC) bootstrap approach, in which all unknown model parameters and their joint covariance matrix are estimated by an expectation maximization algorithm. We determine and analyze the power function of this bootstrap test via a closed-loop MC simulation. We also demonstrate the application of this test to a real accelerometer dataset within a vibration experiment, where the initial measurement phase is characterized by transient oscillations and modeled by a time-variable AR process.

Keywords

Bootstrap test EM algorithm Monte Carlo simulation Regression time series Scaled t-distribution Time-variable autoregressive process 

Notes

Acknowledgements

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—386369985. The presented application of the PCB Piezotronics accelerometer within the vibration analysis experiment was performed as a part of the collaborative project “Spatio-temporal monitoring of bridge structures using low cost sensors” with ALLSAT GmbH, which is funded by the German Federal Ministry for Economic Affairs and Energy (BMWi) and the Central Innovation Programme for SMEs (ZIM Kooperationsprojekt, ZF4081803DB6). In addition, the authors acknowledge the Institute of Concrete Construction (Leibniz Universität Hannover) for providing the shaker table and the reference accelerometer used within this experiment.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Hamza Alkhatib
    • 1
    Email author
  • Mohammad Omidalizarandi
    • 1
  • Boris Kargoll
    • 2
  1. 1.Geodetic InstituteLeibniz University HannoverHannoverGermany
  2. 2.Institut für Geoinformation und Vermessung DessauAnhalt University of Applied SciencesDessau-RoßlauGermany

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