TY - GEN
T1 - A Bootstrap Approach to Testing for Time-Variability of AR Process Coefficients in Regression Time Series with t-Distributed White Noise Components
AU - Alkhatib, Hamza
AU - Omidalizarandi, Mohammad
AU - Kargoll, Boris
N1 - Conference code: 9
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Bootstrap test
KW - EM algorithm
KW - Monte Carlo simulation
KW - Regression time series
KW - Scaled t-distribution
KW - Time-variable autoregressive process
UR - http://www.scopus.com/inward/record.url?scp=85092174716&partnerID=8YFLogxK
U2 - 10.1007/1345_2019_78
DO - 10.1007/1345_2019_78
M3 - Conference contribution
AN - SCOPUS:85092174716
SN - 9783030542665
T3 - International Association of Geodesy Symposia
SP - 191
EP - 197
BT - 9th Hotine-Marussi Symposium on Mathematical Geodesy
A2 - Novák, Pavel
A2 - Crespi, Mattia
A2 - Sneeuw, Nico
A2 - Sansò, Fernando
PB - Springer Science and Business Media Deutschland GmbH
CY - Cham
T2 - 9th Hotine-Marussi Symposium on Mathematical Geodesy, 2018
Y2 - 18 June 2018 through 22 June 2018
ER -