Multivariate trend function testing with mixed stationary and integrated disturbances

Trend models are important in describing nonstationary behavior of a time series. In this paper we propose valid tests for the trend coefficients in a multivariate system with mixed stationary, integrated or nearly integrated errors. Cross-sectional and serial dependence in innovations are left unsp...

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Bibliographic Details
Published in:Journal of multivariate analysis 2016-05, Vol.147, p.38-57
Main Author: Xu, Ke-Li
Format: Article
Language:English
Subjects:
Deterministic trends
Efficient estimation
Estimating techniques
Fixed-b asymptotics
HAC standard error
Mathematical functions
Multivariate analysis
Multivariate time series
Nearly integrated processes
Seemingly unrelated regression (SUR)
Statistical inference
Studies
Time series
Citations: Items that this one cites
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Description
Summary:Trend models are important in describing nonstationary behavior of a time series. In this paper we propose valid tests for the trend coefficients in a multivariate system with mixed stationary, integrated or nearly integrated errors. Cross-sectional and serial dependence in innovations are left unspecified beyond regularity assumptions. We consider two sets of tests based on OLS and SUR estimation of the transformed system. A modified SUR estimator corrected for serial correlation of unknown form is shown to be asymptotically efficient. The standard tests under stationarity are also analyzed and potential misleading inferences are demonstrated. The framework is general allowing for linear and nonlinear trend functions. Asymptotic theory, simulations and an empirical application are provided.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2015.12.011