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Multivariate trend function testing with mixed stationary and integrated disturbances

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  • Xu, Ke-Li

Abstract

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.

Suggested Citation

  • Xu, Ke-Li, 2016. "Multivariate trend function testing with mixed stationary and integrated disturbances," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 38-57.
    • Handle: RePEc:eee:jmvana:v:147:y:2016:i:c:p:38-57
    DOI: 10.1016/j.jmva.2015.12.011
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    More about this item

    Keywords

    Deterministic trends; Efficient estimation; Fixed-b asymptotics; HAC standard error; Multivariate time series; Nearly integrated processes; Seemingly unrelated regression (SUR);
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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