Spurious regression under broken-trend stationarity. (English) Zbl 1112.62096

Two spurious linear regression models are considered of the form \(y_t=\alpha+\delta x_t+u_y\) and \(y_t=\alpha+\beta t+\delta x_t+u_y\), where \(u_t\) is an error term, and \(x_t\) and \(u_t\) are the observed time series generated independently as trend-stationary processes. The trends of \(x_t\) and \(y_t\) are linear with multiple breaks. The asymptotic behaviour of OLS estimates for \(\alpha\), \(\beta\), \(\delta\) and the t-statistics for hypotheses like \(H_0:\;\delta=0\) is investigated. It is shown that the phenomenon of spurious regression occurs asymptotically independent of the error structure in the data generating process but the rate of divergence of the t-statistics is lower (\(T^{1/2}\)) than in the case of linear trends without breaks (\(T^{3/2}\)). Results of simulations are presented.


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62J05 Linear regression; mixed models
62F12 Asymptotic properties of parametric estimators
62F03 Parametric hypothesis testing
62G10 Nonparametric hypothesis testing
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