Spurious regressions between \(I(d)\) processes. (English) Zbl 0819.62075

Summary: This paper develops an analytical study for the nonsense or spurious regressions that are generated by quite general integrated (of order \(d\)) random processes. In doing this, we generalize the work of P. C. B. Phillips [J. Econ. 33, 311-340 (1986; Zbl 0602.62098)] who provided an analytical study of linear regressions involving only I(1) stochastic processes. Our generalization of Phillips’ work to the \(\text{I} (d)\) case is made employing fractional differencing techniques.


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)


Zbl 0602.62098
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