Granger, C. W. J.; Hallman, Jeff Nonlinear transformations of integrated time series. (English) Zbl 0721.62088 J. Time Ser. Anal. 12, No. 3, 207-224 (1991). Summary: We consider the effects of nonlinear transformations on integrated processes and unit root tests performed on such series. A test that is invariant to monotone data transformations is proposed. It is shown that series are generally not cointegrated with nonlinear transformations of themselves, but the same transformation applied to a pair of cointegrated series can result in cointegration between the transformed series. Cited in 4 ReviewsCited in 33 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) Keywords:integrated processes; autocorrelations; Dickey-Fuller statistics; effects of nonlinear transformations; unit root tests; invariant to monotone data transformations; cointegration PDF BibTeX XML Cite \textit{C. W. J. Granger} and \textit{J. Hallman}, J. Time Ser. Anal. 12, No. 3, 207--224 (1991; Zbl 0721.62088) Full Text: DOI OpenURL References: [1] DOI: 10.1016/0304-4076(87)90085-6 · Zbl 0649.62108 [2] Feller W., An Introduction to Probability Theory and Its Application 1 (1968) · Zbl 0155.23101 [3] C. W. J. Granger(1988 ) Introduction to processes having equilibria as simple attractors:the Markov case. Discussion Paper, University of California, San Diego. [4] C. W. J. Granger, and J. J. Hallman(1988 ) The algebra of I(1). Finance and Economics Discussion Series 45, Board of Governors of the Federal Reserve System. [5] Hallman J. J., Econometrica 55 pp 277– (1989) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.