On the evidence of non-linear structure in Canadian unemployment

Abstract

This study focuses on and examines the empirical evidence of non-linearity in aggregate Canadian unemployment. Contrary to the conclusion reached in many studies, and using a corrected for bias simple non-parametric test (SNT), the null hypothesis of a linear structure for Canadian unemployment is rejected.

Acknowledgements

The first author is grateful to the McGill Major Fellowship for financial support, to John W. Galbraith and to the seminar participants at the University of Central Florida for helpful comments.

Notes

Originally proposed by Grassberger and Procaccia (1984) as a U-statistic estimator, the correlation integral determines the fractal dimension of an attracting set. The class of U-statistics was first introduced by Hoeffdring (1948), wherein he showed that this class could be approximated using a projection representation as the sum of i.i.d. random variables.

Note that rejecting the null of i.i.d. on the residuals of fitted linear time series models does not imply that the alternative is only a non-linear time series model. This point is similar in essence to that of Poirier (1997). The rejection of the null simply implies that the linear specification is not accurate; no hints are given regarding its alternative.

For a detailed derivations, see Mizrach (1994) and Cromwell et al. (1994, pp. 32–6).

To examine this ‘spatial’ correlation, the time series x(t) must be embedded in m-space by constructing a vector. The choice of m for the dimensionality of the vectors is subjective. See Cromwell et al. (1994, p. 33) for details.

The support of Bruce Mizrach is acknowledged in making the FORTRAN code available. The code was modified to compute the SNT directly. The SNT test was compiled and run on a Linux (kernel 2.4.20.19-7) server.