Semiparametric estimation of the fractional differencing parameter in the UK industrial production index

Abstract

The order of integration of the industrial production index in the UK is investigated by means of semiparametric techniques in the time and in the frequency domain. Several methods like the R\S statistic, along with others proposed by Robinson in a number of articles are applied to various differenced transformations of the log of the series. These methods perform poorly when using the time domain approaches, however, when using the frequency domain, the results are fairly conclusive. Evidence is found of a unit root at the zero frequency in the logged series whether or not the series is monthly seasonally differenced first.

Acknowledgements

The author gratefully acknowledges financial support from the Government of Navarra (‘Ayudas de Formación e Investigación y Desarrollo’), Spain.

Notes

 Taking first differences is a standard practice. Velasco (1999a, 1999b) shows however that the long memory parameter d can be semiparametrically consistently estimated even for nonstationary series by means of tapering.

 Under Gaussianity, Robinson (1995a) showed that

. The t-ratios for the different estimates were also computed and the estimates were not significantly different from zero.