Real GDP growth rates across countries: long memory and mean shifts

Abstract

This article deals with the analysis of the long memory property in the growth rates of the real GDP series across various countries, allowing for a mean break at an unknown period of time. We use a procedure suggested by Hsu and Kuan (1998, 2000) and the results show that the mean break takes place at 1933 for the UK, at 1944 for the US and at 1946 for Germany and Japan. The order of integration seems to be around zero for Germany and Japan; it is slightly positive for the UK, and negative for the US. Thus, we only obtain some evidence of mean reversion in the real GDP series for the case of the US.

Acknowledgement

The author gratefully acknowledges financial support from the Minsterio de Ciencia y Tecnologia (SEC2005-07657, Spain).

Notes

¹ An I(0) process is defined as a covariance stationary process with a spectral density function that is positive and finite at the zero frequency.

² An alternative definition of long memory is a process with an infinite value in the spectral density function at the zero frequency.

³ See also Phillips and Shimotsu (2004, 2005).

⁴ The exact requirement is that (1/m) + ((m ^{1+2 α} (log m)²)/(T ^{2 α} )) → 0 as T → ∞, where α is determined by the smoothness of the spectral density of the short run component. In case of a stationary and invertible ARMA, α may be set equal to two and the condition is (1/m) + ((m ⁵(log m)²)/(T ⁴)) → 0 as T → ∞.