Testing unit roots, structural breaks and linearity in the inflation rates of the G7 countries with fractional dependence techniques
Luis A. Gil-Alaña
OlaOluwa S. Yaya
Enitan A. Solademi
Applied Stochastic Models in Business and Industry, Vol. 32, Issue 5
North America, Europe

In this paper, we have examined the inflation rates in the Group of Seven countries, investigating issues such as the existence of unit roots, structural breaks, fractional integration and potential non-linearities using a fractional dependence (FD) approach based on Chebyshev polynomials in time. This robust FD approach allows one to test for persistence as well as non-linearity of the series. We first tested for stationarity and structural breaks using classical approaches and observed inconclusive results with regard to the stationarity levels of the series. Using Bai–Perron tests, we actually confirmed significant structural breaks, even up to five, in each of the inflation series. However, noting that structural breaks are significantly related to fractional differentiation, this latter approach was also conducted. Here, we observed that the estimates of the differencing parameter were quite stable across time, and evidence of unit roots was found in the cases of the UK, Canada, France, Japan and the USA; for Germany, we found some evidence of mean reversion, while estimates of d above 1 were found in the case of Italy. On the other hand, non-linear deterministic trends were clearly rejected in all cases.