Use of fresh water over the long run measuring persistence

Abstract

In this article, we carry out a study of the degree of persistence of a time series of data on freshwater use in the long term, using fractional integration or I(d) techniques. Using annual data from 1901 to 2014, we observe that the order of integration of the series is close to 1 if the errors are not correlated, and if they are correlated, then it is greater than 1. This shows that the series is highly persistent. On the other hand, we detect two structural breaks, one at 1951 and the other one at 1980. In these cases, we observe a reversion to the mean since the integration orders are much lower in the subsamples. This supports the hypothesis that when these breaks are not taken into account, there is an overestimation of the differentiation parameter, misspecifying the reversion to the mean of the data. The series also shows segmented trends with the higher time trend coefficient observed during the years 1951 and 1980.