This paper examines income poverty in Africa by looking at the time series properties of the series corresponding to the household consumer expenditures in 53 African countries.Using fractional integration the results indicate that the series are highly persistent, displaying orders of integration in the interval (0, 1) in some countries or values equal to or higher than 1 in some others. The main implication of the empirical findings is that long term policies aimed at addressing income poverty in the continent such as the policies on expansion of infrastructure and social amenities will have have long-lasting effects on poverty reduction.

In this paper the degree of persistence of the sulfur dioxide emissions in a group of 37 OECD countries is examined by looking at the order of integration of the series. However, instead of using integer degrees of differentiation (i.e., 1 in case of unit roots and 0 for stationarity), fractional values are also considered. The results indicate high degrees of persistence and very little evidence of mean reversion. In fact, this property only holds for the three Latin American countries examined, namely Chile, Colombia and Mexico if the error follows a white noise process. If autocorrelation is permitted, however, the confidence intervals are wider and mean reversion is not found in any single case.

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This paper examines geopolitical risk in terms of time series persistence. In doing so we are able to determine the nature of the shocks, which are either transitory or permanent depending on the integration order of the series. We examine 19 countries from January 1985 to February 2020. Our results show evidence of positive time trends in the cases of Mexico and Venezuela, and negative ones for South Africa and Argentina. These results are robust across seasonal and non-seasonal data and for different modelling assumptions for the error term. With respect to the degree of persistence, the different parameter is found to be in the range (0, 1) although we also observe heterogeneity across all countries.