Temperature and precipitation in the US states: long memory, persistence, and time trend

Abstract

This paper investigates the time series properties of the temperature and precipitation anomalies in the contiguous USA by using fractional differentiation. This methodology allows to capture time trend components along with properties such as long-range dependence and the degree of persistence. For aggregated data, we find out that long memory is present in both precipitation and temperature since the integration order is significantly positive in the two cases. The time trend is also positive, being higher for the temperature. In addition, observing disaggregated data by states, for the temperature, there are only seven states where the time trend is not significant, with most of them located in Southeast areas, while for the rest of cases, the time trend is significantly positive. All cases exhibit long-range dependence, though the differencing parameter substantially changes from one state to another, ranging from 0.09 in Nebraska and Kansas to 0.18 in Florida and Michigan. For precipitation, the time trend is insignificant in a large number of cases, and the integration order is smaller than for the temperature. In fact, short memory cannot be rejected in fourteen states, and the highest orders of differencing are obtained in Arizona (d = 0.11) and Texas (0.12). In general, we highlight that one cannot draw conclusions about persistence and trends in these two climate-related variables based on aggregate information of the overall USA, given widespread heterogeneity across the states. Tentatively, the degree of dependence across the states seems to be negatively correlated with their level of climate-related risks and the associated preparedness in terms of handling climate change, but this conclusion requires more elaborate research in the future.