Global Warming and the Problem of Testing for Trend in Time Series Data

In recent years a number of statistical tests have been proposed for testing the hypothesis that global warming is occurring. The standard approach is to examine one or two of the more prominent global temperature datasets by letting Yt = a + bt + Et, where Yt represents the temperature at time t and Et represents error from the trend line, and to test the hypothesis that b = 0. Several authors have applied these tests for trend to determine whether or not a significant long-term or deterministic trend exists, and have generally concluded that there is a significant deterministic trend in the data. However, we show that certain autoregressive-moving average (ARMA) models may also be very reasonable models for these data due to the random trends present in their realizations. In this paper, we provide simulation evidence to show that the tests for trend detect a deterministic trend in a relatively high percentage of realizations from a wide range of ARMA models, including those obtained for the temperature series, for which it is improper to forecast a trend to continue over more than a very short time period. Thus, we demonstrate that trend tests based on models such as Yt = a + bt + Et, where Yt for the purpose of prediction or inference concerning future behavior should be used with caution. Of course, the projections that the warming trend will extend into the future are largely based on such factors as the buildup of atmospheric greenhouse gases. We have shown here, however, that based solely on the available temperature anomaly series, it is difficult to conclude that the trend will continue over any extended length of time.