SELECTING A MODEL FOR DETECTING THE PRESENCE OF A TREND

The authors consider the problem of determining whether the upward tre nding behavior in the global temperature anomaly series should be fore cast to continue. To address this question, the generic problem of det ermining whether an observed trend in a time series realization is a r andom (i.e., short-term) trend or a deterministic (i.e., permanent) tr end is considered. The importance of making this determination is that forecasts based on these two scenarios are dramatically different. Fo recasts based on a series with random trends will not predict the obse rved trend to continue, while forecasts based on a model with determin istic trend will forecast the trend to continue into the future. In th is paper, the authors consider an autoregressive integrated moving ave rage (ARIMA) model and a ''deterministic forcing function + autoregres sive (AR) noise'' model as possible random trend and deterministic tre nd models, respectively, for realizations displaying trending behavior . A bootstrap-based classification procedure for classifying an observ ed time series realization as ARIMA or ''function + AR'' using linear and quadratic forcing functions is introduced. A simulation study demo nstrates that the procedure is useful in distinguishing between realiz ations from these two models. A unit-root test is also examined in an effort to distinguish between these two types of models. Using the tec hniques developed here, the temperature anomaly series are classified as ARIMA (i.e., having random trends).