Using autocorrelation analysis and autoregressive integrated moving average (ARIMA) modelling, we analysed a time series of the monthly number of 1° grid squares infested with desert locust Schistocerca gregaria swarms throughout the geographical range of the species from 1930–1987. Statistically significant first- and higher-order autocorrelations were found in the series. Although endogenous components captured much of the variance, adding rainfall data improved endogenous ARIMA models and resulted in more realistic forecasts. Using a square-root transformation for the locust data improved the fit. The models were only partially successful when accounting for the dramatic changes in abundance which may occur during locust upsurges and declines, in some cases successfully predicting these phenomena but underestimating their severity. Better fitting models were also produced when rainfall data were added to models of an equivalent series for desert locust hoppers (nymphs) that incorporated lagged data for locust swarms as independent variables, representing parent generations. The results are discussed in relation to predicting likely changes in desert locust dynamics with reference to potential effects of climate change.