Keywords: Bootstrap, ARMA models, Forecasts, Drought Risks, Water Resources

Abstract: Hydrologists sometimes use periodic auto-regressive moving average (PARMA) models of monthly streamflows to forecast drought risks and evaluate operation plans for water resources systems.Often the monthly time series of streamflows are required at multiple cross correlated sites. Traditionally forecasts are generated by assuming normal errors and using a random number generator to produce the required innovations. However, this approach may not exploit all the information in the sample.

The method presented here is to randomly resample with replacement observed residuals to produce the forecasts. Bootstrapping the residuals eliminates the need to make specific assumptions about the distribution of the residuals, provides a means for accounting for parameter uncertainty, and simplifies parameter estimation. Cross correlations between multiple sites are preserved by a contemporaneous resampling scheme. The effects of long-range (90-day) weather forecasts can be included by modifying the probabilities that relatively large positive residuals or relatively large negative residuals will be randomly drawn.