The Use of Time Series Analysis Techniques in Forecasting Meteorological Drought

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  • 1 NOAA Climatologist for Ohio, and Department of Geography, The Ohio State University, Columbus 43210
  • | 2 Department of Economics, The Ohio State University, Columbus 43210
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Abstract

Using an exponential smoothing procedure and an autoregressive-moving average process; forecasts for the monthly Palmer Drought Severity Index were calculated. The autocorrelation and partial autocorrelation functions of severity index values were used as a starting point for the autoregressive-moving average model selection process. Of the many possible autoregressive-moving average models, the one that was selected provided the best forecasts based on the mean square error. Monthly data for the period 1929–1969 were utilized in a nonlinear least-squares computer routine to arrive at estimated parameter values for the autoregressive-moving average model. Monthly forecasts with a lead time of one month were generated using the exponential smoothing and autoregressive-moving average procedures for the period 1970–1972. These forecasts were compared with the myopic (persistence) forecasts, Xt+1=Xt. The mean square errors of the forecasts were 0.63 for the autoregressive-moving average model, 0.65 for the myopic model, and 0.79 for the exponential smoothing model. From the mean-square-error calculations, it appears that there is no statistically significant difference between the forecasts given by the Box-Jenkins and myopic models; however, the 95% confidence intervals for these two models overlap only slightly during the first part of the forecast period indicating that there may be some advantage to using the Box-Jenkins model instead of the myopic model. Both of these models are superior to the exponential smoothing model. These results demonstrate the usefulness of the relatively new autoregressive-moving average time series analysis procedures.

Abstract

Using an exponential smoothing procedure and an autoregressive-moving average process; forecasts for the monthly Palmer Drought Severity Index were calculated. The autocorrelation and partial autocorrelation functions of severity index values were used as a starting point for the autoregressive-moving average model selection process. Of the many possible autoregressive-moving average models, the one that was selected provided the best forecasts based on the mean square error. Monthly data for the period 1929–1969 were utilized in a nonlinear least-squares computer routine to arrive at estimated parameter values for the autoregressive-moving average model. Monthly forecasts with a lead time of one month were generated using the exponential smoothing and autoregressive-moving average procedures for the period 1970–1972. These forecasts were compared with the myopic (persistence) forecasts, Xt+1=Xt. The mean square errors of the forecasts were 0.63 for the autoregressive-moving average model, 0.65 for the myopic model, and 0.79 for the exponential smoothing model. From the mean-square-error calculations, it appears that there is no statistically significant difference between the forecasts given by the Box-Jenkins and myopic models; however, the 95% confidence intervals for these two models overlap only slightly during the first part of the forecast period indicating that there may be some advantage to using the Box-Jenkins model instead of the myopic model. Both of these models are superior to the exponential smoothing model. These results demonstrate the usefulness of the relatively new autoregressive-moving average time series analysis procedures.

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