Artificial Immune System for Forecasting Time Series with Multiple Seasonal Cycles

Many time series exhibit seasonal variations related to the daily, weekly or annual activity. In this paper a new immune inspired univariate method for forecasting time series with multiple seasonal periods is proposed. This method is based on the patterns of time series seasonal sequences: input ones representing sequences preceding the forecast and forecast ones representing the forecasted sequences. The immune system includes two populations of immune memory cells – antibodies, which recognize both types of patterns represented by antigens. The empirical probabilities that the forecast pattern is detected by the kth antibody from the second population while the corresponding input pattern is detected by the jth antibody from the first population, are computed and applied to the forecast construction. The empirical study of the model including sensitivity analysis to changes in parameter values and the robustness to noisy and missing data is performed. The suitability of the proposed approach is illustrated through applications to electrical load forecasting and compared with ARIMA and exponential smoothing approaches.