The paper describes a method for predicting climate time series that consist of significant annual and diurnal seasonal components and a short-term stockastic component. A memory-based method for modeling of the non-linear seasonal components is proposed that allows the application of simpler linear models for predicting short-term deviations from seasonal averages. The proposed method results in significant reduction of prediction error when predicting error time series of ambient air temperature from multiple locations. Moreover, combining the statistical predictor with meteorological forecasts using linear regression or Kalman filtering further reduces error to typically between 1 ◦ C over a prediction horizon of one hour and 2.5 ◦ C over 24 hours. Machine Learning Journal This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research pu...