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Abstract:
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In real-time prediction settings, such as a public health agency monitoring infectious disease incidence, analysts construct series of real-time forecasts over time; for example, we might update predictions each week as new data arrive. We develop an ensemble approach that combines probabilistic forecasts from multiple component models through model averaging. The model weights are obtained as a flexible function of observed inputs such as the time of the year at which the prediction is made and recent observations of the process being predicted. We estimate the parameters of the model weights function by optimizing the log-score of the combined predictive distribution subject to a penalty encouraging the model weights to change slowly as a function of the observed covariates. We apply our method to influenza data using three component models: a seasonal autoregressive integrated moving average model, a semiparametric method combining kernel conditional density estimation and copulas, and a simple approach based on kernel density estimation. We demonstrate that averaging across all time points in a held-out test data set, the ensemble approach outperforms the individual models.
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