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Prequential analysis of stock market returns

The Brier score and a covariance partition due to Yates are considered to study the probabilistic forecasts of a vector autoregression on stock market returns. Probabilistic forecasts from a model and data developed by Campbell (1991) are studied with ordinary least squares. Calibration measures and the Brier score and its partition are used for model assessment. The partitions indicate that the ordinary least squares version of Campbell's model does not forecast stock market returns particularly well. While the model offers honest probabilistic forecasts (they are well-calibrated), the model shows little ability to sort events that occur into different groups from events that do not occur. The Yates-partition demonstrates this shortcoming. Calibration metrics do not.