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The process of assessing the quality of a sequence of predicted future values, such as $$\hat{y}_{i+1}, \hat{y}_{i+2}, \dots, \hat{y}_{i+5}$$, is accomplished by applying an evaluation model. This model utilizes a probability function, represented generally as $$Pr(\cdot)$$ or more specifically as $$p(\cdot)$$, to determine the likelihood of the predicted sequence.

Evaluating Predicted Sequences

A team is developing a system to predict the next five stock market price movements (e.g., 'up', 'down', 'stable'). They test two different predictive models on the same initial data. An evaluation model then calculates the probability of each predicted five-day sequence occurring. Given the results below, which model's prediction should be considered higher quality, and why?

Selecting the Best Predicted Sequence

When assessing the quality of a predicted sequence of future values, the most effective method is to calculate the probability of each individual value in the sequence and then average these probabilities to find the overall quality score.

A system generates several possible sequences of values to predict a future outcome. An evaluation model then calculates the probability of each entire sequence occurring. Based on this method, which of the following predicted sequences would be considered the highest quality prediction?

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