I am trying to apply the Brier Score methodology in a long term forecasting work, a type of mixed mixed methodology study with ARIMAX. The purpose of this is to help us provide a more accurate means of forecast for inflation.
A brier score is a way to verify the accuracy of a probability forecast. A probability forecast refers to a specific event, such as there is a 25% probability of it raining in the next 24 hours. The score can only be used for binary outcomes, where there are only two possible events, like “it rained” or “it didn’t rain.” It could also be used for categorical outcomes as long as they can be structured as binary outcomes (i.e. “true” or “false”).
- The best possible Brier score is 0, for total accuracy.
- The lowest possible score is 1, which mean the forecast was wholly inaccurate.
Smaller scores (closer to zero) indicate better forecasts. Scores in the middle (e.g. 0.44, 0.69) can be hard to interpret as “good” or “bad”, so these are sometimes converted to Brier skill scores.
A Brier skill score has a range of -∞ to 1.
- Negative values mean that the forecast is less accurate than a standard forecast.
- 0 = no skill compared to the reference forecast.
- 1 = perfect skill compared to the reference forecast
The Brier score is a proper score function that measures the accuracy of probabilistic predictions. It is applicable to tasks in which predictions must assign probabilities to a set of mutually exclusive discrete outcomes.
[ https://en.wikipedia.org/wiki/Brier_score]
The following link may be helpful:
https://www.pinnacle.com/en/betting-articles/Soccer/brier-score-method-to-measure-surprises-in-premier-league/9BE2PL9DK4UM54FY
The Brier Score is probably the most commonly used verification measure for assessing the accuracy of probability forecasts. The score is the mean squared error of the probability forecasts over the verification.
https://www.met-learning.eu/pluginfile.php/5277/mod_resource/content/6/www/english/msg/ver_prob_forec/uos2/uos2_ko1.htm
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