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I'm planning to use weather data to predict crime in Chicago. I'm confused which to use as features: historical weather forecast data or historical actual weather data? And what is the underlying logic here? I'm assuming later only forecast data is available for prediction. Thank you for any input.

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Using historical weather data implicitely means that you trust meteorologists and weather forecasters to improve their model over time and you let them the full responsability of it; however once your own model deployed a bias in the forecast may create a bias in your model response.

Using weather forecasts instead should give better results because your model will directly capture potential bias in the forecasts; however if the weather forecasters update their forecasting model, and if you miss this update, your model response may suffer from it.

I wouldn't use both historical weather data and weather forecasts in the same model; I would consider to build two models, one with historical data and one with weather forecasts, then go for historical data if the improvement of using weather forecasts is not significant.

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You could you both forecast and actual weather, then see which provide better features for forecasting? Obviously there will be a lot of correlation between the forecast and the actual weather, but you could use feature selection to choose the most important?

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I'd suggest trying both simultaneously. My thought is that certain weather conditions make for better situations to commit crime. If my assumption is true, then it is likely that criminals use this to their advantage and look at weather predictions. Don't laugh at me.

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You are better off using the forecasts. In deployment your model will be relying on weather forecasts, which are obviously not 100% accurate. Therefore, if you train your model on the actual weather you may artificially inflate your accuracy. Using the forecasts will give you a better estimate of the accuracy of your model moving forward.

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