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Should we optimize parameter "N" from N-day-ahead stock returns?

Hi Pros,

When we form our stock prediction question as a classification model to predict stock to go up or down in the future, the target variable Y can be set as N-day-ahead stock returns e.g. one-day-ahead stock returns or 30-day-ahead stock returns.

we set Y as one-day-ahead returns for a short-term prediction and set it as one-month-ahead returns for a long-term prediction.

So when it comes to yield a better prediction accuracy, should we optimize this parameter "N" by trying say 1 day, 5 days, 10 days, 15 days, 30 days..etc.. to see which value n yield the best accuracy?

Or is it not appropriate to have a comparison this way because it is not an apple to apple comparison?

Thank you for your answer in advance

Regards,
Kelvin