Estimating Beta: OLS vs Rolling vs Kalman

A study tries static OLS and a 4-bar rolling OLS on training, then keeps whichever did better on test. What is wrong?

• Nothing, as long as both were fitted on training only
• Choosing by test result is selection, so both count as trials
• Rolling OLS is never allowed on training data

Which β sizes the legs during the test window?

• The latest Kalman estimate, updated every test bar
• The estimator's value at the last training bar, frozen
• The average of the training and test estimates