I am currently analyzing investment strategies, and have implemented a backtest accordingly. This essentially means that I predict returns each month by using all prior historical data. Consequently, when I predict the last period, the sample will be much bigger than for the initial sample.

I am also using a validation sample which I use to determine the shrinkage parameter via a grid search. Now I noticed that as the sample increases, more coefficients are set to zero. Is there a reason for this? I would expect with more data the coefficients can be estimated more accurately and hence do not need to be set to zero?

Also when examining the added penalty term for Lasso, I can't come up with a good reason.

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