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I am currently doing a backtest of a financial data set with an expanding window. For this, I estimate a Lasso model each month. Hence, each month that I estimate the model, I will have more data.

Now, I noticed that in the beginning of my sample, i.e. when there is relatively little data, Lasso does not penalize that much in the sense that many parameters are nonzero. Whereas in later periods, i.e. when there is more data available, I am seeing sparser models where more variables are set to zero.

Intuitively, I would expect less penalization in case there is more data available, as the coefficients may be estimated more accurately. Does anyone know what a reason could be for the opposite observation? In other words, why do we see more penalization when there is more data?

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