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I am dealing with the LASSO regression in (pure AR-regressions) context. I have a lot of observations (around 4000). Therefore I would try to use the train/validation/test method. The idea was to train the data, lets say on the first 2500 observations, then using 500 to determine the Tuning Paramter and then applying a rolling window on the test set.

After I determined my tuning Parameter, should I estimate the model on the sample of train and validation set and then applying the rolling window or do I have to use only the train set ?

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I would say that your approach is correct if you mean that you first perform hyperparameter selection based on training and validation sets and then, you will fit your model with those hyperparameters (which would be the best) employing together training data and validation data. Finally, you would be able to get the generalisation error predicting in your test set.

This post has a great visual explanation about the topic and Andrew Ng explains it here.

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