Can / should I use past (e.g. monthly) label columns from a database as features in an ML prediction (no time-series!)?

Question

The question: Is it normal / usual / professional to use the past of the labels as features? I could not find anything reliable on this, although it is a basic question.

Edited: Please mind, this is not a time-series question, I have deleted the time-series tag now and I changed the question. This question is about features that change regularly over time, yes! But we do not create a time-series from this, as there are many other features as well which are not like the label and are also important features in the model. Now please think of using past labels as normal features without a time-series approach.

I try to predict a certain month of data that is available monthly, thus a time-series, but I am not using it as a time-series, it is just monthly avaiable data of various different features.

It is a classification model, and now I want to predict a label column of a selected month of that time-series. The previous months before the selected label month are now the point of the question.

I do not want to just drop the past months of the label just because they are "almost" a label (or in other words: they were just the label columns of the preceding models in time). I know the past of the label, why not considering it as features as well?

My predictions are of course much better when adding the past labels of the time-series of labels to the features. This is logical as the labels usually do not change so much from one month to the other and thus can be predicted very well if you have fed the data with the past of the label. It would be strange not to use such "past labels" as features, as any simple time-series regression would then be better than the ml model.

Example: Let's say I predict the IQ test result of a person, and I use her past IQ test results as features in addition to other normal "non-label" features like age, education aso. I use the first 11 months of "past labels" of a year as features in addition to my normal "non-label" features. I predict the label of the 12th month. Predicting the label of the 12th month works much better if you add the past of the labels to the features - obviously. This is because the historical labels, if there are any, are of course better indicators of the final outcome than normal columns like age and education.

Possibly related p.s.:

p.s.1: In auto-regressive models, the past of the dependent variable can well be used as independent variable, see: https://de.wikipedia.org/wiki/Regressionsanalyse

p.s.2: In ML you can perhaps just try any features and take what gives you the best results, a bit like >Good question, try them [feature selection methods] all and see what works best< in https://machinelearningmastery.com/feature-selection-in-python-with-scikit-learn/ >If the features are relevant to the outcome, the model will figure out how to use them. Or most models will.< The same is said in Does the feature selection matter for learning algorithm with regularization?

p.s.3: Also probably relevant is the problem of multicollinearity: https://statisticsbyjim.com/regression/multicollinearity-in-regression-analysis/ though multicollinearity is said to be no issue for the prediction: >Multicollinearity affects the coefficients and p-values, but it does not influence the predictions, precision of the predictions, and the goodness-of-fit statistics. If your primary goal is to make predictions, and you don’t need to understand the role of each independent variable, you don’t need to reduce severe multicollinearity.

Answer 1

It is perfectly possible and also good practice to include past label columns as features, though it depends on your question: do you want to explain the label only with other features (on purpose), or do you want to consider other and your past label columns to get the next label predicted, as a sort of adding a time-series character to the model without using a time-series?

The sequence in time is not even important, as long as all of such monthly columns are shifted in time consistently by the same time when going over to the predicting set. The model does not care if it is just January and February of the same column type, for the model, every feature is isolated.

Example: You can perfectly run a random forest model on various features, including their past label columns that repeat the same column type again and again, only representing different months. Any month's column can be dealt with as an independent new feature in the ml model, the only importance is to shift all of those monthly columns by the exactly same period to reach a consistent predicting set. In other words, obviously you should avoid replacing January with March column when you go from a training set January-June to a predicting set February-July, instead you must replace January with February of course.

Update 202301: model name is "walk-forward"

This model setup is called "walk-forward", see Why isn’t out-of-time validation more ubiquitous? --> option 3 almost at the bottom of the page.

I got this from a comment at Splitting Time Series Data into Train/Test/Validation Sets.

In the following, it shows only training and testing set. It writes "validation set", but it is known that this gets mixed up all over the place, see What is the Difference Between Test and Validation Datasets?, and it must be meant as the testing set in the default understanding of it.

Thus, with the right wording, it is:

This should be the best model for labels that become features in time.

validation set in a "walk-forward" model?

As you can see in the model, no validation set is needed since the test data must be biased "forward" in time, that is the whole idea of predicting the "step forward in time", and any validation set would have to be in that same biased artificial future - which is already the past at the time of training, but the model does not know this. The validation happens by default, without a needed dataset split, during the walk-forward, when the model learns again and again to predict the future and the output metrics can be put against each other. As the model is to predict the time-biased future, there is no need to prove that or how the artificial future is biased and sort of "overtrained by time". It is the aim of the model to have the validation in the artificial future and predict the real future as a last step only.

But then, why not still having a validation set on top of this, at least if it is just a small k-fold validation? It could play a role if the testing set has a few strong changes that happen in small time windows but which are still important to be predicted, or at least hinted at, but should also not be overtrained within each training step. The validation set would hit some of these time windows and might show whether the model can handle them well enough. Any other method than k-fold would shrink the power of the model too much. The more you take away from the testing set during training, the less it can predict the future.

Wrap up:
Try it out, and in doubt, leave the validation aside and judge upon the model by checking its metrics over time, during the "walk-forward". This model is not like the others.

Thus, in the end, you can, but you do not have to, split a k-fold validation from the testing set. That would look like:

After predicting a lot of known futures, the very last step in time is then the prediction of the unknown future.

This also answers Does the training+testing set have to be different from the predicting set (so that you need to apply a time-shift to ALL columns)?.