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I did some forecasting (stock) for my thesis. I only used a fix amount of 600 Samples (can't change that). Because of the small dataset i only did a Train and Test Split (no validation etc.). I found some settings where i get very good results (MAPE and R2) for both train and test. But i only have the loss curve of the train set. I am wondering if that is enough, or is it a must to have both train and validation loss-curve?

Because of that thought, i split it three ways (10% holdout test), and 70% train and 20% Validation. There i have both loss-curves, and i get good results for the MAPE score (around 3-5 %for all three) in Train Val and Test, only the R2 is bad in the val-set (0,7 and in train/test 0,95)

So can i use the first option, and only use the train-loss-curve?

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I do not think a validation set will be necessary in this case if you are only training on a single data model. To my understanding, the validation set would be more useful if you are training on multiple various models, and that would help you decide which is the best fit.

https://machinelearningmastery.com/difference-test-validation-datasets/