Given a stack of sequential vectors, I want to predict the next. I use the mean squared error loss, however, it appears to not be correcting my vectors element-wise. It appears that my mean of my vector gets accurately captured. In fact when I kept predicting for multiple vectors ahead, the element-wise values are completely off between the prediction and the ground truth but the mean and variance is accurately captured (first and second moment, given data is scaled to have zero mean). Has anyone experienced this? I didn't find any literature addressing this or even mentioning this even if they've stumbled upon it. Let me know if anyone has any ideas?