Hi Keith, I think what you are seeing is that the autocorrelation values are still in your dataframe for all of the data. I address this point in the 1st caveat near the end of the post. What you can either do is, remove the autocorrelation terms all together or put the predict in a loop to get a single day prediction ahead of time and then use that value to append to the autocorrelation terms appropriately.

This post was meant to give an introduction to this flavor of neural network that performs very good with many X variables. It just happens that this dataset does not have many X variables originally, but I thought it was a simple enough dataset to demonstrate the technique. If you have a dataset that is just a target variable you want to forecast without any additional X variables, you might want to experiment with an LSTM approach as well.