How to construct confidence bound for Time Series Prediction?
There is a technique called "Quantile Regression" which allows you to calculate a percentile of your $Y$ variable, the way a quantile regression works is by giving more penalty to the data far to the desired percentile.

Quantile Regression

As you used deep learning (I don't know in which software), maybe you could tailor a penalty function which does the same as quantile regression does or maybe the code you are using has it implemented.