## How to construct confidence bound for Time Series Prediction?

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I have some time series data and am using some Deep Learning techniques to get its prediction. Now, I would like to construct confidence bounds for it.

I calculated the residuals, their mean and standard deviation. Then I plotted prediction vs residuals and calculated mean + 3$$\sigma$$ and mean - 3$$\sigma$$, and plotted them on my graph. So, I have something like this

Now, I would like to use a similar technique so that I can have confidence bounds on time series plots.

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Related 10814. See confidence interval plot for time series prediction near end of that answer.

– Edmund – 2019-05-29T01:02:37.453

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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.