I have a question about the prediction intervals in multistep forecasting using TimeGPT. Should I interpret each interval individually, or should I be considering them in a more interconnected way? For example, can I summarize the forecast by assuming it will always be at the upper or lower bounds across multiple periods, or is this an incorrect interpretation?

Hi @Vidar Ingason You should consider prediction intervals as interconnected. However, you shouldn’t assume that the forecast will always be between the upper and lower bounds. Instead, consider prediction intervals as a range of values that the forecast (a random variable) can take with some specified probability. So if you have a 95% prediction interval, you can assume that it is very likely the actual value will fall within that interval, but it is not a certainty. For more, I recommend checking out the classic book by Rob Hyndman.

Hi @Mariana Menchero I'll take a look at his book, been a while since I read it first. What I'm trying to do is to give a client extra information regarding the forecast I've created, i.e. cumulative forecast over the whole horizon. It's easy to sum the forecast itself but more tricky to sum the upper or lower bound. Just wanted to check with you 🙂

Ah! I now understand your problem better and the answer is not that straightforward. Prediction intervals for individual forecasts reflect the uncertainty at each point in the future and are not necessarily additive. So summing the upper or lower bounds of the prediction intervals for each period doesn’t provide a statistically valid prediction interval for the total forecast across the forecasting horizon. In practice, however, as a rough estimate, they can work ok. I used to wok for a consulting company that generated forecasts for retailers and this approach was pretty common and seem to be enough for the purpose of planning.

Thank you so much @Mariana Menchero, I found a blog from Hyndman regarding this. He used simulation. I tested his code and compared it to the outcome of just summing the upper and lower bound. In that simple test I did, the difference was not huge. So this might be ok in some cases.