support more than 2 percentiles to be passed for `predict_interval` about skforecast HOT 5 CLOSED

Hi @JoaquinAmatRodrigo, @JavierEscobarOrtiz, thanks for your comments. Yes, I can definitely start with quantile calculation in sktime.

I just created sktime/sktime#5447 with solution 1 above, and will switch to 2 when available. It'll be great if you can take a look and give some feedbacks on other parts and the feasibility of the TODO comments mentioned in the PR.

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Hi @yarnabrina,
Thanks for using skforecast.

What you suggest makes perfect sense. Since the heavy computation relies on the bootstrapping process, the user may benefit from calculating multiple quantiles with a single function call.

@JavierEscobarOrtiz What are your thoughts? We will need to check if this change affects the other parts of the API to estimate the effort required. But if all goes well, this may be a feature to include in the next release.

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Hello @yarnabrina,

Thanks for opening the issue!

Your suggestion sounds very interesting. It is true that sometimes you are not interested in the lower and upper bounds of an interval, but you are looking for some specific quantiles.

Regarding our method predict_interval, we have discussed and decided to leave it as it is, since the purpose of this method, as its name suggests, is just to get an interval (lower and upper bound).

So, two solutions come to my mind at this point:

1. You can imitate our predict_interval code and modify the line you pointed out. As I see it, you will not need a for loop because all the calculations are done in predict_bootstraping and you just have to call the desired quantiles with the numpy quantile method.

2. Since I may be missing some behavior in your code and the feature you suggest is very interesting, we will create a method called predict_quantiles with the behavior you mention for the next version. 😄 This will also help us to avoid making a lot of changes in the code of functions like backtesting_forecaster (since they use the predict_interval method internally).

Hope this comment fits your needs.

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Closed by #577 based on my understanding.

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@yarnabrina correct,

There will be a change where the output columns of predict_quantile will be named as q_0.05, q_0.50 ...

It will come in a future PR.

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