I analysing time-series to see the range of an asset. I have data for GBPUSD so i could only analyze this so far.
I have used both empirical rule and percentile. Of course they give different solutions. When i take a look at monthly data, i can forecast the minimum and maximum values using percentile. For example i can say GBPUSD will be between 1.27 - 1.35 by the end of the month (95th percentile). FYI: this is not a real forcast.
Assume that, by the 29th of the month, assume that GBPUSD is very close to 1.34. However our forecast was between 1.27 - 1.35. Now the odds are close to 1.35.
The confusing part is this one. Is 1.27 still 95th percentile? It looks like not even 1%. Do we have to calculate percentile day by day for such problems? Or using empirical rule (68-95-99.7), do we have to recalculate?
I am just training and working on economical dataset. This dataset can be anything else.