Question regarding standard deviation, probabilities and confidence intervals/bands
(please note that for all questions I am assuming normal distributions)
I have 5 years of historical spot copper prices. I can compute the standard deviation of the historical/realized prices. I can then apply this to the spot price to compute a 1,2 and 3 standard deviation up and down move through time. Note that I use the “exp x stdev x sqrt of time” function to project out through certain dates/time periods.
Question One: is it mathematically correct to use the probabilities associated with standard deviations can be used as the probabilities of a price being within a certain band? Specifically, if spot copper is $3.00, a one year one stdev move is $0.25 (with the “exp x stdev x sqrt of time” function applied), can I say that in one year, I am 68% certain that the price of copper will not fall below $2.75?
Question Two: Can I use the “normsinv” function, specify 90%, get 1.25 stdevs, and then use the results to say that… “I am 90% certain that copper prices in one year will be at or above” a certain price?
Question Three: Could you please provide a layman’s definitions and understanding of the differences between standard deviation “percentages” (68%, 95% and 99%) vs. confidence intervals vs. tolerance bands.
Cheers & thanks for the help,
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