a raw data basis consists of measurements of a certain quantity over time taken every 1 minute. But these data are not available for me.
What I have are the empirical distributions for the maximum variation of the quantity every 15 minutes, 1 hour and 1 day together with the expected value of the quantity taken over the complete set of raw data.
Is it possible to construct sample paths over time for the quantity from this information ? If yes - what do you suggest ?