Suppose you're tracking the day-to-day price fluctuations of the price of gasoline. From your data set that is 100% accurate( just entertain this idea.) you know that there is a 70% chance the price of gasoline will move +/- 10% in 7 calendar days.

Let's now assume the price of gasoline starts at $1.00. From day 1-6 the price of gas is in flux and comes back to $1.00 for a net change of 0% on day 6.

Now, your data for 1 day gasoline price movement is +/- 3% with a 70% probability. Day 7 is about to occur and you have two observations, the 7 day and the 1 day. Which one is correct?

I'm not a statistics person but this problem has me confused. Any help in this problem would be helpful.

If the 7 day and 1 day are both correct (are they???), is it therefore the case that on day 7 there is still a 70% chance that it will move +/- 10%? (If not then how have the odds changed?) If the one day is also correct, is it is still true that there is a 70% chance of a +/- 3% occurrence. It could also mean that there is a higher probability that this is one of the 30% occurrences that doesn't move +/- 10% , but that still shouldn't change the overall distribution of the odds so I believe it shouldn't change the overall probability of a +/- 10% in the 7 day period. My conflict comes when I believe (possibly incorrectly - please enlighten me if so) that the 7 day probabilities must hold true no matter the price on day 6 for the full 7 day calculation. Therefore it would make sense to me to assume there is a high probability of a larger than expected ( the 3% 1 day move) in this situation. However, these are independent observations so they can't influence one another, so that can't be true... or can it?!

Oh I'm getting myself lost, please help me understand this process and how I could use any of this information if possible to create some type of statistical edge for prediction. Thanks.

Let's now assume the price of gasoline starts at $1.00. From day 1-6 the price of gas is in flux and comes back to $1.00 for a net change of 0% on day 6.

Now, your data for 1 day gasoline price movement is +/- 3% with a 70% probability. Day 7 is about to occur and you have two observations, the 7 day and the 1 day. Which one is correct?

I'm not a statistics person but this problem has me confused. Any help in this problem would be helpful.

If the 7 day and 1 day are both correct (are they???), is it therefore the case that on day 7 there is still a 70% chance that it will move +/- 10%? (If not then how have the odds changed?) If the one day is also correct, is it is still true that there is a 70% chance of a +/- 3% occurrence. It could also mean that there is a higher probability that this is one of the 30% occurrences that doesn't move +/- 10% , but that still shouldn't change the overall distribution of the odds so I believe it shouldn't change the overall probability of a +/- 10% in the 7 day period. My conflict comes when I believe (possibly incorrectly - please enlighten me if so) that the 7 day probabilities must hold true no matter the price on day 6 for the full 7 day calculation. Therefore it would make sense to me to assume there is a high probability of a larger than expected ( the 3% 1 day move) in this situation. However, these are independent observations so they can't influence one another, so that can't be true... or can it?!

Oh I'm getting myself lost, please help me understand this process and how I could use any of this information if possible to create some type of statistical edge for prediction. Thanks.

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