I have a dataset of daily price changes, represented as decimals. Perhaps: 0.5, 1.5, 2.0. That's to say it lost 50%, then it gained 50%, then it gained 100%.
I'd like to know how confident I should be that the true mean growth rate is within some margin of the sample mean growth rate.
I've read that I can "Just take logs of the datapoints, then compute arithmetic mean of those results, and then variance, and standard deviation, and compute confidence intervals like you would for arithmetic data, and then once you have the upper and lower bounds of the confidence interval, take exponents".
I think there are answers to this elsewhere in this stack, but I'm not a math major, and get a bit lost with all the exotic Greek symbols, so I'm just wondering if I've understood this correctly, and if I can get this answered using simpler language, and algorithmically. My questions are:
Is that above statement to do with taking logs correct?
What does "take logs" mean? Does it mean ln(), or log10(), or "It doesn't matter what the base is, so long as you use the same base when taking the exponents of the upper and lower bounds later on?"
Assuming it is correct, and the answer is "use ln()", would this be the correct method?
Generate a dataset by taking the ln() of every datapoint of my growth dataset.
Calculate arithmetic mean, variance, and standard deviation of that dataset.
Let N = the sample size, and for 95% confidence, calculate the error like this: Error = (1.96 * σ) / square_root(N)
Let the upper bounds, U = e^(M + Error), and the lower bounds L = e^(M - Error)
I am 95% confident that the true mean growth of this commodity is greater than L, and less than U.
Is that correct?