I have a question about t-test and CLT assumptions.
I am currently analysing prices of several futures contracts. I needed to run t-tests to determine if the mean of the price series of each contract differs from some value (one-sample t-test).
T-test requires that the data are collected from a representative, randomly selected portion of the total population. In my case, I was thinking about this as my "representative" sample is some contract (mostly 9 months trading, I am using just 60 last days before maturity) from the whole population of futures prices in the timespan from the launch of futures contracts in, let's say 1992, until today. Now, I am not sure if the particular daily prices within my sample necessarily need to me random/independent as well?
At the same time I needed to apply CLT to satisfy normality assumption for t-test. CLT requires random sample, again (my random sample would be prices of some contract) and also the theorem requires that the sample values are independent of each other. As I have strong autocorrelation among prices. I was solving this issue by using autocorrelation-robust standard errors by Newey-West.
Is independence of particular values of the sample required in t-test even when I weren't using CLT? Could somebody, please, help me to understand this?