I have a time series with daily frequency that has a seasonal pattern, with higher values in the summer and lower values in the winter.
To create a sample of the data for estimating the mean, median and standard deviation, I'm calculating the sample size using
$n = 4\sigma^2/M^2$
I estimated $\sigma^2$ from the history of a similar process. How can I verify if the seasonal aspect and autocorrelation are preserved in the sample, if I can't access the original time series?
EDIT: edited the question to (hopefully) make it more clear.