# Determine sample size of a time series with seasonal variation

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

$n = 4\sigma^2/M^2$

with

for $M=\sigma^2/10$.

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.

• There is nothing in your question that would rule out using all the data, which obviously is optimal in terms of obtaining an accurate estimate of the mean. Can you provide further information that would clarify your objectives and the nature of the data? – whuber Aug 29 '17 at 19:44
• The full data set is too big to be manipulated with the available resources, so I need to estimate a few statistics before trying to use the entire dataset. – Ivan Aug 30 '17 at 13:37
• There's a disconnect here: three years of daily data is so small that it's possible to analyze it with pencil and paper if need be (less than 1100 numbers). How could the "available resources" not be a match for such a small problem? Regardless, there seems to be nothing special about estimating the mean in this question. Indeed, the effort needed to go through a formal determination of some kind of optimal sample size would likely be greater than finding the mean of the data outright. – whuber Aug 30 '17 at 15:01