Statistically speaking, If I have 720 0000 unique customer information, how best can I sample from this population such that it is a representative of the whole data set? Also how large should my number of observations be? Does it make statistical sense to build a time series model based on a sample and use that model to make predictions on the whole data set?
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$\begingroup$ There's a mystery about this question: since you have the entire dataset, why would you want to make predictions about it? $\endgroup$– whuber ♦Commented May 13, 2019 at 18:32
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If you have the whole population why sample at all. Generally speaking if you want to sample and know the whole population than a random sample is best. Sometimes you have to over sample certain groups because they have a known tendency to not respond. Its more complex to analyze such samples (they require the use of weights to analyze). Most of the more complex sampling methods are done when you are not able to sample from the entire population (usually because you don't know it). How many to sample depends on what error you can live with, commonly beyond about 1,000 does not reduce error much. My links are down, but it is easy to find information on this, look at sampling error on line or margin of error of poll.
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$\begingroup$ One has to be careful about the term sample and population however. Depending on one's perspective one might have or not have the whole population. For example I work at a state agency and have our whole population at any moment in time. I could consider this a population (and that matters among other things whether p scores and the related assumptions of regression that influence them matter). But, from a different perspective I have a sample of other states populations or of my state over time. That is admittedly not the way sample's are thought of, it applies most in terms of random effects $\endgroup$ Commented Oct 22, 2020 at 15:46