My task is to summarize the descriptive statistics of time series data ( mean, SD , standard error ). It is fairly straightforward for a stationary series. But How do we find out the mean, standard deviation, standard error of the non stationary time series data?
I have been reading about the stationary series and how to make a time series stationary by differencing the series. If we take the mean of the differenced series, will that be a reflector of mean of the original data.
Any inputs on this?
Best Answer
Well, if a time series not is stationary, it does not have a well-defined mean or variance. Non-stationary means (among others) that the marginal distribution of $X_t$ depends on $t$. So (the distribution of) each $X_t$ (could) have a mean, variance, etc, but how do you estimate it based on only one observation?
As to your question If we take the mean of the differenced series, will that be a reflector of mean of the original data? the answer is NO. If your series is a random walk, it has no mean, but the differenced series has a mean of zero!
So your question how to do descriptive statistics on a non-stationary time-series is a tough one, and difficult to answer in generality, as will depend on context. But
In short, generally non-stationary series need some serious modeling as a help for interpretation. Maybe we can say more if you give some context.