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Given a sample path from a process supposed to be stationary, I saw the sample autocorrelation function of the sample path is used to estimate the autocorrelation function of the process. But this requires that the stationary process is ergodic. So

  • is ergodicity checked on the sample path before estimation of the autocorrelation function? If yes, how is ergodicity checked?

  • is the estimation done assuming ergodicity without checking it, and after the estimation, testing/checking if the estimation fits the data? If yes, how is the testing done?

A side question: how is stationarity is tested for estimation of autocorrelation function?

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