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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?

kjetil b halvorsen
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Tim
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    Possible duplicate of [How do you check ergodicity of a stochastic processes from its sample path(s)?](https://stats.stackexchange.com/questions/83808/how-do-you-check-ergodicity-of-a-stochastic-processes-from-its-sample-paths) – kjetil b halvorsen Sep 05 '18 at 13:37
  • The side Q: https://stats.stackexchange.com/questions/182764/stationarity-tests-in-r-checking-mean-variance-and-covariance and search this site – kjetil b halvorsen Sep 05 '18 at 17:58

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