joint pdf for autocorrelation autocorrelation

  1. What is autocorrelation in real life? Any example?
  2. How does autocorrelation dependent on time difference? Here is Xt1 and Xt2 how comes \phi{tau}?
  • $\begingroup$ you need to learn about ergodicity. a process is ergodic when probabilistic averages are the same as time averages. $\endgroup$ – robert bristow-johnson Feb 2 at 2:11
  • $\begingroup$ it's nice if one can understand those things for sure because the concept of covariance stationarity becomes clearer. But, as far as your question, $\tau$ is the difference $(t_2 - t_1)$. The definition given there assumes that the process is covariance stationary which means that the correlation between observations spaced $\tau$ periods apart, only depends on $\tau$. For purposes of understanding, think of autocorrelation(tau) as the correlation coefficient of the observations in the series that are $\tau$ periods apart. $\endgroup$ – mark leeds Feb 2 at 5:06

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