Our Professor couldn't explain the clear difference between the Yule Walker equation and the Modified version of it that is used in Stochastic models. Please explain both the equations and why we modified them. Also, its significance, if you can.Taken from Statistical Signal Processing by Monson.H.Hayes

The image is from Statistical Signal Processing by Monson Hayes

  • $\begingroup$ hi! I'm not aware of a single canonical "modified YW equation"; could you add the definition or a citation to your question? Otherwise, you're basically asking us to explain the difference between something that we know and something that we don't know for sure. $\endgroup$ Oct 17, 2022 at 20:35
  • $\begingroup$ Also, the 1927 paper by Yule is about the random sunspot process, and Walker in 1931 refines the methods of solving the equations of that autoregressive model of a stochastic process. So, I'm really not sure how to state Yule-Walker equations for something deterministic. $\endgroup$ Oct 17, 2022 at 20:42
  • $\begingroup$ Yule Walker Equation relates the autocorrelation data to the filter coefficients, given a process. Modified version just relates the autocorrelation data to only one of the filter coefficients (the AR coefficients). $\endgroup$ Oct 17, 2022 at 21:03


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