Posted on Tuesday, 10th April 2012

I have posted Chapter18-APR10.pdf. Please read Secs 18.1-18.2.3 but skip 18.2.1-18.2.2. Then post a comment.

Posted in Class | Comments (14)

  1. Eric VanEpps Says:
    April 10th, 2012 at 4:44 pm

    It’s not clear to me what “s” represents in the autocovariance function or the autocorrelation function. Could you clarify what it is and how it fits into the functions described?

  2. Shubham Debnath Says:
    April 11th, 2012 at 7:07 pm

    In the AR(p) model and selecting order p, what is a typical range for p? And so what is a relatively large value to start with?

  3. Scott Kennedy Says:
    April 11th, 2012 at 8:29 pm

    I have no intuition about the significance of the magnitude of phi in the autoregressive model. Does this mean it is always decreasing?

  4. Sharlene Flesher Says:
    April 11th, 2012 at 9:41 pm

    How do you decide if slow varying trends should be treated as oscillatory or as sources of long range dependence, as in the LFP example (18.1)?

  5. Ben Dichter Says:
    April 11th, 2012 at 10:25 pm

    Could you go through the math in the autocorrelation illustration?

  6. Rex Tien Says:
    April 11th, 2012 at 11:05 pm

    You mention that harmonics can often be fitted with the form omega_2 = k*omega_1, where k is an integer. Could we also use fractional k values? Is there some mathematical reason why harmonics with integer k’s should improve the fit?

  7. Jay Scott Says:
    April 12th, 2012 at 12:15 am

    I do not understand the generalization of 18.26 to 18.27:

    X_t = phi*X_(t-1) + W_y
    to
    X_t = Summation i=1 to p of [phi_i*X_(t-i) + W_y].

    or how the magnitude of phi determines causality(pp527-8).

  8. David Zhou Says:
    April 12th, 2012 at 3:13 am

    I’m not clear about the utility of spectral analysis – you mention it but it doesn’t seem to factor into autocorrelation analysis – is it more important for Fourier analysis (which we skipped)?

  9. Amanda Markey Says:
    April 12th, 2012 at 5:24 am

    You say, “many physical phenomena may be described by applying this technique”. What are more of these?

  10. Yijuan Du Says:
    April 12th, 2012 at 6:38 am

    I don’t quite understand, in the example of EEG and EPSC, ‘the time scale their variation occurs’, compared to observation interval..

  11. Rich Truncellito Says:
    April 12th, 2012 at 7:26 am

    In describing the autocovariance function on p. 512, you define h = t – s. Does this definition of h also apply to the h in the description of “strictly stationary” on the previous page? In other words, does the number of elements in each set of variables {Xt, Xt+1,…, Xt+h} and {Xs, Xs+1,…, Xs+h} have to agree with h = t – s?

  12. Rob Rasmussen Says:
    April 12th, 2012 at 8:01 am

    Could you explain more about the difference between ACF and PACF?

  13. Matt Bauman Says:
    April 12th, 2012 at 8:23 am

    I’ve heard some forms of AR(p) models being referred to as Wiener Cascades or Wiener Filters — are there any differences between these three terms? Or are they just synonyms?

  14. Thomas Kraynak Says:
    April 12th, 2012 at 8:29 am

    Could you go over how you formulate the sample ACF?

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