🚀 go-pugleaf

In article <1389@mrsvr.UUCP> kohli@gemed.ge.com (Mr. Bad Judgment) writes:
>1. Are the AR "parameters" the poles of the waveform?
>	If so, does this mean that an AR parameter of magnitude
>	> 1 indicates an unstable system (assuming no zero to
>	counteract it)?

There are many different families of AR parameters.  One could
consider the poles the parameters; then the requirement for stability
is that they be inside the unit circle.  But the most common choices
of parameters to use are either the filter coefficients, the
coefficients of the A(z) polynomial in the model, where
           1
   H(z) = ----
          A(z)

so the poles are the roots of A(z).  But you're probably thinking about
the reflection coefficient parameters, which can be obtained from the
autocorrelations or the filter coefficients using the Levinson recursion.
The requirement for stability is that all reflection coefficients have
magnitude <= 1.

>2. (And the MA parameters *are* the zeroes?)

It's sufficient to specify the poles and zeros, though people usually
specify the coefficients of the numerator and denominator polynomial
instead.

>3. Is the noise process usually neglected when
>	using the AR and MA parameters to model the
>	time series?

Not at all.  It's usually explicitly assumed that the process is the
result of a white noise process being filtered by a pole-zero filter.
In some methods, we basically look for a filter that will convert the
data into white noise; the model is simply the inverse of this filter.

-- 
-- Joe Buck, just visiting/consulting at Entropic
-- write me at: jbuck@janus.berkeley.edu 
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