R help - Feb 2009 - residuals from a fractional arima model and other questions

Dear list and Martin,

I'm testing different approaches to fit an electricity demand time series
and come upon the fracdiff package (v 1.3-1) for fitting fractional ARIMA
models. The following questions are motivated by this package.

1. Despite having a help page, the residuals and fitted functions don't seem
to have implementation, or did i miss something obvious? Alternatively, having a
fitted fracdiff object, how do I calculate the residuals? (Please forgive me if
this is totally obvious which I'm sure it may be. Is it just a matter of
expanding out the (1-L)^d term?)

2. I don't have access to the cited Haslett & Raftery (1989) paper, but
could someone explain to me the little cautionary note in the help page stating
that "nar and nma should not be too large (say < 10) to avoid degeneracy
in the model." I see that a different implementation of the FARIMA
procedure in Splus could lead to an explosive, ie. non-stationary model when
it's used to fit a log volatility data set (Zivot & Wang, p.291). Zivot
explains that it might be due to canceling roots in the AR and MA polynomials.
Is this a caution against a similar problem. Which leads to my next question,

3. Is the FARIMA procedure known to be unstable at time? Is there a better way
(with a different package perhaps) to model long range dependence ?

4. When my model is fitted, i got a warning that it's unable to compute the
correlation matrix. Output looks like,

Call:
  fracdiff(x = res.iact.ts, nar = 9, nma = 9, M = 100)

*** Warning during fit: unable to compute correlation matrix

Coefficients:
      Estimate Std. Error    z value Pr(>|z|)
d    4.745e-01  0.000e+00        Inf   <2e-16 ***
ar1  8.897e-01  0.000e+00        Inf   <2e-16 ***
ar2 -3.386e-01  0.000e+00       -Inf   <2e-16 ***
ar3  3.339e-01  2.044e-17  1.634e+16   <2e-16 ***
ar4 -4.406e-01  0.000e+00       -Inf   <2e-16 ***
ar5  3.924e-02  6.349e-18  6.182e+15   <2e-16 ***
ar6 -5.184e-01  2.558e-17 -2.026e+16   <2e-16 ***
ar7  8.988e-01  0.000e+00        Inf   <2e-16 ***
ar8 -7.568e-01  3.112e-16 -2.432e+15   <2e-16 ***
ar9  3.442e-01  2.175e-22  1.582e+21   <2e-16 ***
ma1 -1.190e-01  1.470e-18 -8.097e+16   <2e-16 ***
ma2 -9.343e-02  0.000e+00       -Inf   <2e-16 ***
ma3  2.140e-01  0.000e+00        Inf   <2e-16 ***
ma4 -2.107e-01  0.000e+00       -Inf   <2e-16 ***
ma5 -2.892e-01  0.000e+00       -Inf   <2e-16 ***
ma6 -7.197e-01  2.888e-08 -2.492e+07   <2e-16 ***
ma7  3.021e-01  0.000e+00        Inf   <2e-16 ***
ma8 -1.395e-01  0.000e+00       -Inf   <2e-16 ***
ma9 -2.493e-02  3.013e-21 -8.274e+18   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1
[d.tol = 0.0001221, M = 100, h = 0.004807]
Log likelihood: -4.562e+05 ==> AIC = 912360.4 [1 deg.freedom]
Last question : why are some of z-values infinite?

Thanks in advance.

Horace Tso



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