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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