Sorry if the notation is unclear. You got it right:
P(x) = (1 - a_1*x - a_2*x^2) * (1 - b_1*x^23 - b_2*x^24) * (1 - c_1*x^168).
The a_i's, b_i's and c_i's are the coefs of the polynom P.
And there is also an MA part, which is Q(B) epsilon(t). Here epsilon(t) is
the error process, and Q is another polynom of the same type as P (it could
be different, that does not change the problem).
Q(x) = (1 - alpha_1*x - alpha_2*x^2) * (1 - beta_1*x^23 - beta_2*x^24) * (1
- gamma_1*x^168).
I can write X(t) = ..., but I'm not sure it would be a lot clearer...
X(t) = a_1*X(t-1) + a_2*X(t-2) + b_1*X(t-23) + (b_2 + a_1*b_1)*X(t-24) +
(a_1*b_2 + a_2*b_1)*X(t-25) + a2*b2 X(t-26) + the terms around X(t-168)
+ ... the MA part.
I hope everything is clear now.
From: Leeds, Mark (IED) [EMAIL PROTECTED]
To: Laurent Duvernet [EMAIL PROTECTED], r-help@stat.math.ethz.ch
Subject: RE: [R] estimating an ARIMA model with constraints
Date: Tue, 13 Mar 2007 10:56:47 -0400
are the carats in your notation meant to be time subscripts ?
also, I think I know what a and b are meant to be ( the coefficients of
the polynomaisl corresponding
To the ar part of the model but correct me if I'm wrong ) but is there
an ma piece to it also ?
And I don't see an error term ?
I think you need to be clearer on your notation and write out the full
model in terms of X(t) = whatever because then more people will reply.
-Original Message-
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] On Behalf Of Laurent Duvernet
Sent: Tuesday, March 13, 2007 10:36 AM
To: r-help@stat.math.ethz.ch
Subject: [R] estimating an ARIMA model with constraints
Hi,
I am trying to estimate an ARIMA model in the case where I have some
specific knowledge about the coefficients that should be included in the
model. Take a classical ARIMA (or even ARMA) model:
P(B) X(t) = Q(B) epsilon(t),
where X(t) is the data, epsilon is a white noise, B is the backward
operator and P and Q are some polynoms. Additionally, assume that you
know in advance how P and Q look like. Typically, P could be something
like this:
P(x) = (1 - a(1)*x - a(2)*x^2) * (1 - b(1)*x^23 - b(2)*x^24) * (1 -
c(1)*x^168)
(That is in the case of hourly data, with lags 23 and 24 corresponding
to the day, and lag 168 for the week.) How do you estimate this kind of
model with R? The arima() and arima0() functions in the stats package do
not allow this kind of constraints on the polynoms. I've searched in the
packages dedicated to time series analysis, but I have not found a
solution. Has anyone an idea?
Thanks in advance!
Laurent Duvernet
EDF RD
__
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
_
mobile comme sur PC ! http://mobile.live.fr/messenger/bouygues/
__
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
