R help - Mar 2007 - 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 R&D

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: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Laurent Duvernet
Sent: Tuesday, March 13, 2007 10:36 AM
To: r-help at 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 R&D

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