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 R&D > >______________________________________________ >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.