How to implement dynamic regression model like
(1 - u1*B-u2*B^2)*(1-u24*B^24)*(1-u168*B^168)*Yt = (vo+v1*B+v2*B^2)*Xt + Et
with Et WN?
I have just read the proc arima user guide...And I don't know to transform my model in a transfer function model....
please help me!
Thank for the reply:
If I write my ARX like this
Yt = (v0 + v1*B + v2*B^2)/((1-u1*B - u2*B^2)*(1-u24*B^24)*(1-u168*B^168))*Xt + 1/((1-u1*B - u2*B^2)*(1-u24*B^24)*(1-u168*B^168))*Et
(whit NOINT option) the parameters of the two denominator are estimated different:
Yt = (v0 + v1*B + v2*B^2)/((1-u1a*B - u2b*B^2)*(1-u24a*B^24)*(1-u168a*B^168))*Xt + 1/((1-u1b*B - u2b*B^2)*(1-u24b*B^24)*(1-u168b*B^168))*Et
whit uia != uib
You can specify Y = (numerator poly) / (denominator poly) X + E / (AR Poly) type model for your polynomials as follows:
proc arima data=test;
identify var=y crosscorr=x;
estimate p=(1 2)(24)(168)
input=((1 2)/(1 2)(24)(168) x)
It will indeed happen that the estimated denominator polynomial coefficients in the transfer function will generally be different from the estimated AR polynomial coefficients. Currently PROC ARIMA does not allow constraining these coefficients to be the same.
You seem to be dealing with hourly data and are trying to capture hour of the day and hour of the week seasonal patterns. Is this particular model very important for you or some other model might do that still does a good job?
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