## dynamic regression model

Occasional Contributor
Posts: 11

# dynamic regression model

Hello

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....

Occasional Contributor
Posts: 11

## dyanmic regression

Hello

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?

Super User
Posts: 10,035

## Re: dyanmic regression

```If it is about Time Series Analysis, plz post it at Forecasting Forum.

Proc arima can do dynamic regression.

```
Occasional Contributor
Posts: 11

## Re: dyanmic regression

Ok..I post there my msg.

Occasional Contributor
Posts: 11

## Re: dyanmic regression

But I have just read the proc arima user's guide.....It declare to write in a transfer function form..In my case is not ok!

SAS Super FREQ
Posts: 93

## Re: dynamic regression model

you could try the following estimate statement in proc arima:

estimate p=((1,2)(24)(168)) input((1,2)x);

Occasional Contributor
Posts: 11

## Re: dynamic regression model

I think, in this case, to write Yt = (v0 + v1*B + v2*B^2)*Xt + 1/((1-u1*B - u2*B^2)*(1-u24*B^24)*(1-u168*B^168))*Et

right or not?

SAS Super FREQ
Posts: 93

## Re: dynamic regression model

i think you need to divide the backshift operator for Xt as well..

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

Occasional Contributor
Posts: 11

## Re: dynamic regression model

Yes i think so! there is a way to impose the two denominator to be equal?
Occasional Contributor
Posts: 11

## Re: dynamic regression model

Anyone have others idea?

SAS Super FREQ
Posts: 93

## Re: dynamic regression model

Sorry, what do you mean by "impose the two denominator to be equal?"? One more thing, you need to add an NOINT to the ESTIMATE statement as there is no intercept term in ur model.

Occasional Contributor
Posts: 11

## Re: dynamic regression model

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

Occasional Contributor
Posts: 11

## Re: dynamic regression model

but in my model uia ==uib

SAS Employee
Posts: 57

## Re: dynamic regression model

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)

noint;

run;

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?

Occasional Contributor
Posts: 11