How do you implement an ADL model in Matlab using ARMAX?

Question

Robert Dickson 2011-11-21

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I am trying to implement an ADL(autoregressive distributed lag) model and I believe the ARMAX funciton is appropriate for this but the help documention is very unclear. Has anyone used the ARMAX function to impement an ADL model? I'm tyring to estimate a time series of the following form:

Y(t) = Betahat1Y(t-1) + Betahat2X(t-1) + Betahat3Z(t-1) + Et

Where Y(t-1) is the first lag of Y, X(t-1) and Z(t-1) are the first lags of exogenous explanatory variables and Et is the error term. Thanks.

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Answer 1

Rajiv Singh 2013-5-2

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You have 2 inputs with minimum lag of 1 sample each. Also you have only one term of each variable. So set up ARMAX orders as:

 na = 1;
 nb = [1 1];
 nk = [1 1];
 data = iddata(y,[u1 u2],Ts); % Ts is sample time; can use Ts=1 if it is irrelevant
 model = armax(data,[na nb nk]);