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How can we determine the parameters of ARMA(1,1) model using MLE techniques?

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Contributor
Posts: 23

How can we determine the parameters of ARMA(1,1) model using MLE techniques?

Hi everyone,

Do you think this is the right algorithm to approach the problem?

Start with a dummy parameters(omega, alpha, beta)

Calculate the cost function ( J=mod(h(xi)-yi)^2/n    y=h(xi)=omega + alpha * xi-1 + beta * ei) is the regression function)

And do a Gradient Descent algorithim with a  certain learning rate to find the optimum value of alpha , beta and omega where J is min .

Can this works this way?

Thanks and Regards,

Sudipta

Contributor
Posts: 23

Re: How can we determine the parameters of ARMA(1,1) model using MLE techniques?

Hi , In addition to my previous question,Can someone share the algorithm for ARIMA model, I want to cross check the output with real time data .

Respected Advisor
Posts: 2,655

Re: How can we determine the parameters of ARMA(1,1) model using MLE techniques?

In PROC ARIMA, specify METHOD=ML in the ESTIMATE statement to get maximum likelihood estimates.  The algorithm is Marquardt's method for nonlinear least squares estimation.

Steve Denham

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