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White Noise inputs in forecasting ARMA variables

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Occasional Contributor
Posts: 5

White Noise inputs in forecasting ARMA variables

Hi All,

I have the following time series model for prediction purposes

Loss_t = b1* Loss_(t-1)   +  b2*GDP_t  +  b3*W_(t-1)  where W_t is the usual white noise variable.

So this is similar to ARMA(1,1) except that it also contains an extra predictor, GDP at time t.

I have only 20 observations on each variable except GDP for which I know till 100 values.

For predicting say, the 22nd value for Loss (i.e.Loss_22),  how do I input the value of the W_21 variable, because this variable (W_21) is generally proxied via the error in prediction (i.e. observed - predicted value of Loss) in the 21st stage, but since I don't know the observed value of Y_21, there is no way to calculate the error in this stage (21st) .

Also, the way I have calculated the coefficients in the above model is non-standard (differencing, bootstrapping, ridge regression), hence I cannot use the general ARMA codes in SAS for prediction.

So it would be great if you could help on this method or let me know what algorithm SAS uses to solve this problem.

Appreciate your help.

Thanks,

Preetam

SAS Employee
Posts: 416

Re: White Noise inputs in forecasting ARMA variables

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