Hi ive got an ARMA model, and im struggling to theoretically quantify the benefit of using it to generate forecasts for various lead times, compared to using the mean level of the process. I think the ratio of variance of forecast error using ARMA to variance of forecast error using the mean will give me what i need. I really need help though!(adsbygoogle = window.adsbygoogle || []).push({});

If the process is standard normal then the best estimate of the process without an ARMA model is simply 0, and the variance of the mean square error is var((0-Xt+1)^2) ≈ 2.

The equation given in box and jenkins for the variance of ARMA forecast errors for various lead times, l:

var(e(l)) = (1 + (ψ1)^2 + (ψ2)^2 + ... +ψ(l-1)^2) (σa)^2

is always 1 for lead time 1, irrespective of the parameters or level of correlation of the model so according to my misunderstanding of the B&J all standard normal ARMA processes would result in a 50% decrease in forecast error variance for lead time 1. This cant be correct because surely the variance of the forecast errors would depend on the amount of correlation of the process.

Any tips would be really useful!!!

many thanks

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# ARMA forecasting - forecast error variance

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