## Does the MA(1) process prove that the forward solution applies?

Assume that the true model is

Apt = bp1^pt-1 + £pt: bpl < 1

and the the following model is estimated by means of instrumental variables

Apt = bpiApt+i + £pt – What are the properties of efptl

£pt = APt – bpiAPt+i-

Assume, as is common in the literature, that we find that bfpi и 1. Then

£fpt и APt – APt+i = – A2Pt+i

= — [£pt+i + (bpi — 1)^pt + ••• ]•

So we get a model with a moving average residual, but this time the reason is not forward-looking behaviour but mis-specification.

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