# Fit process parameters to a transformed AR(1) process

I would like to fit the parameters of an exponented AR(1) process using Mathematica's EstimatedProcess, however, the function does not seem to evaluate to anything.

First of all I create the exponented process, and generate a series:

S = TransformedProcess[Exp[P[t]], P \[Distributed] ARProcess[0, {0.5}, 1], t];
test = RandomFunction[S, {0, 100}]


Then I try to fit the same type of transformed process to the data:

EstimatedProcess[test, TransformedProcess[Exp[P[t]], P \[Distributed] ARProcess[c, {rho}, \[Sigma]], t]]


However, the function seems to return unevaluated. Does anyone know where I am going wrong? I have also tried FindProcessParameters, but to no avail.

Best,

Ben

It might be that you require a parametric process, the transformed process might not fit the bill.

As a workaround how about doing this?Take the data back to a parametric process.

S = TransformedProcess[Exp[P[t]],
P \[Distributed] ARProcess[0, {0.5}, 1], t];
test = RandomFunction[S, {0, 1000}];

EstimatedProcess[TimeSeriesMap[Log, test],
ARProcess[c, {rho}, \[Sigma]]]
(*ARProcess[-0.000577181, {0.504678}, 1.02154]*)

• Thanks for that - good idea! So it appears that EstimatedProcess only works for out of the box processes, not custom ones. Best, Ben – ben18785 Feb 16 '15 at 17:55