Dear Colleague,
I need your response to the following query.
In standard fMRI analysis, we assume often that the errors form an AR
sequence. This means (a) an AR structure and (b) assumption of
stationarity. In other words, (i) below will consitute (a) and (ii) +
(iii) will constitute (b).
(i) e_{1}, e_{2} - rho . e_{1}, ... , e_{T} - rho . e_{T-1} are
independent,
(ii) e_{2} - rho . e_{1}, ... ,e_{T} - rho. e_{T-1} are i.i.d.
N(0,sigma^{2}).
(iii) e_{1} is N(0, sigma^{2}/(1-rho^{2})).
I was asking myself how important is the assumption of stationarity.
Can we work instead under the assumption (iv), where
(iv) e_{1}, e_{2} - rho . e_{1}, ... ,e_{T} - rho . e_{T-1} are
i.i.d. N(0, sigma^{2})?
Any suggestion?
With regards,
S. Purkayastha.
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Theoretical Statistics and Mathematics Unit
Indian Statistical Institute
203 B.T. Road. Kolkata 700 108. INDIA
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