Serial correlation in random effects

Hi all,



I would love to apply linear mixed models in Risk Management as they seem
to be tailor suited to many problems we face. We often assume that for
example credit default risk is driven by observable latent random factors
and we wish to understand the dynamics of these latent factors based on
repeated historical observations. Typically, these random factors consist
of different groups (e.g. credit defaults in different industry sectors
over different time periods). The industry sectors are correlated between
each other but that are also assumed to be serially correlated over time.
For example, the state of the industry sector ?telecommunication? in year t
is the result of both the auto correlation with ?telecommunication? in year
t-1 and the year t correlation with other industry sectors like
?information technology?.



I would use the representation (-1 + sector|time) to estimate the model.


I generated dummy data based on different modeling assumptions and I am
able to estimate successfully the parameters that were used in generating
the data.



However I have some questions:



First of all, if I estimate the variance of the BLUPs, I get different
values for the variance covariance matrix than if I look directly at the
estimated variance covariance matrix as an estimation output. I understand
that there is a methodological difference between the BLUPs and the
estimated variance covariance matrix, because one is focusing on the
realized sample while the other is focused on the specific realised sample
(I found the directly estimated variance covariance to be a better fit,
while the BLUPs underestimated the variance covariance matrix). So how
valid is inference based directly on the BLUPs?



More specifically, I wish to estimate AR1 parameters for the BLUPs in order
to model the serial correlation described above. Is there a way to
determine this serial correlation of random effects directly in the
estimation with any available r package? I found many options to model
autocorrelation in the residuals but not serial correlation in the random
effects, especially when there also exists correlation between different
random effects groups.



Thank you!


Regards

Daniel Bartling

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