# Dealing with temporal autocorrelation

#### mmercker

##### Member
Hi,

assume we have a measured value for each year from 1990-210, and we want to estimate a linear trend. Now there is a problem of autocorrelation, i.e., the measured values do not scatter randomly around the fittet line but rather resemble a "smooth function" wriggeling around the linear fit (i.e. sinus-like). Finally, assume that I cannot use the standard AR- or MA-approach to deal with this, since it is not provided by the software I use. But I could use mixed modelling or additive modelling instead. As far as I see, I have two possibilities to deal with this violation of idependence, and I am not sure which one is better:

(1) Beside the linear predictor ''year'' I additionally introduce ''year'' as a random intercept factor variable. Would this solve the problem? Since the mean value of the random term is zero it would not bias the linear trend estimate. But is the temporal autorrelation appropriately covered by such a term?

(2) Beside the linear predictor ''year'' I additionally introduce ''year'' as an cyclic smoothing term. Cyclic means here that both ends of the smoother would match up to second derivatives. This would prevent this variable from interfering with the linear trend estimate.

Which of these two possibilities (if at all) is the better choice? Thanks in advance

Last edited:

#### rogojel

##### TS Contributor
hi,
I have no great experience with time series but I would guess that much will depend on the precise structure of your series. E.g is the autocorrelation for a lag of one or is it something more complex? If only short term effects (small lags , essentially 1 ) are important you could model the differences instead of the values themselves.
regards

#### noetsi

##### Fortran must die
Personally I would get better software or learn R

There are well accepted ways of addressing autocorrelation and they are not the ones you suggested [most involve specifying lags of Y; MA are not generally addressed for multivariate time series in part I think because most think those are unlikely in the social sciences].