### Answer:

Yes, starting with Version 3.5, the software can estimate the autocorrelation parameter.

If you select "Fit an autocorrelated errors model based on the data", the autocorrelation parameter will be estimated separately for each by-group using the method described in Section 2.3 of Kim et al. (2000). Under this option, the autocorrelation parameter is estimated for the model with the default maximum number of joinpoints or the maximum number of joinpoints set by a user.

Although the autocorrelation may be estimated from the data, correcting for autocorrelation with this estimate may seriously reduce the power to detect joinpoints (see Section 3 of Kim et al. (2000)). We found in our simulations in Table IV of that paper that adjusting for autocorrelation was helpful in maintaining proper size of the tests of joinpoints when there was large autocorrelation. We also found that if there was no autocorrelation then the adjustment seriously affected the power of the test to detect joinpoints. For example we see in Table IV (b) with φ = 0, the power goes from 90% to 68%. This is because it is difficult to differentiate between autocorrelation and joinpoints in a model.

If you suspect that your data are positively autocorrelated, we suggest using the "Fit an autocorrelated errors model with parameter =" option to see how sensitive your results are to changes in autocorrelation. The option should be used as follows:

- Fit the model with the uncorrelated errors option.
- If the user suspects that there is positive autocorrelation in the data, then repeat the analysis trying several values of the autocorrelation parameter, say for example 0.1, 0.2, and 0.3. If the results are very similar with different values of the autocorrelation parameter, then the user knows their results will still hold if there is autocorrelation present. If the results change as the autocorrelation parameter changes, then the user may end up presenting the series of results, to show how the results depend on different assumptions about the autocorrelation.

If you suspect negative autocorrelation, the uncorrelated errors model will suffice (see Kim et al., 2000).