I am reading a journal where it is written "Time series are based on annual-mean translation speeds from 1949-2016. Trends are estimated by linear regression. The P values of the regression are based on the full degrees of freedom in the 68-year time series. Because some of the time series exhibit autoregressive (AR(1)) persistence, as determined from a Durbin–Watson test, confidence intervals are provided with degrees of freedom adjusted when needed. Statistical significance is based on the two-sided 95% confidence intervals (not the P values)". I am struggling with understanding the following question:
What is the relation between Autoregressive persistence and adjusting the confidence interval? Since I have a similar set of data set how can I adjust confidence interval when needed?