Rolling regression for estimating persistence in a time series
I have to construct a measure of persistence of a time series and I want to use rolling regression to do so. In particular, I'm studying inflation persistence, and I want to replicate the following exercise in order to obtain a time series of persistence values 
I'm using Stata and I tried the following possibilities: - Rolling window on the inflation series, first-difference inflation series and the seasonally adjusted inflation series (Hodrick Prescott filter); for all three variables I execute both and AR(1) and the ACF. - Recursive analysis and Reverse recursive analysis on the same things listed above
The problem is, I never obtained results similar to the picture, thus I'm wondering what I have to do in order to obtain the fi rst-order autocorrelation coefficient for each year? Is there somebody that can tell me what am I doing wrong?
Thank you all
I'm using Stata and I tried the following possibilities: - Rolling window on the inflation series, first-difference inflation series and the seasonally adjusted inflation series (Hodrick Prescott filter); for all three variables I execute both and AR(1) and the ACF. - Recursive analysis and Reverse recursive analysis on the same things listed above
The problem is, I never obtained results similar to the picture, thus I'm wondering what I have to do in order to obtain the fi rst-order autocorrelation coefficient for each year? Is there somebody that can tell me what am I doing wrong?
Thank you all
