# Test of significance between autocorrelation coefficients for two time series

I have a time series measured at monthly intervals, and I want to determine if the first half of the series is less persistent than the second half of the series. My initial thinking was to the estimate coefficients for the autocorrelation function using each half of the initial time series.

For each series I have estimated coefficient for lags 1-25. As I initially imagined, the coefficient on each lag is higher in the second series and this difference between the estimates increases with the lag. What I want to know is whether the difference is statistically significant.

I imagine there is a straightforward way to do this, but I am new to statistics and none of the methods I understand well seem to fit. I am also using R if that matters.