# HAC Confidence Interval in Interrupted Time Series

I have a dataset about quarterly deaths over the last 18 years (Q1 2000-Q4 2018). In Q3 2004 there was a policy change which might had lead to an increase in the number of deaths.

I fitted an Interrupted Time Series with OLS estimation with the following specification:

$$Y_{t} = \beta_{0} + \beta_{1}T_{t} + \beta_{2}Post_{t}+ \beta_{3} T_{t} Post_{t} + \varepsilon_{t}$$

Where $$T_t$$ is time elapsed since start of study period and $$Post_t$$ whether it was before/after the intervention period. Given that the model has a bit of autocorrelation, and I do not want to go into ARIMA models for several reasons, I corrected the standard errors with HAC std. errors.

However, I would like to know if there was a significant change in the slopes before vs after i.e., ($$\beta_1$$ vs $$\beta_1+\beta_3$$) and how I could derive a confidence interval for the post-intervention period.

I haven't found a way to estimate such HAC confidence intervals and suggestions regarding significance check for slopes like using ANOVA for comparing before and after do not seem to work because of different samples (before and after).

I would really appreciate some suggestions! Thank you all.