Ground level ozone formation and NO2 dependence over time
I am unsure of the details of your dataset (length, temporal resolution, location, etc.)

For he one day time lag, it is easily explained. NO2 is consumed to produce ozone, so as NO2 decreases, O3 increases. However, for that reaction to occur, you need UV radiation. So as NO2 decreases, ozone increases.

For the fourth day lag, I would be a bit suspicious to take meaning out of this, due to my lack of knowledge on details of the dataset. For example, it could've been cloudy preventing the production of NO2 and ozone, but letting NO build up, such that when the sky cleared, the NO was allowed to photlyze, but that is just a guess.