Temperature vs stratospheric ozone levels

Is there a correlation between ozone levels and surface temperature?

I downloaded the stratospheric ozone level figures from here (for Southern Hemisphere, but those are the only detailed ones I could find) and the Central England Temperature Record figures from here (I know that England is not in the Southern Hemisphere, but their figures are reliable).

Annual averages jump about, so I used the five-year rolling average for temperatures.

The co-efficient of correlation for a year's five-year average and the same year's ozone levels is 60%. It increases steadily to 80% if you assume that the temperature lag is one, two, three... eight years (and falls off again after that - it's down to 50% if you assume twelve years, 37% if you assume thirteen years), which conveniently suggests that ozone levels are the cause and temperature is the effect, so I went with an eight-year lag.

The left hand axis for ozone levels is inverted, as we expect lower ozone levels to cause higher temperatures.

Here's the chart. Looks fairly convincing to me. There is a clear mismatch from 2011 to 2016, but it's all back in line from 2017 onwards. If there is a link - and I cheerfully admit that this might all be sheer coincidence - then we'd expect to see average temperatures to fall slightly over the next five years*. Not sure what happens after that:
* The average temperature for May 2020 to 2021 is slightly lower than that for May 2015 - April 2016, so the 2021 5-year average will drop towards the number 'predicted' by 2013's ozone levels.