The graph provides support for the contention that old storm records are unreliable. I would not recommend using storm counts prior to 1890.
I had posted a graph of 17-year central moving averages of NH sea surface temperature and named storm series, reproduced below. You will note I had placed a vertical line around the year 1890 in order to indicate there was some sort of point of change there.
I didn't use any mathematical analysis to determine that 1890 was in any way special. It was simply obvious, visually, that something was not right in the named storms series prior to 1890. Of course, the central moving average smoothing helped in terms of being able to see that.
Enter Vecchi & Knutson (2008), a NOAA study of North Atlantic historical cyclone activity. The authors determined, based on known ship tracks, that early ships missed many storms, especially in the 19th century.
Now, this study is being touted as evidence that global warming and the number of storms in the Atlantic are not associated. Clearly, that is nonsense, if you just look at the figure above. If you'd like to see some Math, I have done a detrended cross-correlation analysis as well. All that is necessary to demonstrate an association is to do a linear detrending on series that go from 1900 to the present time. The detrending should take care of any problems related to unreliability of old storm counts. I can further report that even after detrending the series based on 6th-order polynomial fits, a statistically significant association is still there, provided storms are presumed to lag temperatures by at least one year.