Barron 55 pilot reported the aircraft began uncommanded climbs and descents after entering IMC in an area of turbulence and precipitation. Pilot exited conditions and continued to destination in VMC.

Narrative

I was flying northbound in VMC conditions on an IFR flight plan at 9;000 ft. from ZZZ direct to ZZZ1. I was approaching a thunderstorm extending from 50 miles to the west to 30 miles to the east; moving to the east. The storm was forty to fifty miles at its deepest from north to south with both leading and trailing edges narrowing to about ten miles. I was being controlled by ZZZ ATC handed off to ZZZ [TRACON] when I asked to divert to the east for the storm. The NEXRAD showed generally to moderate to severe precipitation which I also believed to be moderate to severe turbulence. To the east the leading edge of the storm showed light green and some dark green on the NEXRAD with clear area just 10 miles north of the southern base of the east edge of the storm. I believed this light and darker green would be indicative of light to moderate turbulence. Immediately upon entering solid IMC the aircraft began a series of uncommanded climbs and descents. The attitude indicator was generally level. The vertical speed indicator was pegged at 2;000 ft. per minute both up and down. Actual vertical speeds when observing the altimeter were much greater. The top ascent was to 12;000 ft. and the bottom descent was to 8;000 ft. I proceeded north and east. The times in these conditions seemed like about 5 to 6 minutes. I flew out of these conditions into VMC; continued north about 40 miles; and then reestablished direct to ZZZ1 and continued the flight in VMC conditions.