You mean stable like the US dollar which went from $35 per ounce of gold when Nixon closed the gold window to $668 ten years later? By contrast the aureus, the solidus, the fiorino and many other metal based currencies preserved their value over several centuries. What eventually destroyed those currencies was not the lack of a central bank but on the contrary eventual debasement by the central authority.
Looking at the Coinbase graphs reminds me of reading CPU charts, comparing resource use between 3 web servers. Sometimes one coin will spike or dip independently, indicating higher utilization of one coin over the other 2 - an arbitrage opportunity; other times all 3 coins see a matching dip or raise, likely indicating a systematic cause.