Musk has been a big proponent of dogecoin over the years. Amid the post-election stock market boom, Musk's new position as co-head of DOGE sent the cryptocurrency soaring on Wednesday. It's remained high with slight fluctuations since then.

Dogecoin (DOGE) is down 4% on Thursday after key figures, including Elon Musk, shared views on its token design and what a deflationary path could mean for its appeal as a currency. Meanwhile, traders Ali Martinez and Peter Brandt highlighted key similarities between Dogecoin's current price movement and historical data.