Jeremy Grantham, long known for his bearish views, says the market’s next move could take stocks higher. Dramatically higher.

“As a historian of the great equity bubbles, I also recognize that we are currently showing signs of entering the blow-off or melt-up phase of this very long bull market,” Grantham, the chief investment strategist for GMO in Boston, wrote in a letter to investors Wednesday. 

Grantham, 79, is best known for his accurate prediction in 2000 that U.S. stocks would lose ground for the next decade. In today’s letter, he called the current market one of the highest-priced in history.

Grantham cited the recent acceleration of U.S. equity prices, a concentration of leadership in stocks and growing media coverage of events such as bitcoin’s surge and Amazon.com Inc.’s success as signs that the final phase of a bubble could be coming in the next six months to two years.

He warned investors to keep an eye on what is showing on television in restaurants. “When most have talking heads yammering about Amazon, Tencent and bitcoin and not Patriot replays -- just as late 1999 featured the latest in Pets.com -- we are probably down to the last few months,” he wrote. “Good luck. We’ll all need some.”

Boston-based GMO managed $74 billion as of Sept. 30.