If the Federal Reserve loosens monetary policy again, the dollar could fall.

If inflation comes down to a point that appeases the Federal Reserve, the dollar's rise could be capped.

The last two years have been "exploding" according to Emanuel. Wall Street may have been too hasty in assuming the Fed will reverse the tightening of its monetary policy.

The dollar is close to 20-year highs so far this year. In the last five months, the central bank has raised benchmark interest rates four times.

Edward Moya, senior market analyst at OANDA, said that the dollar trade is cooling after hitting historic levels with the euro and Japanese currency.

The dollar is already benefiting from recession worries in countries like China and the UK, so sluggish growth elsewhere could push the dollar higher. As safe-haven flows grow, dollar dominance will likely remain in favor.

"China's growth slowdown this year has also contributed to US dollar strength particularly against Asian EM currencies such as the Chinese yuan and Korean won," said Tan. Through the new year, Tan expects his firm to appreciate.

Even if the dollar index breaks, it would still be supportive for both the dollar and the Japanese currency.