The Twitter Inc. logo is seen behind a phone displaying the company's mobile application. The blue badge with white tick is the sign that an account is verified.

Macquarie Research lowered its rating on shares of Twitter to "neutral" from "buy" on Wednesday, saying the best is behind the stock after moving nearly 50 percent move higher since the firm upgraded the stock in April.

"After [the] recent rise in the stock, valuation will likely limit upside from current levels," the firm said in a note to investors.

Twitter stock fell 3 percent in trading Wednesday, closing at $43.34 per share. The company's shares are up 80 percent this year.

Macquarie said its Twitter rating raise in April was for five reasons: "negative headlines created a buying opportunity," the company's business had both strong momentum and an attractive valuation, while Twitter was also improving both its profitability and its product.

"While we expect business fundamentals to continue to improve ... the valuation, after the recent rise in the stock, will likely limit upside from current levels," Macquarie said.

The firm also raised its price target on Twitter shares to $42 from $36.