Hedge fund billionaire Bill Ackman said Tuesday that investors will closely watch the Federal Reserve to decide when it is time to buy stocks again. The Pershing Square founder told CNBC's " Squawk Box " that equities can rebound once the central bank stops its rate hikes and the market becomes confident that inflation is trending in the right direction. "Once people realize that the Fed doesn't have to keep increasing rates and will soon be taking rates down, that's kind of a buy signal for markets," Ackman said. "I think the question is how far in advance does the market predict that kind of outcome. I think if people see inflation come off 8.5%, you start to see a pretty powerful continuing trend, then I think people will expect at some point the Fed to ease." "But what they're not going to do is take rates to 4% and see a good inflation print and start taking interest rates down again. They're not going to make that mistake," he added. Stocks have struggled this year as inflation spiked to four-decade highs and the central bank has aggressively hiked rates. The market had a mid-summer rally as some investors began to price in a potential policy pivot, but stocks have since fallen for three straight weeks due in part to a blunt promise to fight inflation from Fed Chair Jerome Powell in a speech at Jackson Hole, Wyoming. Ackman has said several times this year that the central bank should focus on fighting inflation , calling rising prices the biggest threat to the U.S. economy. Ackman said Tuesday that there are "indications" that inflation is now cooling. Inflation readings in July showed price rises are slowing, helped by declines at the gas pump. The Fed's next policy meeting is Sept. 20-21. The market expects a hike of three-quarters of a percentage point, according to CME FedWatch .