The S&P has risen more than 50 percent in the last three years. It has inched nearly 2 percent higher so far this year.
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Global trends like volatile Chinese stock markets and Greece's effect on the euro zone have spooked investors this year. But the founder and president of Birinyi Associates shook off concerns that the years-long bull market would not persist.
"There's no reason why we can't keep on going," Birinyi said.
Individual stocks look more appealing than specific sectors, he added. Birinyi contended that stocks including Chipotle, Google and Visa would continue grinding higher.
Still, some negative market trends have caught Birinyi's eye. Apple—his biggest holding and the world's largest company by market cap—has shed nearly 6 percent in the last five days.
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Birinyi noted that he could not explain what has held back the stock.
"It is a concern to me because I don't know what's going on," he said.
On the other hand, short seller Bill Fleckenstein, who correctly predicted the financial crisis in 2007, told "Fast Money" the entire market could be heading for calamity in the coming months.
Read MoreShort seller who called crisis foresees calamity