Yardeni said that stock valuations were key.
"I'll be the first one to admit that the four seasons, the four patterns, is not science," he said. "While it's true that it doesn't feel like everyone is euphoric, look at the valuation multiples."
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Yardeni added that stock buybacks and an increase in mergers and acquisitions have as much to do with the market's strong performance as earnings.
Once valuations begin to reach into multiples of 18 to 20 for mid-cap stocks, "that would be a melt-up," he added.
"It's not inevitable that we're going to have a melt-up. My preference would be that the market just go sideways for a while so that we could have a secular bull market, which I think is still possible," he said. "And even if you have a melt-up followed by a meltdown, that does not necessarily mean that a bear market's inevitable. Bear markets happen when we have recessions."
Ritholz Wealth Management's Josh Brown said that stock-price multiples weren't going to tell the whole story.
"Valuation is not going to tell you when the run ends. We were reasonably valued in 2007. The economy fell off the cliff," he said.
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Brown also said he agreed with Yardeni that there was "no sign of a recession."
"Those are usually what coincide with the end of a bull market," he said. "I'm not telling you P/E expansion takes us significantly higher, but earnings growth could, revenue growth could, and in the second half of this year, we should be seeing a meaningful uptick based on what analysts are expecting at the moment. So, I think it's smarter to be constructive than to be worried about the next 5 percent in either direction."
— By CNBC's Bruno J. Navarro. Follow him on Twitter @Bruno_J_Navarro.