Based on his research of historical stock market valuations, Nobel Prize-winning economist Robert Shiller said Thursday he sees the "risk of substantial declines" ahead.
Even with the recent turmoil, which pushed the Dow industrials, S&P 500, and Nasdaq into correction last week and again this week, "the market is high now," the Yale University professor told CNBC's "Squawk Box."
As of Wednesday's close, the Dow remained in a correction, despite strong gains. But the rally in the S&P and Nasdaq composite pulled those measures out of correction territory.
Shiller measures valuation with his cyclically adjusted price-to-earnings (CAPE) ratio, which looks at price divided by 10-year average earnings.
"The CAPE ratio right now is around 25. It's high," he said. The historic average is around 17, a level that would correspond with about 11,000 on the Dow and 1,300 on S&P 500. A retracement to those levels would represent more than 30 percent declines.
Shiller said he's not saying that will happen, just the CAPE ratio serves as a "warning signal."
In fact, based on history, the stock market could climb because the CAPE has been much higher in the past before the air came out of the market, he said.