U.S. stock markets may have recovered slightly from sharp falls at the end of last year, but there's still a risk of a significant downward trend, Robert Shiller, a professor of economics at Yale University and a Nobel laureate, told CNBC Wednesday.

"I'm not confident of my ability to predict, but I think there's a risk (of a bear market in 2019), yes," he said. "I categorize risks in terms of 'narratives' and this bear market narrative has taken a strong hold."

"There is a feeling that the stock market might be due for some deflating now because it's been a long time, and we've seen some hints of it and we haven't seen the real deflation yet," he told CNBC at the World Economic Forum (WEF) in Davos, Switzerland.

Shiller, who won the Nobel Prize for Economics in 2013 for his work on asset prices and inefficient markets, said he didn't pay as much attention to fundamentals driving markets but was "more interested in psychology" and popular "narratives."

The economist has previously told CNBC that the 1920-21 Depression, the Great Depression of the 1930s and Great Recession of 2007-9 were largely driven by narratives.

"I have this quarrel with economists about fundamentals, I'm writing a book on 'narrative economics' and think it's stories that drive markets more than fundamentals," he said.

"I'm thinking that some narratives that have been live in the recent past might come back. There was the narrative that began at the beginning of 2018. And in January and February we had a correction and 10 percent decline. And then we had another downturn between September and Christmas Eve last year, and on the S&P 500 it went down from peak to trough 19.8 percent and it almost made this classical definition of a bear market," he said.

"And I think these things weigh on people's mind and there's a sense that maybe it's finished for people who see a buy signal, or maybe it's going to complete the job and go down further."

The term "bear market" on Wall Street is synonymous with serious, long-lasting declines in stock markets. In numeric terms, a bear market is a 20 percent or more drop from a recent peak. The S&P 500 hit that milestone on December 24, dropping 20 percent from its 52-week high. But that was on an intra-day basis and not when taking into account closing prices for the index. Since the start of the year the S&P 500 has risen by around 5 percent.