Closely watched market strategist Jim Paulsen said Monday he's more optimistic on stocks, but wary about whether the market has bottomed.

"My guess is we're going to break back down again yet; and break 1,800 [on the S&P 500], get everyone convinced we're headed for recession, scare everyone it's a bear market," the chief investment strategist at Wells Capital Management told CNBC's "Squawk Box."