U.S. stocks were higher Thursday, the first day of trading in June. The month is usually flattish, with average returns for the S&P 500 around 0.7 percent. It is the fourth worst in terms of S&P performance.
It also marks the start of what is a historically weak season for equities.
Moore sees a "sustainable and stronger economic picture ahead." She believes investors need to focus on guidance from companies about their future expectations, as well as the tone coming from early announcements on second-quarter earnings.
"I don't think you have to fight the momentum at this point."
However, that doesn't mean investors should put all their chips just in the high-flyers, she noted.
"There are a lot of stocks that are being under recognized by the market for their earnings potential that we should really be taking a look at. Stuff more that would fall into the value camp across all sectors."
Meanwhile, noted bear Marc Faber, known as "Dr. Doom," recently told CNBC he believes there is a "bubble in everything."
The editor and publisher of The Gloom, Boom & Doom Report said Wednesday on "Fast Money Halftime Report" that even if the S&P 500 dropped 20 percent, it still wouldn't make him bullish on the U.S. stock market.
— CNBC's Patti Domm, Jeff Cox and Tae Kim contributed to this report.