"Many believe Alcoa officially kicks off earnings season this week. However, 22 companies reporting May quarter ends are already on the 2Q earnings clock by the major data service providers," Nick Raich, CEO at the Earnings Scout, wrote in emailed research.
Collectively, third-quarter 2014 EPS estimates fell 2.57 percent for those 22 companies, which represent 4 percent of the S&P 500, according to Raich's calculations.
"For most of the past two years, Alcoa's earnings estimates were falling on an absolute basis. However, its stock price has doubled in value because its underlying earnings expectation trend has been steadily improving as the magnitude of the downward revisions became less severe," wrote Raich.
"For Alcoa's stock price to continue to rise, its second-half 2014 earnings expectations will need to be raised after it reports this week as 'beat and lower by a lesser amount' no longer cuts it," Raich noted.
Family Dollar Stores and Progressive report on Thursday, and Fastenal and Wells Fargo report on Friday.
Earnings expectations from Wells Fargo have held fairly steady during the past two years. However, over the past year there has been no improvement in the bank's earnings expectations while its stock price has continued to rise, making Wells Fargo stock "expensive relative to its underlying earnings expectation trend," said Raich.
On Monday, U.S. stocks retreated from all-time highs, as investors looked to the start of the earnings season.
Read MoreStocks retreat from records; earnings and Fed ahead
—By CNBC's Kate Gibson