The coming week says goodbye to May and a cautious hello to June, a month in which the Federal Reserve could decide to raise rates for the first time since December.

The deciding factor could be the U.S. jobs report for May, which will be released on Friday after a shortened holiday week.

"We think May payrolls could be weak and if we're right, this would likely spark concern about the domestic outlook and foil the Fed's hopes for a mid-year hike," BNP Parabis analysts wrote in a note. "A strong payrolls report, on the other hand, could give the Fed a green light to hike in June or July (after the 'Brexit' vote) if markets price it in smoothly."

The chances for a rate hike in June grew exponentially after the release of minutes from the Fed meeting in April suggested the majority of Fed officials were comfortable with a rate increase as soon as the summer. An interest rate increase in June currently has a 30% probability, according to CME Group, after having a virtually non-existent chance at the beginning of May.

The consensus pick for the May jobs report is for around 160,000 jobs to have been added to nonfarm payrolls, in line with a reading a month earlier. Job gains will likely have been moderated by a strike at Verizon Communications (VZ) - Get Report

Aside from Friday's jobs report, investors will also get anecdotal evidence of economic growth in the Fed's 12 districts via the "Beige Book" on Wednesday afternoon.

Europe's monetary policy will be on watch on Thursday as the European Central Bank convenes for a meeting in Vienna. The ECB is expected to keep its benchmark rate unchanged at zero, though a fresh quarterly forecast could give clues as to future moves. ECB President Mario Draghi will hold a press conference on Thursday morning following the meeting's conclusion.  

U.S. markets will be closed on Monday for Memorial Day with operations resuming as normal on Tuesday morning.

Elsewhere on the economic calendar, personal income and outlays for April will be released Tuesday morning, the ISM Manufacturing Index for May is set for Wednesday, the Energy Information Administration's weekly read on crude inventories will be shifted a day later to Thursday, and international trade for April is due on Friday.

There are a few more stragglers of the first-quarter earnings season yet to report in the coming week. 

On the earnings calendar, TiVo (TIVO) - Get Report  and Workday (WDAY) - Get Report will report on Tuesday; Box (BOX) - Get Report , Lands' End (LE) - Get Report , Michael Kors (KORS)  and Vera Bradley (VRA) - Get Report are set for Wednesday; and Conn's (CONN) - Get Report , Five Below (FIVE) - Get Report , Joy Global (JOY)  and Ambarella (AMBA) - Get Report are slated for Thursday. 

The first quarter has seen the same kinds of issues that plagued companies in the final months of 2015. A stronger U.S. dollar, weaker global demand, wild market moves and a prolonged period of lower commodity prices kept investors bearish. S&P 500 companies have reported another decrease in average earnings in the first quarter, the fourth straight quarter in decline and the worst losing streak since the Great Recession.