* Fed's Rosengren said stimulus should only be removed gradually
* Swiss franc falls sharply as reserves data weighs
* Euro resists more falls, helped by inflation data
* Focus this week on Fed minutes, U.S. jobs data
NEW YORK, Jan 7 (Reuters) - The dollar rose broadly on Tuesday, buoyed by U.S. trade deficit data that could inflate estimates for fourth-quarter growth in the world's largest economy as market participants eye key events later in the week.
The U.S. trade deficit fell to its lowest level in four years in November as exports hit a record high and weaker oil prices restrained import growth, the latest evidence of strengthening economic fundamentals.
The measure goes into the calculation of gross domestic product, so the narrowing of the deficit could prompt economists to bump up their growth estimates for the last quarter of 2013.
"Since 2013, the trade balance has been spiky and narrowing," said Patrick Newport, U.S. economist at IHS Global Insight in Lexington, Massachusetts.
"Net trade will be a positive for growth in the fourth quarter, but a negative this year as a pickup in U.S. growth brings in more imports," he said.
Signs of more robust growth could also prompt the Federal Reserve to speed up the tapering of its monthly bond purchases, but most contend the U.S. central bank will gradually wind down its monetary stimulus.
Boston Federal Reserve Bank President Eric Rosengren, one of the Fed's most dovish policymakers, on Tuesday said the economy remains vulnerable the longer inflation remains too low and he again warned that policy stimulus should be removed "only gradually."
In midday trade, the dollar was 0.3 percent higher at 104.54 yen, but remained below a five-year peak of 105.44 yen set last week. The dollar fell as low as 103.88 yen on Monday, its lowest since Dec. 23.
The dollar index, which tracks the greenback against a basket of six major currencies, was last up 0.2 percent at 80.818.
The Swiss franc, meanwhile, fell to its lowest against the euro since October, with some analysts arguing global economic optimism had laid the ground for a retreat for the one of the world's safe-haven currencies.
Data on Tuesday also showed Swiss National Bank foreign currency reserves fell by almost 700 million francs in December, suggesting pressure on its cap on the franc - which previously forced it to buy billions of euros - had eased.
"It further underscores the bank's resolve to fight Swiss franc appreciation and could make alternative measures like penalty rates on bank excess reserves or negative policy rates more attractive," said Valentin Marinov, G10 strategist at CitiFX, a division of Citigroup.
The euro rose 0.4 percent to 1.2364 francs, its highest since October and above the 1.20-per-euro cap which the SNB has held in place for more than two years. Against the dollar, the franc also lost 0.3 percent to $0.9070.
"We expect more Swiss franc downside from here given that the Swiss franc remains excessively overvalued," Marinov said. "The firm prefers to express any bearish view against the dollar rather than the euro."
UBS pointed to signs that Swiss funds and banks are beginning to invest and loan money abroad again - something they have not done since 2008 and an important precondition for the franc falling back.
"People tended to play the weaker franc last year and a lot of them got frustrated. Now there may be a new attempt," said Beat Siegenthaler, currency strategist with UBS.
"The question has always been what would be a trigger (for a turnaround in the franc). It could have been the easing of the euro crisis and that didn't happen. So maybe it is the change in the U.S., the feeling of broader optimism and change in the dollar that may come from economic improvement there."
UBS has a near-term target of 1.25 francs to the euro, Siegenthaler noted.
Looking ahead, currency trading will likely be swayed by Friday's U.S. jobs report, which may give a clue as to how quickly the Fed will taper its bond buying. Overall the outlook on interest rates is against the euro.
Ahead of the jobs data, market participants will focus on minutes from the Fed's last monetary policy meeting, scheduled for release on Wednesday.
Meanwhile, the euro was helped by a euro zone inflation number which was not expected to be low enough to force the European Central Bank into more action immediately to loosen monetary policy. The ECB meets on Thursday.
German retail sales and unemployment data were also better than expected, while Ireland's successful bond issue offered more optimism on countries in the bloc under sovereign bailout programs.
The euro rose as high as $1.3656, but last traded down 0.1 percent at $1.3618, remaining above Monday's one-month low of $1.3570, according to Reuters data.