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* Apple falls more than 3 pct on demand worries
* Earnings season picks up this week
* Transocean rises as Icahn acquires stake
* Futures: S&P down 1.1 pts, Dow down 18 pts, Nasdaq down 13.25 pts
By Leah Schnurr
NEW YORK, Jan 14 (Reuters) - U.S. stock index futures fell on Monday as shares of Apple were hit by demand concerns, while the corporate earnings season was set to pick up this week.
Apple slid more than 3 percent in premarket trade after a report that the tech company has cut orders for LCD screens and other parts for the iPhone 5 this quarter due to weak demand. The stock was down 3.8 percent at $500.80.
Earnings season picks up the pace this week with reports expected from companies including Goldman Sachs, Bank of America, Intel and General Electric.
Overall earnings are expected to grow by just 1.9 percent in this reporting period, according to Thomson Reuters data. Thirty-eight S&P 500 companies are due to report results this week.
"I think there's going to be more misses than hits in terms of revenue and margins. It's going to be a little bit light this earnings season compared to the last one," said Peter Cardillo, chief market economist at Rockwell Global Capital in New York.
"But the underlying factor is that there's economic growth and that the global economy is picking up."
Investors will also be watching a speech from Federal Reserve Chairman Ben Bernanke, who will be speaking on monetary policy, recovery from the global financial crisis and long-term challenges facing the American economy at 4 p.m. (2100 GMT).
Top Fed official Charles Evans said earlier on Monday the U.S. economy is expected to grow by 2.5 percent in 2013, improving to 3.5 percent growth in 2014.
S&P 500 futures fell 1.1 points and were below fair value, a formula that evaluates pricing by taking into account interest rates, dividends and time to expiration on the contract. Dow Jones industrial average futures fell 18 points, and Nasdaq 100 futures were down 13.25 points.
Transocean Ltd has disclosed that billionaire activist investor Carl Icahn has acquired a 1.56 percent stake in the offshore rig contractor and is looking to increase that holding. Its shares rose 3.3 percent to $55.89.
Hewlett-Packard rose 1.8 percent to $16.45 after JPMorgan raised its price target to $21 from $15.
Boeing could come under renewed pressure after Japan's transport ministry launched an investigation into what caused two fuel leaks on a 787 Dreamliner jet owned by Japan Airlines Co 9201.T. U.S. transportation officials have also said they will take a comprehensive look at the plane to ensure there were no flaws.
United Parcel Service Inc said it would drop its 5.2 billion euro ($7 billion) bid for Dutch delivery firm TNT Express on the expectation of an EU veto.