* Dollar index bounces off trough, but still down on week

* U.S. jobless claims falls, services PMI hits six-month high

* Speech by Fed Chair Yellen next in focus

By Ian Chua

SYDNEY, March 27 (Reuters) – A sudden turnaround in the dollar’s fortunes overnight saw the currency trading broadly higher early in Asia on Friday, but still on track to end softer for a second straight week.

Since the U.S. Federal Reserve’s dovish steer last week, dollar bulls have been much more cautious. But a set of encouraging data on Thursday and a rise in U.S. Treasury yields helped the greenback stage a modest rebound.

The dollar index climbed to 97.397, bouncing off a three-week trough of 96.170. Against the yen, it rallied to 119.28 yen, from a one-month low of 118.33.

The euro eased back to $ 1.0876 from $ 1.10525, failing to stay above $ 1.1000 for a fourth time in the past two weeks.

“The inability of EURUSD to hold tests above $ 1.10 also supports our expectation that longer-term-oriented market participants are keen to sell the currency at better levels,” analysts at BNP Paribas wrote in a research note to clients.

“We think low and falling real rates are likely to keep euro zone and Japanese investors focused on selling their currencies into rallies, and we expect the USD to benefit.”

Providing a welcome relief for dollar bulls, data on Thursday showed the number of Americans filing new claims for jobless benefits fell more than expected last week. A separate report showed activity in the services sector hit a six-month high in March.

Two Fed officials also said the central bank should remain on track to raise interest rates later this year despite the economy’s weak start to the year.

Still, the dollar index is 0.5 percent lower on the week, extending last week’s 1.2 percent fall.

“We expect the current USD correction to be relatively short-lived,” analysts at ANZ wrote in their monthly FX outlook.

“The Fed’s recent more dovish shift shouldn’t have been that much of a surprise, vulnerabilities in emerging markets are likely to continue to surface as USD liquidity tightens. China is a source of downside economic and financial risks, and hedging activity remains dollar supportive.”

Commodity currencies have also been unsettled by volatile commodity prices and worries about slower growth in China.

The Australian dollar, for example, is back near 78 U.S. cents, down from a two-month high of $ 0.7939 set earlier in the week.

Trading in Asia is likely to be relatively uneventful with investors cautious about taking aggressive positions in the run-up to a speech by Fed Chair Janet Yellen.

Yellen is scheduled to speak on “Monetary Policy,” before the Federal Reserve Bank of San Francisco Conference later in the day.

(Editing by G Crosse)