Wall Street capped a week of remarkable volatility with a big advance Thursday that left stocks higher for the week but didn't silence all...

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NEW YORK — Wall Street capped a week of remarkable volatility with a big advance Thursday that left stocks higher for the week but didn’t silence all of investors’ concerns about the economy and the financial system.

The Dow Jones industrial average rose 261.66, or 2.2 percent, to 12,361.32.

Microsoft, one of the 30 Dow stocks, added 56 cents to close at $29.18 a share. Boeing, also a Dow stock, gained $1.35 to $74.80.

Broader stock indicators also advanced. The Standard & Poor’s 500 index rose 31.09, or 2.4 percent, to 1,329.51, and the Nasdaq composite index rose 48.15, or 2.2 percent, to 2,258.11.

A week that opened with fearful questions over the soundness of the financial system after the near collapse of Bear Stearns ended on a more upbeat note, thanks in part to the Federal Reserve’s efforts to inject both liquidity and calm into the markets.

Economic readings Thursday exemplified the mixed signals investors are getting. The Labor Department said the number of newly laid-off workers filing for jobless benefits rose last week by a more-than-anticipated 22,000 to 378,000.

Meanwhile, the Conference Board said its index of leading economic indicators fell, as expected, for the fifth straight month in February.

But Wall Street found reason to buy back into stocks when the Philadelphia Fed said manufacturing activity is dropping in March by less than it did in February, and by less than many economists anticipated.

And another day of sharp declines in commodities prices gave investors hope that lower energy and food prices might boost consumers’ discretionary spending and ease inflation concerns.

Crude oil fell, and gold prices declined sharply.

Still, the markets are likely to stay volatile for some time, as investors digest news on the economy and the troubled financial sector.

“It’s the every-other-day theory — up one day, and down the next,” said Scott Brown, chief economist at Raymond James & Associates.

Thursday’s gain gives the blue-chip Dow index a gain of more than 3 percent for the week. Broader indexes posted gains of 2 to 3 percent for the week. The markets are closed today for Good Friday.