NEW YORK — The stock market is showing signs of life as investors find glimmers of hope for an economic turnaround.

Stocks rallied today after a week of heavy selling on word of a possible Chinese economic stimulus package and an Obama administration plan to help struggling homeowners. A slightly better-than-expected report on the services sector also helped. All the major indexes rose more than 3 percent.

The advance followed a week of unrelenting selling that has left major indexes plunging to levels not seen in more than a decade.

"Virtually everyone was expecting some sort of a bounce, we just didn't know exactly when that would occur," said Randy Frederick, director of trading and derivatives at Charles Schwab. "You can't go down forever."

Investors were encouraged by details of a government program designed to help as many as 9 million borrowers stay in their homes through refinanced mortgages or loans that are modified to lower monthly payments.

Wall Street followed the lead of overseas markets, which rallied on optimism over a possible Chinese economic stimulus plan. Prices for oil and other commodities also climbed.