By Ellis Mnyandu

NEW YORK, April 3 (Reuters) - U.S. stocks should rally further next week, if investors get more signs that the economic slump is abating and earnings season does not get off to a rocky start.

Alcoa Inc (AA.N: Quote, Profile, Research) will report results on Tuesday in the unofficial start of first-quarter company results.

But given that the aluminum producer is expected to post another loss, the outlook it provides will be key to investor sentiment.

In the holiday-shortened week, volume could be light, raising the specter of increased volatility as investors look to string together a fifth straight week of gains. Many market participants are likely to be out of the office next week, when Passover begins. Markets will be closed on April 10 for the observance of Good Friday.

After investors got a boost in recent weeks from economic reports suggesting that the grip of the 16-month-old recession may be easing, analysts said stocks probably would make further headway.

The benchmark S&P 500 .SPX ended on Friday up 24.5 percent from a 12-year low hit in early March.

The broad market's recovery from that significant low helped to propel the Dow Jones industrial .DJI average to its best 4-week advance since 1933. On Friday, the Dow closed back above 8,000 for the first time since early February.

For the week, the Dow advanced 3.1 percent, the S&P 500 rose 3.3 percent and the Nasdaq climbed 5 percent.