NEW YORK (Reuters) - US stocks should rally further this 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 will report results tomorrow 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 this 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 this 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 ended 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 average to its best four-week advance since 1933. On Friday, the Dow closed back above 8,000 for the first time since early February.

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

"I think we've still got quite a bit of room on the upside," said William Stone, PNC Wealth Management's chief investment strategist in Philadelphia. "We seem to have become medicated in March and into early April and have shrugged off some negative numbers," he said.

"The medication was that expectations on the economy got low enough that we were able to get some numbers that while ugly, are a bit better than expected," Stone added.

The highlights of the week's economic releases include Wednesday's minutes from the Federal Reserve's March 17-18 policy meeting, at which it decided to pump an additional $1 trillion into the US economy, partly by buying government bonds for the first time since the 1960s.

On Thursday, the government will release data on the latest weekly jobless claims and the international trade deficit for February.

Besides that, investors will keep tabs on any rhetoric out of Washington as the Obama administration works to prop up the banks and drive initiatives for economic recovery.

"The last couple of weeks, we have been seeing a few green shoots of slightly better macro data," said John Praveen, chief investment strategist at Prudential International Investments Advisers in Newark, New Jersey. The market will be looking for "follow-up on whether we are going to have an improvement in the macro data."

Also set to command attention: The US Securities and Exchange Commission will meet on Wednesday to consider an updated version of the so-called uptick rule to regulate a type of trading blamed for dramatic declines in stocks.

Friday's bleak March non-farm payrolls data became the latest economic data point that the stock market shrugged off, leading some analysts to say the economic damage could not possibly get much worse.

According to the government data, the US unemployment rate soared to 8.5 percent last month, a new 25-year high, as employers cut 663,000 jobs and slashed workers' hours to the lowest on record.

Even so, the benchmark S&P 500, the Dow Jones industrial average and Nasdaq all finished the session in positive territory, and each registered a fourth straight weekly advance.

Still, there are concerns that the stock market's recent run higher could soon hit a pothole.

"We believe a deep pullback to 750-775 in the S&P 500 is the kind of final low we expect to see," JPMorgan US equity strategist Thomas Lee said in a note.

The S&P 500 ended Friday at 842.50, and according to Thomson Reuters data, the index's 200-day relative strength chart shows that it remains well off the range that typically signals overbought conditions.

Analysts expect Alcoa to report a second consecutive quarterly loss this week, mostly due to the fact that the price of aluminum has dropped nearly 10 percent this year.

Alcoa, like most producers, has cut production in the last six months as the global economic downturn stunted demand.