After declines over the past week have sent the Dow Jones Industrials (^DJI 0.67%) down by more than 650 points, early signs this morning point to a potential rebound for the beleaguered U.S. stock market, with projections suggesting about a 70-point rise at the open. Yet even with some favorable news emerging both abroad and domestically, you need to be cautious before concluding that the worst of the recent correction is over.

Overnight, some favorable news has calmed global investors somewhat and sent U.S. stock futures markets higher as well. With the Chinese central bank making reassuring gestures in order to address fears that a credit crisis could further slow the emerging nation's economic growth, Asian stock markets recovered from their worst levels of the trading day, with Chinese stocks in particular rising from lows not seen since the depths of the financial crisis in 2009. European markets are also up broadly, with the major stock indexes in France, Germany, and the U.K. gaining between 1% and 1.5%. With durable-goods orders in the U.S. up 3.6% last month, investors can also point to the prospects for a strong domestic economy in justifying a market advance.

Stock gains in premarket trade are widespread. Industrial powerhouses Caterpillar and Alcoa have posted gains of about 1% right before the open. These two stocks' fortunes are strongly linked to China, with Alcoa suffering from a glut of Chinese aluminum production and Caterpillar falling as overall commodity demand reduces the ability and need for mining companies to buy its equipment.

Bank of America (BAC 2.06%) has also vaulted higher in the premarket hours, gaining 2.3%. A favorable settlement between B of A's Merrill Lynch unit and the government of the Piedmont region of Italy over a derivatives-related dispute is one more example of the bank trying to handle its legal risk, but of greater importance is avoiding any systemic risk of another global financial crisis. If China's efforts to control its credit markets bear fruit, then it represents one less worry for B of A to consider as it tries to spur growth in the face of rapidly rising interest rates.

Keep your eyes on the big picture
Regardless of whether this morning's favorable signs bear out in stock market gains today, any restoration of the bull market in stocks will take a lot longer than a single day to play out. Bond rates are unlikely to drop to their previous levels, barring a major economic slowdown, and the changing environment for stocks, bonds, and other investments will introduce new challenges for investors. By staying focused on longer-term trends, rather than getting caught up in day-to-day noise, you'll be best prepared to handle what the markets throw at you in the weeks and months to come.