Although we don't believe in timing the market or panicking over market movements, we do like to keep an eye on big changes -- just in case they're material to our investing thesis.

Expect a weak start to the stock market today, as the Dow Jones Industrial Average (DJINDICES:^DJI) is set to fall by 41 points to begin the new trading year. The Dow ended 2013 with a total of 51 record-high closes, and while there's no telling how stocks will behave this year, signs are pointing to a sharply improving economy. For example, the unemployment rate is expected to keep falling, reaching as low as 6.5% in 2014. And consumer spending also looks primed to rise as home prices improve and energy costs continue dropping.

With that bigger picture in mind, here's a look at a few stocks that could see heavy trading in today's session.

Apple (NASDAQ:AAPL) shares could see some selling pressure after a Wells Fargo analyst downgraded the stock this morning. Despite some strong potential catalysts ahead in 2014, including launches into new categories like watches and televisions, the analyst expects Apple's gross margin to come under more pressure with the iPhone 6 launch and with wireless carriers potentially scaling back smartphone subsidies. Apple's stock is down 1% in premarket trading after surging nearly 40% in the second half of 2013.

Twitter (NYSE:TWTR) looks set to continue its volatile trading today after an analyst at Evercore hiked his price target to $70 per share. The social media stock is up nearly 50% since its November initial public offering despite mostly bearish Wall Street ratings and no profits to speak of. Still, Evercore sees a shift in online video content under way that Twitter should benefit from by grabbing billions in new ad revenue over the next few years. The stock is down 0.39% in premarket trading.

Finally, Wal-Mart (NYSE:WMT) is recalling a donkey meat snack it had been selling in China after tests showed traces of fox meat in the product. The scandal threatens to hurt Wal-Mart's food reputation in the world's largest grocery market. The company is investigating the incident, which will likely point to the need for more investment in Wal-Mart's supplier management in China. The stock is unchanged in premarket trading.