A file illustration picture shows the search tab for Twitter on a computer screen in Frankfurt, Oct. 21, 2013. REUTERS-Kai Pfaffenbach-Files

Wall Street closed lower on Tuesday during a volatile trading session, as investors continued to weigh the government shutdown and debt ceiling drama in Washington.

Apple Inc. (NASDAQ: AAPL) managed to climb higher and cross above the key $500 mark after news Burberry CEO Angela Ahrendts will take over the tech giant’s retail and online stores beginning next year. In separate news, Apple sent out a media event invitation for Oct. 22, where the company is anticipated to introduce a new version of its iPad.

Shares of Burberry traded lower on Tuesday, while shares of Apple closed up 0.53 percent to end the session at $498.68. In after-hours trading, shares of the iPhone maker edged up 0.11 percent to $499.25.

After the bell, CNBC reported Twitter has chosen the New York Stock Exchange (NYSE) for its highly anticipated initial public offering (IPO), according to an amended S-1 filing with the SEC.

“All of us at Nasdaq wish Twitter well as they pursue their initial public offering,” Nasdaq OMX spokesman Rob Madden said.

The stock will trade under the ticker symbol "TWTR."

“This is a decisive win for the NYSE,” the exchange operator said in a statement via email. “We are grateful for Twitter’s confidence in our platform and look forward to partnering with them.”

The IPO is expected to price on Nov. 14 and begin trading on Friday, Nov. 15, according to CNBC.

On the earnings front, Intel Corporation (NASDAQ: INTC) reported fiscal third-quarter results that exceeded expectations while revenue came in flat from a year ago. The chip maker’s EPS came in at 58 cents a share, earnings excluding items, on revenue of $13.48 billion, compared with a profit of 58 cents a share on revenue of $13.46 billion a year earlier.

Wall Street had expected the company to issue quarterly earnings of 53 cents per share on revenue of $13.47 billion, according to analysts polled by Reuters.

Shares of Intel fell 2.44 percent to $22.82 per share in extended-hours trading.

Also after the close, Yahoo! Inc. (NASDAQ: YHOO) issued earnings that beat EPS expectations while revenue came in line with forecasts. The Internet company reported third-quarter earnings of 34 cents a share on revenue excluding traffic-acquisition costs of $1.08 billion. The company had previously reported a profit of $2.64 a share on revenue of $1.09 billion in the same period a year-ago.

Analysts had expected the Internet company to report third-quarter EPS of 33 cents on revenue of $1.08 billion, according to the consensus estimate of analysts polled by Reuters.

Shares of Yahoo rose 0.96 percent to $33.70 in after-hours trading.

Ahead on the earnings calendar for Wednesday, notable companies reporting include Bank of America Corp. (NYSE: BAC), PepsiCo, Inc. (NYSE:PEP), eBay Inc. (Nasdaq: EBAY) and American Express Co. (NYSE: AXP).

The Dow Jones industrial average dropped 133.25 points, or 0.87 percent, to close at 15,168.01. The S&P 500 Index was down 12.08 points, or 0.71 percent, to end at 1,698.06. The Nasdaq Composite Index fell 21.26 points, or 0.56 percent, to finish at 3,794.01.