Despite it all, the U.S. economy has entered a strong patch.

The outlook in Europe is increasingly gloomy, with the risk rising daily that a financial crisis will cross the Atlantic. Financial markets have remained unsettled, with a 2 percent drop in the Standard & Poor’s 500-stock index on Thursday.

Yet following a year of one economic disappointment after another, a variety of economic indicators are pointing in a more positive direction. The question is whether the U.S. economy has built enough momentum to withstand new shocks from overseas.

On Thursday, the Commerce Department said the number of permits to build new housing units rose 10.9 percent in October, compared with the 2.4 percent gain analysts had expected, suggesting that home-building may be finally picking up. And the Labor Department said the number of people filing new claims for unemployment-insurance benefits fell last week to its lowest level since April, continuing a two-month downward trend.

Earlier in the week, new reports showed strong results on two key measures of economic activity in October: A 0.5 percent gain in retail sales and a 0.7 percent gain in industrial production. Also welcome news: Inflation is becoming more subdued, with consumer prices falling 0.1 percent in October. That leaves the Federal Reserve more flexibility to take action if the economy worsens.

Putting all the recent evidence together, forecasting firm Macroeconomic Advisers projects that the economy will have grown at a 3.2 percent annual rate in the final three months of 2011, compared with a 1.4 percent average pace of growth through the first nine months of the year.

The results confound many analysts’ expectations. When Europe’s debt crisis flared in August, many thought the result would be a slowdown in U.S. growth — a pattern that had been seen in the spring of 2010 and winter of 2011. The opposite has happened.

“I was expecting to see some weakening of the trends that were prevailing over the summer in response to the crisis in Europe, and we’ve not seen any of that,” said Alan Levenson, chief economist at T. Rowe Price.

At the same time, though, analysts are not ready to say that the U.S. economy is in the clear. Late last year, after a similar spurt of positive economic news, analysts rushed to upgrade their forecasts for 2011 economic growth, only to have their hopes of a 3.5 percent or greater rise in gross domestic product dashed as the year progressed (2011 growth is on track to be less than 2 percent).

“We have certainly seen an unambiguous string of upbeat news on the U.S. economy and that is certainly comforting,” Bernard Baumohl, chief global economist at the Economic Outlook Group, said in a report. “At the same time we have to admit there is a sense of deja vu.”

In a speech Thursday, a top Federal Reserve official expressed similar caution about the outlook.

“Although the latest news on the U.S. economy is somewhat more encouraging than that from earlier in the year, we should not take much solace from that,” William C. Dudley, president of the New York Fed, said in a speech at West Point. “As we look toward 2012, the U.S. economy continues to face several obstacles to a robust economy.” He added that he expects 2012 growth of about 2.75 percent and that “significant downside risks” remain, especially tied to Europe.

There are specific reasons to be wary of the economic future. For one thing, the rise in consumer spending the past few months has been driven not by rising incomes but by Americans’ lowering their savings rates. They won’t be able to keep boosting their spending unless the job market improves or wages start rising more rapidly.

There is also a strong possibility that payroll taxes will rise in January if Congress allows a temporary 2 percentage point cut to Social Security and Medicare taxes to expire as scheduled. President Obama and many Democrats are arguing for the tax cut to be extended, and a deal with Republicans in Congress is possible but far from assured.

Finally, despite the U.S. economy’s surprising resilience in the past couple of months, the latest wave of crisis in Europe could undermine it. In recent days, the bond rates for Italy, Spain and even many European countries with generally sound finances have skyrocketed, raising the risk that the crisis could spiral out of control, breaking up the common euro currency.

Europe’s woes affect the United States through several channels, particularly financial markets. The U.S. stock market has moved almost in tandem with Europe’s markets in recent months, so if things truly unravel in Europe, it could wipe out a significant chunk of Americans’ wealth and undermine business confidence.

“It strains credulity that the European situation could worsen further and have no impact on the U.S. economy,” Levenson said.