It's fair to say that the U.S. economy has been in a worrisome funk these past few months. The unemployment rate has barely budged after a slew of disappointing jobs reports that started in April. GDP growth in the second quarter of the year turned out to be a tepid 1.5 percent annualized rate. The Federal Reserve noted glumly that "economic activity decelerated somewhat over the first half of this year."

Poised for a turnaround? (Bloomberg)

Could that turn around in the second half of 2012? In the past few days, a handful of economic indicators have offered some reasons for cautious — very cautious — optimism. The labor market appears to be  strengthening somewhat. Exports have surged of late. And the U.S. housing market, which has long hobbled the economic recovery, is showing glimpses of improvement. So how significant are these trends? Let's take a look:

1) The labor market. On Thursday, the Department of Labor reported that the number of people who were newly filing for unemployment dropped to 361,000 last week. This was better than economists expected. What's more, initial jobless claims over the past four weeks have averaged 368,000, which is down a fair bit from 386,000 at the beginning of July. As the chart below from Calculated Risk shows, weekly claims are back down to their level in March, a period when many forecasters were hopeful that the job market was getting healthier.

July's payroll report was also a marked improvement from previous months, with the U.S. economy adding 163,000 jobs for the month, according to the Bureau of Labor Statistics.

There are, however, two big caveats here. First, it's possible that BLS's seasonal adjustments are making its monthly jobs reports look more erratic than they actually are. The data can be fairly noisy. And second, even if the economy does keep adding 163,000 jobs per month, it will still take 12 years to bring the unemployment rate back to pre-recession levels, according to the Hamilton Project's jobs calculator.

2) Exports. Perhaps the most notable surprise on Thursday was that the U.S. trade deficit for June had narrowed to an 18-month low. Part of that has to do with oil: As crude prices have settled down (thanks to the struggling global economy), the U.S. has needed to pay less for its oil imports. But exports also surged higher than expected, and they're now up 6 percent over the previous year.

Since exports are one component of GDP, this could mean that second-quarter growth was higher than the initial estimate of 1.5 percent. (Though it probably won't be much higher—JP Morgan is revising its second-quarter GDP estimate to a still-weak 1.7 percent.) The trade data also suggests that the U.S. economy has, to some extent, managed to avoid getting dragged down by the never-ending crisis in Europe. Here's JP Morgan's Michael Feroli:

Exports last month increased across a variety of products, including motor vehicles, consumer goods and capital goods... Who is buying this stuff? It's hard to say as the trade-by-country data is not seasonally adjusted, but it appears that exports to, and the U.S. trade balance with, Europe is holding up decently: through the first six months of the year exports to Europe are up 5.0% over the same period a year-ago...

Other analysts, however, caution that the export news could just prove to be a blip. Here's a note from Capital Economics: "The sharp narrowing in the trade deficit in June suggests that the easing in global demand and the strengthening in the dollar have yet to take a major toll on the U.S economy. But we doubt this can last."

3) The housing market. On Tuesday, two reports from Core Logic and Freddie Mac suggested that home prices in the second quarter of 2012 had jumped by the most in seven years. Bill McBride at Calculated Risk explained why this could boost the U.S. economy:

There are many positive economic impacts from flat to rising house prices and we are just beginning to see the positive impact on the overall economy…We might see something like 1 million households that regained a positive equity position at the end of Q2 2012…We will probably also see a meaningful decline in the number of newer mortgage delinquencies…And private mortgage lenders and homebuilders will regain confidence in the mortgage and housing market.

But here, too, there's a catch. As Jordan Weissman explains, one reason why U.S. home prices have stabilized is that 23 percent of homeowners still owe more on their mortgages than their homes are currently worth. Many of these "underwater" homeowners are still reluctant to put their homes on the market, for fear of taking a big hit. That trend has helped prop up prices, but it's not a good sign for the underlying strength of the U.S. economy.

For now, efforts to assist these homeowners are proceeding slowly. As Alan Zibel reports, a record 54,000 underwater homeowners in June took advantage of a program that lets them refinance their mortgage. But that still leaves millions of Americans underwater with few options. And Ed DeMarco, the head of the Federal Housing Finance Agency, has vetoed a plan to enable homeowners with federally backed mortgages from paying less. (See Dylan Matthews for more on that.)

All in all, there are a few encouraging signs. But will they be enough to get the U.S. economy out of its rut—especially with the rest of the world still struggling? That's less clear. Almost right on cue, the spat of good news Thursday morning in the United States was greeted by troubling signs elsewhere in the world. Here's Bloomberg with the kicker: "U.S. stocks were little changed, after a four-day advance in the Standard & Poor’s 500 Index, as concern about a worsening of Europe’s debt crisis offset data showing that American jobless claims unexpectedly declined."