While much of the wild action in bonds may be over for the week, O'Donnell said the year end may spur some buying Thursday and Friday as traders square positions, and that may generate some more volatile moves just because volume is so light.
Traders Thursday are also watching for the release of the final economic reports of the year—weekly jobless claims at 8:30 a.m. and Chicago purchasing managers at 9:45 a.m. Economists expect jobless claims of about 418,000.
"On the claims, it'll probably fall a few thousand after the previous week is revised up. That's been the pattern. It's still a grinding downtrend in the four-week moving average," said Deutsche Bank economist Joseph LaVorgna.
LaVorgna said the bond market's action this week was probably not reflective of much more than a thin year-end market. "At the end of the year, you get these moves and you don't want to read too much into them," he said.
While many strategists believe rates are rising on an improving economy, others, like Boockvar, believe rates are rising on inflation concerns.
"Rates are not going up for a good reason. It's inflation expectations, and of course you're getting higher interest rates in Europe for debt and deficit concerns, and you have rates going up in Asia because central banks are raising rates and they're worried about inflation. You'll probably see a rate hike in Taiwan tomorrow night. Last week, Brazil raised inflation expectations, and the central bank indicated they would raise rates in January," he said.
"Whether it's inflation, deficits or growth, the bottom line is they're still going higher and that'll be a challenge for equities, and again it will matter most for the areas of the world where they're more indebted, like the U.S. and Europe," Boockvar said.
He said the problem with higher rates is that the economy has been depending on cheap money. "Higher interest rates are enough to impact things. You now get a move to 4 percent in the 10-year, and you're going to see 5.5 percent mortgage rates. While that's still historically low, that's a lot higher than where they were, and what's scary is the Fed didn't want that to happen," he said.
Rates have moved higher since the Fed began its $600 billion Treasury purchase program in November. The Fed next week is expected to buy up to $27 billion in Treasury securities and as much as $2.5 billion in TIPS in five days of purchases. This week, it only came to market on two days.
"We have to remember the Fed's buying program ends in June. What's going to happen going into that when everyone knows it's going to stop? Just imagine what's going to happen when everyone knows you're taking the 800-pound gorilla out of the market," Boockvar said.
LaVorgna said that, ironically, the Fed's program could have created market volatility. In theory, the so-called "quantitative easing" program was intended to keep interest rates low and to reflate asset prices, by driving investors into riskier investments. He also said he didn't agree with the Fed's decision to embark on the program.