Global market turmoil coupled with falling commodity prices are leaving bond traders frustrated in terms of trying to guess the next 10 or 15 basis points of movements in Treasurys, Lyngen said.
CRT it expects the Fed to hike at least once this year, which Lyngen said is for the most part fully priced into the short end of the yield curve at this point, and sees the 2-year note yield ending the year at about 75 basis points.
The outlook for the 10-year note yield is less clear, but it doesn't see the first rate hike as a particularly bearish event for long-dated yields. CRT forecasts for it to close the year somewhere between 1.75 percent and 2.35 percent.
Weekly U.S. jobless claims came in at 282,000, above the expected 275,000, while the U.S. trade gap fell to its lowest in five months. The August ISM non-manufacturing index fell to 59 month-over-month but came in above the expected 58.1.
Read MoreTraders fishing for a bottom
Investors also digested the latest Challenger, Gray & Christmas jobs cut report, which showed that job cuts announced by U.S.-based companies plummeted 61 percent in August after rising to a four-year high the previous month.
Despite the delude of data, Treasurys still inched higher along with stocks,which rose about less than 1 percent.
"The U.S. economy still remains a mixed bag however with overall services certainly good, manufacturing lackluster, the oil/gas industry in a recession, retail spending OK, housing seeing some bright spots, capital spending uneven, headwinds with exports, job growth decent, wage gains slow and a potential inventory overhang in the 2nd half of the year," said Peter Boockvar, chief market analyst at the Lindsey Group.
Friday's job report will provide the latest snapshot of employment conditions before the U.S. Federal Reserve meets later this month.
In Europe, the ECB decided to keep its key interest rates unchanged at 0.05 percent and president Mario Draghi said the bank will extend quantitative easing if needed. The central bank also cut its inflation forecast for 2015 to 1.1 percent from 1.5 percent.
Read MoreEuro strength puts pressure on Draghi as ECB meets
"The ECB Governing Council meet after what has been an eventful summer, with turmoil in emerging markets, collapsing inflation expectations and continued uncertainty in Greece all serving to cloud the macroeconomic outlook, and consequently leaving ample room for the dovish messaging on policy to remain intact," said head of U.K. and European rates and economic research at RBC, Peter Schaffrik, in a note to clients Thursday.
Energy prices have seen extreme moves this week. Oil fell on Thursday on a surprise build in U.S. inventory levels and a firm dollar, but a recovery in Asian shares after Wall Street posted decent gains capped losses. Brent crude dropped 43 cents to $50.07 a barrel at around 08:57 a.m. ET, while U.S. crude fell 31 cents to $45.94 a barrel, off the day's low of $45.65.
Trading was relatively calm in China as compared to previous sessions, with mainland share markets in China closed until Monday.
—CNBC's Jenny Cosgrave contributed to this report.