There are two theories of why interest rates are rising. In the first, they are rising because of an improved economic outlook, which leads investors to anticipate a swifter exit for monetary policy. In the second, they are rising because of a change in investor expectations of the monetary exit, independent of economic conditions.
Fortunately, statistics has a way of answering these questions: correlation. (Or at least, helping us answer these questions.) I downloaded the daily time series data of the 10-year Treasury note yield and the S&P 500 stock index from June 2008 through the present. If on days that rates are rising, the stock index also rises, then we can assume that both are driven by changes in the economic outlook. If on days that rates are rising, the stock index is falling, then the "economic outlook" story doesn't hold up -- and a "monetary policy" story fits.
I calculated the 90-day correlation coefficient of their daily percentage changes. I find that it has been plummeting since May, which is when interest rates began to jump. See how it's falling off a cliff at the right end of the chart? That means the first story ("happy days are here again") is wrong, and the second story ("the Fed is tightening") is right. Here's the graph.
Oh, and if you're curious, the correlation coefficient is now near the lows of 2009 and 2010. Both of those times were major monetary easings, so rates were falling as stock prices were rising. You might also observe that though the first two big rallies in stocks were amid low correlation coefficients -- i.e. they were Fed-driven -- rallies since the start of 2012 have occurred amid relatively high correlation coefficients. On days that stocks have been doing well, in other words, rates have been rising.
Here's my editorial comment: If the Fed doesn't intend for all of its talk since the start of May to be perceived as pushing forward the schedule for monetary tightening, independent of the economic recovery, it needs to start clarifying its intentions. Now.