structural break

Say I have the equation:

$y_t = \alpha + \beta*\text{time}$

I'm looking for a structural break test that allows both parameters ($\alpha$ and $\beta$) to potentially change with a structural break. However rather than test these out individually, or jointly, I want a SB test that, say detects a break or series of breaks, and tells you whether the break thus found was $\alpha$ break, a $\beta$ break, or both.

Is there such a test -- that can identify a break and then the type of break?

• You have just defined a research agenda for about a decade. Look at Andrews 1993 and Andrews and Ploberger, and sup tests and CUSUM tests. There are estimators of break dates but usually just for one break. The most rudimentary estimators rely on you eyeballing the break and then see whether it's there. – Hirek Feb 28 '15 at 14:59
• "identify break/classify break type" and "test" are not synonyms. You may like to consider whether your interest is more on identifying the break (and type) or on formal testing. – Glen_b Mar 1 '15 at 2:57