What tests do you recommend for finding breaks in the following time series: log of inward FDI, log of nominal GDP, log of outward FDI from 1980 to 2012?
For a multivariate regression:
If you're testing for a break at a known date, say at a historic event or change in policy regime, I would recommend that you use a Chow test (a special case of an F-test). This will give you an idea of whether the coefficients are constant on each side of the proposed break.
On the other hand, if you want to test for a break at an unknown date, you have three options. You could try a Quandt, Mann-Wald, or Andrews-Ploberger statistic. The choice is up to you, but I like Mann-Wald. To me, it's more intuitive than the others because it's basically the Mean Value Theorem evaluated using a Riemann sum of the F-test at each potential break. Of course, the asymptotic distributions necessary to use any of these methods are beyond my knowledge, but you don't need those if you're modeling in a nice software package with pre-loaded diagnostic tests.
Lastly, testing for "breaks" (as in multiple breaks) is a computational nightmare. You probably have deeper issues with your model (like omitted variables or some sort of misspecification) if you need multiple breaks.
Impulse indicator saturation (IIS) (Santos, 2008) and step indicator saturation (SIS) (Doornik et al., 2013) are relatively new and powerful methods for change/break detections. They are used, for example, in the newer versions of the automated model selection procedure "Autometrics" by Doornik (et al.?).
- Santos, Carlos. "Impulse saturation break tests." Economics Letters 98.2 (2008): 136-143.
- Doornik, Jurgen A., David F. Hendry, and Felix Pretis. "Step-indicator saturation." Dicussion Paper 658 (2013).
Are you testing for just whether or not there are any breaks at all in the data, or are you testing if there is a break/anomaly at a specific point in time that you believe one exists? If it is the latter you could include a dummy for that point and test its significance...