I am working with a short time series consisting of 21 annual data points. I wish to analyze the time series for structural changes, and I have been exploring the strucchange package in R (Zeileis et al. 2002).
If I am going to perform formal statistical tests of breakpoints, is it appropriate to use the serial F-statistic test (strucchange::Fstats), which tests for the existence of a single breakpoint against the null hypothesis of no breakpoints, on my highly non-stationary raw time series data, or must I first difference my data to stabilize the mean? To rephrase in R syntax, is the serial F-stat test valid on the model lm(y ~ x), or must I instead difference y and run the test on lm(diff(y) ~ 1)? I get much higher F-stats (hence lower p-values) for the former test than for the latter, but I want to make sure I am using it correctly. Given the shortness of my time series, I am reluctant to sacrifice the first data point for differencing.