How appropriate would be, if you perform Chow breakpoint test for all points within series (without the very beginning and very ending), then find out where test suggest possible breakpoints (e.g. there are 4-5 points) and analyze them from visual and common-sense point of view - whether it is a real structural break or not?
The test is appropriate and was suggested by Quandt (1960) right after Chow (1960) had introduced it. However the correct asymptotic distribution for computing critical values and p-values was unknown until Andrews (1993) rigorously derived the required theory. An R implementation is available in R package
strucchange (Zeileis et al. 2002) based on the p-values from Hansen (1997). The package also emphasizes visualizations of the sequence of test statistics to accompany the final significance tests.
This analysis can also be extended to multiple change points along with formal breakpoint estimation (Bai and Perron 2003). See Zeileis et al. (2003) for the implementation in
- Andrews DWK (1993). Tests for Parameter Instability and Structural Change with Unknown Change Point, Econometrica, 61, 821-856.
- Bai J, Perron P (2003). Computation and Analysis of Multiple Structural Change Models, Journal of Applied Econometrics, 18, 1-22.
- Chow GC (1960). Tests of Equality Between Sets of Coefficients in Two Linear Regressions. Econometrica, 28(3), 591–605.
- Hansen B (1997), Approximate Asymptotic p Values for Structural-Change Tests, Journal of Business & Economic Statistics, 15, 60-67.
- Quandt RE (1960). Tests of the Hypothesis That a Linear Regression System Obeys Two Separate Regimes. Journal of the American Statistical Association, 55(290), 324–330.
- Zeileis A, Leisch F, Hornik K, Kleiber C (2002). strucchange: An R Package for Testing for Structural Change in Linear Regression Models, Journal of Statistical Software, 7(2), 1-38. http://www.jstatsoft.org/v07/i02/
- Zeileis A, Kleiber C, Krämer W, Hornik K (2003). Testing and Dating of Structural Changes in Practice, Computational Statistics and Data Analysis, 44, 109-123.