I'm trying to search for unknown structural breaks in co-integrated time series.
$$Y_t = c_t + \beta X_t + e_t$$
Searching for breaks in this context is essentially the same as it would if both the series were did not exhibit a stochastic trend. I want to find the combination of breaks the minimizes the residual sum of squares (RSS). The only major difference is since the time series are co-integrated, the distribution of the test statistics and consequently the critical values are different (see Kejriwal and Perron (2010)). Consequently, I would like to use
breakpoints::strucchange to obtain the RSS under different breaks. Then I'll run the tests and compare to the correct critical values.
One solution is to this is for me to run
breakpoints::strucchange which will give me the break dates and then I use these break dates to calculate the test statistics. This approach is problematic. Imagine, for example, that there are really three breaks, however,
breakpoints::strucchange only identifies two, because for my purposes it is using the wrong critical values. The call to
breakpoints::strucchange will simply true date that the two breaks occurred. It however, would not tell me anything about this third breaks. Therefore, I can't construct a test statistic for three breaks.
I'm sure there is a way around this.
breakpoints::strucchange is clearly calculating all these RSS in accordance with Bai and Perron 2003. I'm just not sure how to efficiently obtain this information.