Explain in detail (showing all relevant formulas, test hypothesis details, symbols, etc.) how you would test for a structural break in the parameters of your model if:

a. the break is suspected to occur around the middle of your sample

b. the break is suspected to occur close to the end of your sample

c. Suppose that you have no idea where a break may have occurred, but you want to test for this possibility. Explain which test you would use and briefly explain the intuition of this test.