What assumptions are required for structural breaks tests in time series?

Question

Context
I'm doing research related to structural change in stock price time series. In order to test whether some chosen event is a structural break or the series has a structural change, I conduct a few different tests which are

• Chow Test
• CUSUM Test
• SupF Test
• Bai Perron Test

As the input model, the $AR(3)$ process is used (i.e. $price_{t} = \beta_1 \cdot price_{t-1} + \beta_2 \cdot price_{t-2} + \beta_3 \cdot price_{t-3} + \epsilon_t$).
My concern is that the financial data is highly chaotic so the needed assumptions for the tests are violated.

Question
I wonder what the assumptions that make the structural breaks testing results valid are?

Answer 1

In short, you need assumptions that assure that a standard central limit theorem holds: $\sqrt{n} (\hat \beta - \beta) \rightarrow \mathcal{N}(0, V)$. This permits weak correlations and heteroscedasticity provided that a consistent estimate of the covariance matrix $\hat V$ is used. However stronger dependencies (e.g. GARCH) are excluded as are nonstationary or trending regressors which lead to different limiting distributions under the null hypothesis.

Stationary AR(3) models are fine but the residuals should not have remaining autocorrelation in that case.

For details see the corresponding papers. However note that many papers employ somewhat different sets of assumptions and not necessary the broadest assumptions that are possible.