Combining p-values to Test for Multiple Structural Breaks in Cointegrated Regressions

We propose a multiple hypothesis testing approach to assess structural stability in cointegrating regressions. Underlying tests are constructed via a Vector Error Correction Model and generalize the reduced rank regression procedures of Hansen (2003). We generalize the likelihood ratio test proposed in Hansen (2003) to accommodate unknown break dates through the specification of several scenarios regarding the number and the location of the breaks. We define a combined p-value adjustment, which proceeds by simulating the entire dataset imposing the relevant null hypothesis. This framework accounts for both correlation of underlying tests and the fact that empirically, parameters of interest often pertain to a limited even though uncertain stylized-fact based change points. We prove asymptotic validity of the proposed procedure. Monte Carlo simulations show that proposed tests perform well in finite samples and circumvent Bonferroni-type adjustments. An application to the S&P 500 prices and dividends series illustrates the empirical validity of the proposed procedure.