Essays on Detecting Structural Breaks in Fractional Cointegration and Long-Memory Time Series

This thesis contains three essays on detecting structural breaks in fractional cointegration and univariate long-memory time series in two different ways; Classical statistical tests and real time monitoring. Chapter 1 gives an introduction to the concept of long-memory and fractional cointegration. Further, the concept of real time monitoring models contrary to classical statistical tests is explained. Chapter 2 presents a real time monitoring procedure for fractional cointegration. It can be used to detect a break in deterministic parameters or a break in the fractional cointegration relation itself. Unlike classical statistical tests, this method is designed to consistently test for a structural break each time new data is obtained without size distor- tions. For this we establish a CUSUM-type detector and derive its limiting distribution as well as the behavior under the alternative of a structural break. In a Monte Carlo study good size and power properties are shown for most common settings of fractional cointe- gration. We also apply the monitoring procedure in the context of momentum investing. Here, we show that the detector is able to locate a structural break in a fractional coin- tegration model between the squared returns of the S&P500 and the squared momentum returns during the momentum crash following the global financial crisis in 2008. Chapter 3 takes a more classical statistical testing approach to breaks in fractional cointegration. Here, we introduce a CUSUM-type test for breaks in fractional cointe- gration. Even though the test is used to detect the same kind of breaks as discussed in chapter 2 it is designed to be used solely for historical datasets. This adds the problem of biased parameter estimation in case of the alternative, if the model is estimated on the complete historical sample. To circumvent this problem we introduce a new bootstrap procedure that ensures consistent parameter estimation under a break, while it does not lead to changes in the tests behavior under the null of no break. Monte Carlo simulations demonstrate that the test, in combination with the bootstrap procedure, achieves good size and power properties. At last chapter, 4 presents a monitoring procedure, which works in a similar way as in chapter 2, but deals with univariate long-memory time series and in particular ARFIMA series. To set up the detector we establish a CUSUM test statistic based on the models residuals. Under the null of no structural break these follow white noise and thus the CUSUM statistic converges to a simple Brownian motion. However, under the alternative of a break during the monitoring period the detector diverges and is thus able to detect structural breaks in either the short-memory components of the model or the degree of integration d. The finite sample performance is shown in a Monte Carlo study, in which the procedure shows good size and power levels depending on the location of the break.