| Stationarity and structural stability are two of the most important issues in time series econometrics. This dissertation is a study of the relationship between testing for stationarity and testing for structural change. Specifically, it is shown that a commonly used test for stationarity against the alternative of a unit root proposed by Kwiatkowski, Phillips, Schmidt, and Shin (1992) (KPSS) is algebraically equivalent to a member of a class of tests against structural change at an unknown change-point suggested by Andrews and Ploberger (1994). We extend this class by proposing two new tests for structural change. The maximum value of the KPSS test statistic is derived, and shown to be a non-stochastic cosine function. This result is used to study the asymptotic local power of the test for various alternatives, including structural breaks, unit roots, and fractional integration.; A new class of tests is proposed to distinguish between structural change and unit roots. It involves a two-stage testing methodology that looks at the properties of sub-samples of the data in a second-stage test. The basic idea is that the subsample results should show a localized rejection in the case of a single structural break and widespread rejection in the case of a unit root.; Finally, we examine the empirical properties of Treasury securities. We find evidence of persistence in returns, yields and term-premia, but no evidence for persistence in excess returns. We use the implications above to explore whether the persistence in U.S. debt market returns and yields can be explained through structural change. To this end we look at several methods of splitting the series into sub-samples and testing for persistence within sub-samples. The idea, similar to that pursued by Lobato and Savin (1998) for stock returns and squared returns, is that if the full-sample results are spuriously induced by structural instability, there should not be any evidence of long memory in the sub-samples. We find that the evidence of long memory remains even after accounting for underlying structural changes. |
