Essays on persistence and volatility in financial time series

Abstract

This thesis contains four essays on persistence change tests and non-stationarity tests. Persistence change tests are analysed under non-standard conditions and a new family of tests to detect changes in persistence and unit roots is proposed that is based on the CUSUM testing principle. These can be applied in economic and financial time series. Chapter 1 introduces the existence and implications of persistence in time series and structural changes. Furthermore, the impact of asymmetric volatility and different types of outliers is discussed. A new testing principle based on the concept of squared CUSUM of residuals is developed. Chapter 2 reviews the literature on different methods for persistence change tests including parametric and non-parametric modifications. A family GARCH model is presented to consider different asymmetric conditional volatility models within the persistence change model. The Wild bootstrap approach is introduced and bootstrap analogues of the persistence change tests are derived. The bootstrap procedure is conducted in a comprehensive Monte Carlo study to analyse the behaviour of the tests under asymmetric volatility. The results show that the tests suffer from severe size distortions, while the bootstrap method provides reasonable results in small samples. In an application to the U.S. stock market, asymmetric volatility models are estimated on the return series, where the persistence change tests and the bootstrap analogues are conducted. The main finding is that the tests falsely detect a change in persistence under asymmetric volatility, while the bootstrap analogues assume stationary behaviour. In chapter 3 the effect of outliers on inference in models with changing persistence is under consideration. We introduce the additive and innovative outlier with different outlier detection and removal methods. In a Monte Carlo study, the performance of the tests is investigated and compared in uncontaminated, outlier contaminated and adjusted series. The main finding is that innovative outliers do not affect the size, while additive outliers deteriorate the performance of the tests if the series exhibits a high degree of persistence. We present a modified outlier detection and removal method which is applied in a simulation study. In an empirical application to inflation data of the G7 countries the tests and the new method are conducted. Chapter 4 introduces a new approach to test for a unit root based on squared CUSUMs of residuals. The procedure is based on the squared sum of all different consecutive observations of the time series. The limiting distributions of the tests are derived and consistency can be shown. A comprehensive simulation study in ARMA models suggests that the new method provides better properties. In stationary processes the tests show higher power than commonly used unit root tests, while the size is closer to the nominal significance level, when a unit root is present in the data. The empirical application to the historical Nelson-Plosser data provides slightly different results compared to the findings in the literature. In chapter 5 the same procedure as in chapter 4 is used to develop tests for a change in persistence based on squared CUSUMs of sub-sample residuals. We construct one test for the null hypothesis of a stationary process and another test for the non-stationarity hypothesis. Similar to previous testing procedures a maximum and a ratio based test is constructed for the alternative of a change in persistence in an unknown direction. While common persistence change tests weight the residuals in the partial sums differently or ignore cross-dependencies of the residuals, the presented tests provide squared partial sums of equally weighted observations and exploit the cross-dependencies. The limiting distributions of the tests are derived and consistency against a change in persistence can be shown. The simulation study provides better size and power properties for both developed tests.