Zusammenfassung: | |
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.
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Lizenzbestimmungen: | Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. |
Publikationstyp: | DoctoralThesis |
Publikationsstatus: | publishedVersion |
Erstveröffentlichung: | 2023 |
Schlagwörter (deutsch): | Einheitswurzeln, Persistenz, Strukturbrüche, Volatilität |
Schlagwörter (englisch): | Asymmetric Volatility, Brownian Bridge, Brownian Motion, Change in Persistence, CUSUM Test, Monte Carlo, Outlier Detection, Persistence Change, Unit Root, Wild Bootstrap |
Fachliche Zuordnung (DDC): | 330 | Wirtschaft |