Εφαρμογές του Bootstrap στην ανάλυση χρονοσειρών
Bootstrap applications to time series analysis
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Keywords
Bootstrap (Statistics) ; ΧρονοσειρέςAbstract
The bootstrap, introduced by Efron (1979), is a statistical computational technique that has been
proven to be a powerful tool for estimating the variance and the sampling distribution of a
statistical function, either parametrically or nonparametrically. Although initially developed for
independent data, it has since been extended to more complex problems where the data are
dependent, as is the case with time series. In this thesis, the main bootstrap techniques for time
series will be presented and applied to both simulated and real data. In time series data, there
are two methods of applying the bootstrap. The first is the parametric approach, where it is
assumed that the data come from some parametric model, and the bootstrap is performed on the
residuals obtained after its estimation. The second approach is nonparametric, i.e. model-free,
where resampling is done on blocks of observations from the original time series.
This thesis consists of five chapters. The first three chapters present the theoretical background
of the thesis topic, while the remaining chapters focus on the application of the methods.
Specifically, the first chapter introduces the classical bootstrap method and some variations
relevant to the main part of the work. The second chapter provides an introduction to time series
and models that will be used in the time series bootstrap. The third chapter is the main part of
the work, presenting the theoretical methods of the bootstrap for time series. Subsequently, in
the fourth chapter, the results of applying the methods are visualized and a simulation study is
conducted to demonstrate the behavior of bootstrap methods in a first order autoregressive
process. Finally, in the fifth chapter, the methods are applied to real-world data. The R
programming language is used for the simulation study and data analysis.
Postgraduate Studies Programme
Εφαρμοσμένη ΣτατιστικήDepartment
Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής ΕπιστήμηςNumber of pages
132Language
GreekCollections
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Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα
Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα