Bootstrap Methods for Heavy-Tail or Autocorrelated Distributions with an Empirical Application
Date: 3 August 2017
University of Exeter
PhD in Economics
Chapter One: The Truncated Wild Bootstrap for the Asymmetric Infinite Variance Case The wild bootstrap method proposed by Cavaliere et al. (2013) to perform hypothesis testing for the location parameter in the location model, with errors in the domain of attraction of asymmetric stable law, is inappropriate. Hence, we are introducing ...
Chapter One: The Truncated Wild Bootstrap for the Asymmetric Infinite Variance Case The wild bootstrap method proposed by Cavaliere et al. (2013) to perform hypothesis testing for the location parameter in the location model, with errors in the domain of attraction of asymmetric stable law, is inappropriate. Hence, we are introducing a new bootstrap test procedure that overcomes the failure of Efron’s (1979) resampling bootstrap. This bootstrap test exploits the Wild Bootstrap of Cavaliere et al. (2013) and the central limit theorem of trimmed variables of Berkes et al. (2012) to deliver confidence sets with correct asymptotic coverage probabilities for asymmetric heavy-tailed data. The methodology of this bootstrap method entails locating cut-off values such that all data between these two values satisfy the central limit theorem conditions. Therefore, the proposed bootstrap will be termed the Truncated Wild Bootstrap (TWB) since it takes advantage of both findings. Simulation evidence to assess the quality of inference of available bootstrap tests for this particular model reveals that, on most occasions, the TWB performs better than the Parametric bootstrap (PB) of Cornea-Madeira & Davidson (2015). In addition, TWB test scheme is superior to the PB because this procedure can test the location parameter when the index of stability is below one, whereas the PB has no power in such a case. Moreover, the TWB is also superior to the PB when the tail index is close to 1 and the distribution is heavily skewed, unless the tail index is exactly 1 and the scale parameter is very high. Chapter Two: A frequency domain wild bootstrap for dependent data In this chapter a resampling method is proposed for a stationary dependent time series, based on Rademacher wild bootstrap draws from the Fourier transform of the data. The main distinguishing feature of our method is that the bootstrap draws share their periodogram identically with the sample, implying sound properties under dependence of arbitrary form. A drawback of the basic procedure is that the bootstrap distribution of the mean is degenerate. We show that a simple Gaussian augmentation overcomes this difficulty. Monte Carlo evidence indicates a favourable comparison with alternative methods in tests of location and significance in a regression model with autocorrelated shocks, and also of unit roots. Chapter 3: Frequency-based Bootstrap Methods for DC Pension Plan Strategy Evaluation The use of conventional bootstrap methods, such as Standard Bootstrap and Moving Block Bootstrap, to produce long run returns to rank one strategy over the others based on its associated reward and risk, might be misleading. Therefore, in this chapter, we will use a simple pension model that is mainly concerned with long-term accumulation wealth to assess, for the first time in pension literature, different bootstrap methods. We find that the Multivariate Fourier Bootstrap gives the most satisfactory result in its ability to mimic the true distribution using Cramer-von-mises statistics. We also address the disagreement in the pension literature on selecting the best pension plan strategy. We present a comprehensive study to compare different strategies using a different bootstrap procedures with different Cash-flow performance measures across a range of countries. We find that bootstrap methods play a critical role in determining the optimal strategy. Additionally, different CFP measures rank pension plans differently across countries and bootstrap methods.
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