Bootstrap-based test for volatility shifts in GARCH against long-range dependence
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Measuring volatility has been one of the most critical steps in nancial modeling. One characteristic of volatility is persistence. Numerous methods have been proposed to test whether such persistency is due to volatility shifts in the market or a natural fluctuation explained by stationary long-range dependence. Lee et al. (2014) propose a residual-based cumulative sum test statistic to test volatility shifts in generalized autoregressive conditional heteroscedasticity model against long-range dependence. This thesis continues the study of Lee et al. (2014). It compares the asymptotic size and power proposed by them and the bootstrap size and power. Baek and Pipiras (2012) revise the test statistics based on the local Whittle estimation of the self-similar parameter. This thesis also compares the bootstrap size and power of the local Whittle statistics to the test statistics for no volatility shift by Lee et al. (2014).