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Title: Sieve bootstrap memory parameter in long-range dependent stationary functional time series Authors:  Han Lin Shang - Macquarie University (Australia) [presenting]
Abstract: A sieve bootstrap procedure is applied to quantify the estimation uncertainty of long-memory parameters in stationary functional time series. To estimate the long-memory parameter, we use a semiparametric local Whittle estimator, where discrete Fourier transform and periodogram are constructed from the first set of principal component scores, via a functional principal component analysis. The sieve bootstrap procedure uses a general vector autoregressive representation of the estimated principal component scores. It generates bootstrap replicates that adequately mimic the dependence structure of the underlying stationary process. For each bootstrap replicate, we first compute the estimated first set of principal component scores and then apply the semiparametric local Whittle estimator to estimate the memory parameter. By taking quantiles of the estimated memory parameters from these bootstrap replicates, we can construct confidence intervals of the long-memory parameter. As measured by coverage probability differences between the empirical and nominal coverage probabilities at three levels of significance, we demonstrate the advantage of using the sieve bootstrap in comparison to the asymptotic confidence intervals based on normality.