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Shang HL. Sieve bootstrapping the memory parameter in long-range dependent stationary functional time series. ASTA ADVANCES IN STATISTICAL ANALYSIS 2022. [DOI: 10.1007/s10182-022-00463-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/25/2023]
Abstract
AbstractWe consider a sieve bootstrap procedure to quantify the estimation uncertainty of long-memory parameters in stationary functional time series. We use a semiparametric local Whittle estimator to estimate the long-memory parameter. In the local Whittle estimator, 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. We first compute the estimated first set of principal component scores for each bootstrap replicate 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 nonparametrically 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 compared to the asymptotic confidence intervals based on normality.
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Shang HL, Cao J, Sang P. Stopping time detection of wood panel compression: A functional time‐series approach. J R Stat Soc Ser C Appl Stat 2022. [DOI: 10.1111/rssc.12572] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Han Lin Shang
- Department of Actuarial Studies and Business Analytics Macquarie University Sydney New South Wales Australia
| | - Jiguo Cao
- Department of Statistics and Actuarial Science Simon Fraser University Burnaby British Columbia Canada
| | - Peijun Sang
- Department of Statistics and Actuarial Science University of Waterloo Waterloo Ontario Canada
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Affiliation(s)
| | - Han Lin Shang
- Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, Australia
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