Sieve bootstrapping the memory parameter in long-range dependent stationary functional time series

Abstract We consider a sieve bootstrap procedure to quantify the estimation uncertainty of long-memory parameters in stationary functional time series. use semiparametric local Whittle estimator estimate parameter. In estimator, discrete Fourier transform and periodogram are constructed from first set principal component scores via analysis. The uses general vector autoregressive representation estimated scores. It generates replicates that adequately mimic dependence structure underlying process. compute for each replicate then apply memory By taking quantiles these replicates, we can nonparametrically construct confidence intervals As measured by coverage probability differences between empirical nominal probabilities at three levels significance, demonstrate advantage using compared asymptotic based on normality.