Bootstrapping Long-Run Covariance of Stationary Functional Time Series

Bootstrapping Long-Run Covariance of Stationary Functional Time Series

Blog Article

A key summary statistic in a stationary functional time series is the long-run covariance function that measures serial dependence.It can be consistently estimated via a kernel sandwich estimator, which is the core of dynamic functional principal component regression for forecasting functional time series.To measure the uncertainty of the long-run covariance estimation, we consider sieve and functional autoregressive (FAR) bootstrap methods to generate pseudo-functional time series and study variability associated with the long-run covariance.The sieve bootstrap method is nonparametric (i.

e., model-free), while the FAR bootstrap method is semi-parametric.The Armored Vehicle Kit sieve bootstrap method relies on functional principal component analysis to decompose a functional time series into a set of estimated functional principal components and their associated scores.The scores can be bootstrapped via a vector autoregressive representation.

The bootstrapped functional time series are obtained by multiplying the bootstrapped scores by the estimated functional principal components.The FAR bootstrap method relies on the FAR of order 1 to model the conditional mean of a functional time series, while residual functions can be bootstrapped via independent and identically distributed resampling.Through Downstems a series of Monte Carlo simulations, we evaluate and compare the finite-sample accuracy between the sieve and FAR bootstrap methods for quantifying the estimation uncertainty of the long-run covariance of a stationary functional time series.