A frequency domain bootstrap for general multivariate stationary processes

Developing valid frequency domain bootstrap procedures for integrated periodogram statistics multivariate time series is a challenging problem. This mainly due to the fact that distribution of such depends on fourth-order moment structure underlying process in nearly every scenario. Exceptions are some very special cases like nonparametric estimators spectral density matrix or Gaussian series. In contrast univariate case, even additional structural assumptions – as linearity standardization statistic interest do not solve paper proposes new procedure series, hybrid (MFHB), well functions thereof. Asymptotic validity MFHB established these and class stationary processes satisfying rather weak dependence conditions ranging clearly beyond linear processes. The finite sample performance investigated by means simulations.