Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2019 017

Portmanteau Test and Simultaneous Inference for Serial Covariances

Han Xiao
Wei Biao Wu

The paper presents a systematic theory for asymptotic inferences based on
autocovariances of stationary processes. We consider nonparametric tests for se
rial correlations using the maximum and the quadratic deviations of sample
autocovariances. For these cases, with proper centering and rescaling, the
asymptotic distributions of the deviations are Gumbel and Gaussian, respec
tively. To establish such an asymptotic theory, as byproducts, we develop a
normal comparison principle and propose a sufficient condition for summability
of joint cumulants of stationary processes. We adapt a blocks of blocks
bootstrapping procedure proposed by Kuensch (1989) and Liu and Singh (1992) to
the maximum deviation based tests to improve the finite-sample performance.

Autocovariance, blocks of blocks bootstrapping, Box-Pierce test, extreme value
distribution, moderate deviation, normal comparison, physical dependence
measure, short range dependence, stationary process, summability of cumulants

JEL Classification: