Bootstrapping Whittle Estimators

TL;DR

This paper introduces a frequency domain bootstrap method for Whittle estimators in time series analysis, accommodating model misspecification and weak dependence, with demonstrated effectiveness through simulations and real data.

Contribution

It develops a novel bootstrap approach for Whittle estimators that is asymptotically valid under broad conditions, including model misspecification and weak dependence.

Findings

Bootstrap method performs well in finite samples.

Method accommodates tapered, de-biased, and boundary extended estimators.

Simulation and real data confirm effectiveness.

Abstract

Fitting parametric models by optimizing frequency domain objective functions is an attractive approach of parameter estimation in time series analysis. Whittle estimators are a prominent example in this context. Under weak conditions and the (realistic) assumption that the true spectral density of the underlying process does not necessarily belong to the parametric class of spectral densities fitted, the distribution of Whittle estimators typically depends on difficult to estimate characteristics of the underlying process. This makes the implementation of asymptotic results for the construction of confidence intervals or for assessing the variability of estimators, difficult in practice. This paper proposes a frequency domain bootstrap method to estimate the distribution of Whittle estimators which is asymptotically valid under assumptions that not only allow for (possible) model misspecification but also for weak dependence conditions which are satisfied by a wide range of stationary stochastic processes. Adaptions of the bootstrap procedure developed to incorporate different modifications of Whittle estimators proposed in the literature, like for instance, tapered, de-biased or boundary extended Whittle estimators, are also considered. Simulations demonstrate the capabilities of the bootstrap method proposed and its good finite sample performance. A real-life data analysis also is presented.