Multiple-index Nonstationary Time Series Models: Robust Estimation Theory and Practice

TL;DR

This paper introduces a flexible class of multiple-index nonstationary time series models with robust estimators, addressing high-dimensional challenges and demonstrating strong nonlinear predictability in stock returns through theoretical analysis and simulations.

Contribution

It develops a new multiple-index modeling framework with robust estimation methods and establishes their asymptotic properties for nonstationary time series.

Findings

Robust estimators perform well in finite samples.

Strong nonlinear predictability of stock returns is observed.

The model effectively handles high-dimensional nonstationary data.

Abstract

This paper proposes a class of parametric multiple-index time series models that involve linear combinations of time trends, stationary variables and unit root processes as regressors. The inclusion of the three different types of time series, along with the use of a multiple-index structure for these variables to circumvent the curse of dimensionality, is due to both theoretical and practical considerations. The M-type estimators (including OLS, LAD, Huber's estimator, quantile and expectile estimators, etc.) for the index vectors are proposed, and their asymptotic properties are established, with the aid of the generalized function approach to accommodate a wide class of loss functions that may not be necessarily differentiable at every point. The proposed multiple-index model is then applied to study the stock return predictability, which reveals strong nonlinear predictability under various loss measures. Monte Carlo simulations are also included to evaluate the finite-sample performance of the proposed estimators.