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

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