  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.
