Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2019 030

Combining Penalization and Adaption in High Dimension with Application in Bond
Risk Premia Forecasting

Xinjue Li
Lenka Zboňáková
Weining Wang
Wolfgang Karl Härdle

The predictability of a high-dimensional time series model in forecasting with
large information sets depends not only on the stability of parameters but also
depends heavily on the active covariates in the model. Since the true empirical
environment can change as time goes by, the variables that function well at the
present may become useless in the future. Combined with the instable parameters,
finding the most active covariates in the parameter time-varying situations
becomes difficult. In this paper, we aim to propose a new method, the Penalized
Adaptive Method (PAM), which can adaptively detect the parameter homogeneous
intervals and simultaneously select the active variables in sparse models. The
newly developed method is able to identify the parameters stability at one hand
and meanwhile, at the other hand, can manage of selecting the active forecasting
covariates at every different time point. Comparing with the classical models,
the method can be applied to high-dimensional cases with different sources of
parameter changes while it steadily reduces the forecast error in high-
dimensional data. In the out-of-sample bond risk premia forecasting, the
Penalized Adaptive Method can reduce the forecasting error(RMSPE and MAPE)
around 24% to 50% comparing with the other forecasting methods.

SCAD penalty, propagation-separation, adaptive window choice, multiplier
bootstrap, bond risk premia

JEL Classification:
C4, C5, E4, G1