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

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.