Identifying the time-effect factors of multiple time series

The Peña–Box model is considered for finding the time-effect factors of a multiple time series. This paper first establishes the connection between the Peña–Box model and the vector ARMA model. According to the Peña–Box model, some series can be ignored while modelling the vector ARMA model. A consistent estimator is then proposed to identify the model for nonlinear and nonstationary time series. Finally, the finite-sample behaviour of the estimator is illustrated via simulations.