Order selection of continuous time models: Applications to estimation of risk premiums

This paper develops an order selection criterion for a continuous autoregressive (CAR) time series. Based on the quadratic variation consideration of a CAR(p) process, a new order selection criterion, the quadratic variation criterion (QVC) is proposed. It is shown that this new order selection criterion is consistent and provides an effective means to estimate the order of a CAR(p) model. Simulation studies suggest that the proposed method is efficient and outperforms other order selection criteria. The QVC is applied to select the order of the cumulative excess return process and the effect of the risk premium of a GARCH-M model when changing variance is taken into account.