In this paper, we study the functional central limit theorem (FCLT) for the infinite-order heterogeneous autoregressive model of realized volatility (HAR(∞)). We prove under proper assumptions that the process is L2-NED and then obeys the FCLT. As an application of the FCLT, we derive the limit distribution of the CUSUM statistics to detect the structural change of the model.
Bibliographical noteFunding Information:
This research was supported by Basic Science Research Program through the NRF 2013R1A1A2006828.
- Functional central limit theorem
- HAR(∞) model
- Structural break