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.
|Number of pages||4|
|State||Published - Sep 2014|
- Functional central limit theorem
- HAR(∞) model
- Structural break