The Real Time Monitoring Test for Realized Volatility

Abstract

This paper proposes a monitoring cumulative sum of squares (CUSQ)-type test for structural breaks in real-time via an auto-regressive (AR) approximation framework when data generating process (DGP) is a long memory process. The limiting distribution of the monitoring test follows a Brownian bridge and is free of long memory parameters under the null hypothesis of no break. The test is easy to implement and avoids the issue of spurious breaks found for some retrospective tests for long memory process. Neither does it need to use the bootstrap procedure to find the critical values. Monte Carlo simulations appear to confirm that there exists negligible size distortion and satisfactory power performances in finite samples. The procedure is then applied to monitor the real time pattern of realized volatilities of dollar-Deutschmark and dollar-Japanese Yen.

Keywords: CUSUM of squares tests, long memory, structural change, real time monitoring