Abstract:
In time-series analysis, theoretically, we can reduce the inference error as much as needed by increasing sampling frequency. However, there is the market microstructure noise in nancial data and the e¤ect gets larger with higher frequency data. Those two e¤ects bring the U-shaped inference error, so it is common in the practical applications to choose somewhat moderate sampling frequency. In this paper, I ignore the market microstructure to focus on the main argument. Then the estimation error, typically, decreases as the sampling frequency increases, so it is optimal to choose the highest frequency. This paper present an example where that intuition is violated. If the underlying volatility processes have fast mean-reverting drifts as well as large di¤usion terms, the bipower variations may show the nonmonotonic bias. In those cases, some commonly used moderate frequency data may bring larger size of the (standardized) bias than lower as well as higher frequency data. This nonmonotonic standardized bias of bipower variation can result in hump shaped rejection probabilities of tests for jumps which are based on the bipower variation. To explain that kind of nonmonotonicity, I introduce a modifed in ll asymptotic assumptions and derive several approximating expressions for the bias using the Euler approximation scheme. Through Monte Carlo experiments, the hump-shaped rejection probabilities of tests for jumps are explained by the approximated and simulated bias of bipower variations.
