Abstract
This paper develops a method to select the threshold in threshold-based jump detection
methods. The method is motivated by an analysis of threshold-based jump detection
methods in the context of jump-diffusion models. We show that over the range of sampling
frequencies a researcher is most likely to encounter that the usual in-fill asymptotics
provide a poor guide for selecting the jump threshold. Because of this we develop
a sample-based method. Our method estimates the number of jumps over a grid of thresholds
and selects the optimal threshold at what we term the “take-off” point in the estimated
number of jumps. We show that this method consistently estimates the jumps and their
indices as the sampling interval goes to zero. In several Monte Carlo studies we evaluate
the performance of our method based on its ability to accurately locate jumps and
its ability to distinguish between true jumps and large diffusive moves. In one of
these Monte Carlo studies we evaluate the performance of our method in a jump regression
context. Finally, we apply our method in two empirical studies. In one we estimate
the number of jumps and report the jump threshold our method selects for three commonly
used market indices. In the other empirical application we perform a series of jump
regressions using our method to select the jump threshold.
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