Testing for jumps with robust spot volatility estimators

Jumps in the paths of efficient asset prices have important economic implications. Motivated by the issue of testing for jumps based on noisy high‐frequency data, we develop a novel spot volatility estimator, which is obtained by minimizing the sum of some Huber loss functions, and use it as an ingredient for jump detection. This type of estimators is uniformly consistent in estimating the spot volatilities of the efficient price at numerous time points. We further demonstrate the consistency of the proposed jump test based on the property of the novel spot volatility estimator. We show that in finite samples, the proposed volatility estimator and the test perform favorably compared to some competitors through Monte Carlo simulations. We also illustrate our methodology with the stock prices of Apple and Microsoft.