Identifying jumps in high-frequency time series by wavelets

We discuss a volatility functional model and show that jumps asymptotically impact the volatility estimate. This result is useful because our model shows that significant variations affect the estimation of the volatility and historically price series have structures with this type of behavior. We also discuss a method for detecting and locating jumps at different levels and show that the jumps tend to be detected by wavelet coefficients at lower resolution levels accurately. By checking the wavelet coefficients on the different levels, we can find dyadic intervals in some levels, whose corresponding absolute value of the wavelet coefficient exceeds a threshold, and is significantly higher than the others. We applied the procedure in a simulation study and to a series of Google stocks.