Testing for the Presence of Jumps
When choosing a suitable continuous time process e.g. to model an economic or financial time series one of the first steps is to decide whether a stochastic model is sufficient that produces continuous paths or whether jumps have to be incorporated. To this end, one is faced with the problem to infer from observed data (which is usually only available at discrete time points) whether the underlying model is continuous or allows for jumps. Sometimes this problem is relatively simple to solve e.g. in the situation when very large jumps are easy to identify in a visualization of the time series data.
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