Nonparametric monitoring of financial time series by jump-preserving control charts

Since structural changes in a possibly transformed financial time series may contain important information for investors and analysts, we consider the following problem of sequential econometrics. For a given time series we aim at detecting the first change-point where a jump of size a occurs, i.e., the mean changes from, say, m ₀to m ₀+ a and returns to m ₀after a possibly short period s. To address this problem, we study a Shewhart-type control chart based on a sequential version of the sigma filter, which extends kernel smoothers by employing stochastic weights depending on the process history to detect jumps in the data more accurately than classical approaches. We study both theoretical properties and performance issues. Concerning the statistical properties, it is important to know whether the normed delay time of the considered control chart is bounded, at least asymptotically. Extending known results for linear statistics employing deterministic weighting schemes, we establish an upper bound which holds if the memory of the chart tends to infinity. The performance of the proposed control charts is studied by simulations. We confine ourselves to some special models which try to mimic important features of real time series. Our empirical results provide some evidence that jump-preserving weights are preferable under certain circumstances.