In this project we focus on the effects that jumps and nonlinearities have on the inference in and calibration of economic models. Currently, standard continuous-time dynamical models are extended to include random jumps which represent shocks to the economy as a whole or to some assets in financial markets. Statistical tools to adjust these jump models to empirical data are currently under development. The main interest will be in the distribution of the number and of the size of jumps.
Often, the jumps itself cannot be observed directly, which would require a continuous-time observation of the jump process itself. If the process is only observed at discrete time points, thinking of daily or even much less frequent macroeconomic data, we cannot be sure whether there have not occurred several jumps between two observations and to what extent the jumps are superposed by regular continuous dynamics. In this case we therefore observe the jumps only indirectly and it turns out that already in simple cases estimating the distribution of jump sizes is a complex nonlinear inference problem which involves all the difficulties of a nonparametric deconvolution problem.
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