## Report in Wirtschaftsmathematik (WIMA Report)

- 142
- An online approach to detecting changes in nonlinear autoregressive models (2011)
- In this paper we develop monitoring schemes for detecting structural changes in nonlinear autoregressive models. We approximate the regression function by a single layer feedforward neural network. We show that CUSUM-type tests based on cumulative sums of estimated residuals, that have been intensively studied for linear regression in both an offline as well as online setting, can be extended to this model. The proposed monitoring schemes reject (asymptotically) the null hypothesis only with a given probability but will detect a large class of alternatives with probability one. In order to construct these sequential size tests the limit distribution under the null hypothesis is obtained.

- 138
- A uniform central limit theorem for neural network based autoregressive processes with applications to change-point analysis (2011)
- We consider an autoregressive process with a nonlinear regression function that is modeled by a feedforward neural network. We derive a uniform central limit theorem which is useful in the context of change-point analysis. We propose a test for a change in the autoregression function which - by the uniform central limit theorem - has asymptotic power one for a large class of alternatives including local alternatives.

- 137
- Testing for parameter stability in nonlinear autoregressive models (2011)
- In this paper we develop testing procedures for the detection of structural changes in nonlinear autoregressive processes. For the detection procedure we model the regression function by a single layer feedforward neural network. We show that CUSUM-type tests based on cumulative sums of estimated residuals, that have been intensively studied for linear regression, can be extended to this case. The limit distribution under the null hypothesis is obtained, which is needed to construct asymptotic tests. For a large class of alternatives it is shown that the tests have asymptotic power one. In this case, we obtain a consistent change-point estimator which is related to the test statistics. Power and size are further investigated in a small simulation study with a particular emphasis on situations where the model is misspecified, i.e. the data is not generated by a neural network but some other regression function. As illustration, an application on the Nile data set as well as S&P log-returns is given.