Change point analysis of second order characteristics in non-stationary time series

An important assumption in the work on testing for structural breaks in time series consists in the fact that the model is formulated such that the stochastic process under the null hypothesis of "no change-point" is stationary. This assumption is crucial to derive (asymptotic) critical values for the corresponding testing procedures using an elegant and powerful mathematical theory, but it might be not very realistic from a practical point of view. This paper develops change point analysis under less restrictive assumptions and deals with the problem of detecting change points in the marginal variance and correlation structures of a non-stationary time series. A CUSUM approach is proposed, which is used to test the "classical" hypothesis of the form $H_0: \theta_1=\theta_2$ vs. $H_1: \theta_1 \not =\theta_2$, where $\theta_1$ and $\theta_2$ denote second order parameters of the process before and after a change point. The asymptotic distribution of the CUSUM test statistic is derived under the null hypothesis. This distribution depends in a complicated way on the dependency structure of the nonlinear non-stationary time series and a bootstrap approach is developed to generate critical values. The results are then extended to test the hypothesis of a {\it non relevant change point}, i.e. $H_0: | \theta_1-\theta_2 | \leq \delta$, which reflects the fact that inference should not be changed, if the difference between the parameters before and after the change-point is small. In contrast to previous work, our approach does neither require the mean to be constant nor - in the case of testing for lag $k$-correlation - that the mean, variance and fourth order joint cumulants are constant under the null hypothesis. In particular, we allow that the variance has a change point at a different location than the auto-covariance.Comment: 64 pages, 5 figure

Portable Dual-Modular Immunosensor Constructed from Bimetallic Metal–Organic Framework Heterostructure Grafted with Enzyme-Mimicking Label for Rosiglitazone Detection

Immunosensor with photoelectrochemistry and fluorescence responsibility is widely used in biomedical detection, health monitoring, and food safety inspection. The cumbersome configuration and low integration of the current immunosensors, however, have brought challenges for their practical applications. To address these challenges, a portable and phone-APP controlled dual-modular immunosensor based on a bimetallic metal–organic framework (MOF) heterostructured photoelectrode, ZnO/NiZn-MOF/CdS, grafted with an enzyme-mimicking Au@CuO/Cu2O label is constructed to achieve simultaneous photoelectrochemistry and fluorescence signage. In the electrode design, the construction of a bimetallic NiZn metal–organic framework (NiZn-MOF) into the common ZnO/CdS photoresponsive structure achieves significant and stable photocurrent output under a very low-power LED light source for not only accelerating the transfer of photogenerated electrons from CdS to ZnO, but also stabilizing the holes of CdS to improve its photocorrosion resistance. After the graft of multifunctional enzyme-mimicking Au@CuO/Cu2O label clusters, a portable dual-modular immunosensor is built for the detection of rosiglitazone, a common antidiabetic drug and strictly restricted food residual, over a range from 10−3 to 1 µg L−1. This MOF-based immunosensor offers insights into highly sensitive dual-modular responsive material innovations and provides miniaturized biomedical detectors with promising commercialization potentials.</p