The Multiple Change Points Estimation And Multiple Outlier Detection Of Bilinear Time Series Model

The research on bilinear model gets an increasing importance in the field of time series analysis, which is based on the fact that the bilinear model can fit many nonlinear phenomena well in reality. The change point estimation and outlier detec-tion are two main research problems among the research of bilinear model. In this paper, Bayesian method and wavelet method are used to detect the bilinear model with multiple change points and different types of outliers (single outlier and patches of outliers).Firstly, the Bayesian method is used to solve the change point estimation prob-lem and outlier detection problem in the bilinear time series model. For the change point estimation problem, we treat all of the change points as random variables, and use the Bayesian approach to estimate the change points based on the results of previous studies; For the outlier detection problem, in this paper, the standard Gibbs sampling is used to detect the single outlier and the adaptive Gibbs sampling is used to detect the patches of outliers. Secondly, in view of the same problem, this paper proposes a new method based on wavelet transformation to detect the change points and outliers of the bilinear model. On the one hand, for the change point estimation problem, we carry on the multi-scale wavelet decomposition to the sequence, each scale equivalent to a layer, and we find multiple change points in each layer, then map them to the original sequence, and get the estimation of the change point; on the other hand, for the outlier point detection problem, this paper applies the method of Wavelet Transform Modulus Maximum to detect the outlier of the sequence based on the theory of Wavelet Transform Modulus Maximum.Finally, the feasibility of the two detection methods is validated by the simula-tion example. By comparing the methods of Bayesian and wavelet transformation, the following conclusions are found in this paper:The Bayesian method is more ac-curate and can get the effect size of outlier; The running time of the wavelet method is much less than that of the Bayesian method on the basis of satisfying the accuracy.