Since the time series data have the characteristics of a large amount of data and non-stationarity, we usually cannot obtain a satisfactory result by a single-model-based method to detect anomalies in time series data. To overcome this problem, in this paper, a combination-model-based approach is proposed by combining a similarity-measurement-based method and a model-based method for anomaly detection. First, the process of data representation is performed to generate a new data form to arrive at the purpose of reducing data volume. Furthermore, due to the anomalies being generally caused by changes in amplitude and shape, we take both the original time series data and their amplitude change data into consideration of the process of data representation to capture the shape and morphological features. Then, the results of data representation are employed to establish a model for anomaly detection. Compared with the state-of-the-art methods, experimental studies on a large number of datasets show that the proposed method can significantly improve the performance of anomaly detection with higher data anomaly resolution.
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This paper extends the quadrature method to price exotic options under jump-diffusion models. We compute the transition density of jump-extended models using convolution integrals. Furthermore, a simpler and more efficient lattice grid is introduced to implement the recursion more directly in matrix form. It can be shown that a lot of running time can be saved. At last, we apply the developed approach to the different jump-extended models to demonstrate its universality and provide a detailed comparison for the discrete path-dependent options to demonstrate its advantages in terms of speed and accuracy.