Study On Change-point Detection Of Periodic Time Series Based On ARIMA Model

The time series consists of determined values measured in chronological order,in which each observation is recorded at a specific time to form a collection that is arranged in chronological order.The detection of change point of time series data can reveal important time-independent information and knowledge,and provides more effective decision-making for many data stream applications.Now it has been widely used in industry,computer engineering,video surveillance and other fields.Therefore,the detection of change point of time series is of great significance.The periodic time series is an important category of the time series.Due to the periodicity or seasonality of the periodic time series,the detection efficiency of the original change detection algorithm is not promising.Therefore,it is meaningful to develop a change detection algorithm for the periodic time series.Because the periodic time series has periodicity,it will affect the subsequent change point detection method.Therefore,we must first make period estimation method for the periodic time series.This thesis proposes a period estimation method based on dynamic time warping,which transforms the period estimation problem into the candidate segments matched to the optimization problem iteratively,and the effectiveness of the period estimation algorithm is verified on simulation experi-ments.Finally,the influence of noise on the period detection algorithm is further quantitatively analyzed.After estimating the period,we developed a change point detection algorithm for the periodic time series.The algorithm can be divided into three steps:the model of time series,anomaly measure,change point detection.Firstly,the math-ematical model is used to represent the time series state changes,and the periodic time series is mapped into a linear model.The periodic time series model based on Autoregressive Integrated Moving Average(ARIMA)is proposed,and the corresponding model parameters are used as the basis for calculating anomaly measure.Secondly,the temporal anomaly is calculated by the residual value between the predicted value and the observed time series value.Through the anomaly calculation,we can quantitatively describe the time series fluctuations.In the end,the decision-making mechanism based on the change point of martin-gale test is used to make the change point detection.The change point detection is to achieve the rejection and acceptance of the hypothesis test through Ran-domized Power Martingale and combining Doob's maximum inequality on the basis of the temporal anomaly measure.In order to verify the validity and feasibility of the algorithm,we conducted a large number of experiments,first we established three different types of simu-lation data,and performed on three evaluation indicators(recall,precision,F1).The results prove that our proposed method has a good effect.Furthermore,we conducted experiments on electrocardiogram data,climate data,and rotating machine data.Experiments on electrocardiogram climate and rotating machinery can prove the effectiveness of the proposed algorithm on the detection of change point.Finally,we analyzed and discussed the computational efficiency of the al-gorithm.The results show that the proposed framework has a good effect on the computational time and computing complexity,so this method can be applied in the real world.The research results show that the proposed change point detec-tion algorithm of periodic time series have three advantages:(1)it can update its own parameters automatically;(2)it does not require reference model and prior knowledge;(3)it can be used on real-time online detection.Finally,we summarize the content of this thesis and discuss the future work.