Detection Of Outliers Based On Wavelet Analysis In Time Series

In time series,a variety of reasons often can appear abnormal data which has obvious gap of other data,these kind of data are called outliers.Generally when modeling,outliers is easy to ignore,but compared with the ordinary data,these points contain more information,for emergencies,the cause of wrong operation data,or the change of internal mechanism,these points may influence the current of value,or influence the following value,so that the model predictions produced is very difficult to earth.Therefore,identify outliers in time series can improve the correctness of the model prediction.In this paper,useing the method of wavelet analysis detection of Outliers in Time Series for single variable.First of all,the selection for Haar wavelet base of discrete wavelet transform(DWT),the time sequence of discretization,to obtain the wavelet detail coefficients and approximation coefficients.Secondly,by using Monte Carlo simulation screen out a maximum of the sequence,take the average value as a threshold.Third,in order to avoid "masking effect",finding the location which corresponding to the maximum detail coefficients,and the detail coefficient at this position is set to a suitable value,then we get a new sequence.Finally,by inverse discrete wavelet transform(IDWT)will reconstruct the residual sequence,so circulates,until all of the absolute value of wavelet detail coefficients is less than the threshold,then get the location of the collection,inspection and identify outliers.Empirical aspect,this article is based on the wavelet analysis respectively test the benchmark Shanghai composite index and shenzhen composite index closing price of outliers.Through autocorrelation and partial autocorrelation test,we know the sequence has a slow decay autocorrelation problems,this paper simulates the model of logarithmic yield residual sequence;By describing the statistical characteristic of the sequence to approximate normal distribution;Through the unit root test can be detected is smooth;According to wavelet analysis test steps to find outliers.Among them,the normal distribution of approximate obey Monte Carlo simulation of the selected threshold.Set according to the threshold and IDWT position,use the location of the abnormal value of the collection of positions,to analyze its causes.Finally,through the comparative analysis of the Shanghai composite index and shenzhen composite index test results,further verify the feasibility of test method of this paper.