Improving Time Series Stationarity Test Segmented Testing Base On Tukey

Many data in the real world are always stored in the form of time series which exists in a wide fields.By analysis and modeling the existing time series data,the future can be predicted.However,before modeling,the stationarity of a series is required to determine initially,and then a stationary time series is modeled.segmented testing is a kind of stability test of time series,in which the series divided into segments firstly and a hypothesis test is taken into consideration to judge whether the mean and covariance function are equal among this segments.When all hypotheses are set up,the original time series is considered to be station-ary.On the contrary,the sequence is regarded as non-stationary.Iorder to test the stationarity of time series,multiple hypothesis testing must be taken here.Eevry test may made the first type mistake is,and the hypothesis of the mean paragraphs and autocovariance function are equality,the probability of accumulating the first kind of mistake is more than ever.In other words,because of the randomness of the samples,the probability that the mean segments and the autocovariance function is misjudged to be not all equal will be increased.the stationarity of time series is misjudged as non-stationary probability increases,thus,the reliability of sub-section detection is reduced.In the process,the workload that the mean and covariance function are tested respectively is huge.When the variance of each segment is equal and unknown,Tukey method is proposed and applied in the classical piecewise test,in which t maximum difference statistics is constructed by comparing the mean value and self-covariance function.When the variance of each seg-ment is equal and known,the function of the extreme difference of the sample can be discussed according to the maximum and minimum order statistics so that standard normal sample size distribution can be obtained.Similarly,Tukey method is also applied in the piecewise test,in which standard normal difference statistics is also constructed by comparing the mean value and self-covariance function.When the variance of each segment is equal and known,Tukey method is applied to the piecewise test to construct a chi square statistics with a degree of freedom 1.The critical value of each case and the size of the comparative statistics and their corresponding critical values are given respectively.If it is less than the corresponding critical value,there is no significant difference between the mean value or the self-covariance function of each segment.It also means that the probability of the first class error of the subsection inspection prisoners is reduced.Therefore,it reduces the probability that the sequence is mis-judged to be non-stationary,and improves the validity of the piecewise test of time series.Classical and improved piecewise test are applied to judge the stability of a given sequence that is PM_2.5.5 series and two sets of randomly generated simulation data.The empirical test results are consistent with the analytical derivation,indicating that the improved segmentation test reduces the computation and improves the validity of the test.