Bootstrap Test For Relevant Change In Time Series

With the in-depth research of the change point,we found that if the sample size is sufficiently large,any consistent test will detect arbitrarily small change point.Many economic,financial and other data not only have a large amount of data,but also may contain many change points of different sizes and types.Therefor,some small change point may not be important,in the case of small changes in parameters,the benefits brought by modifying the statistical analysis method may be far from enough to hedge the cost of modifying the analysis method.It means that the relevant change point in the research data has important practical significance.This paper studies the relevant mean and variance change point in several types of series based on the Bootstrap method.The main contents are as follows:First,we concentrate on the relevant mean change point detecting in heavy tailed time series.We applied a CUSUM statistic to test this problem and proposed a Bootstrap method to compute its critical values.Monte Carlo simulations indicate that the proposed test procedure can control the empirical size well and obtain satisfy empirical power.Specially,it has better empirical power performance than the available method when the relevant change point nears to the edge of time series.Finally,we illustrated our test procedure via a set of Nile River data.Second,we concentrate on the relevant variance change point detecting in time series.We constructed a SCUSUM statistic to test this problem and proposed a Bootstrap method to compute its critical values.Simulations and empirical example demonstrate the effectiveness and feasibility of our method via a set of air PM 2.5concentration data in Xining City.Finally,we conduct an empirical analysis on the log return series of the Shanghai securities composite index and compare with some existing empirical results.The results indicated that the daily fluctuation of market price has burstiness and significance.Estimating the position of all the change points is unnecessary in the relevant variance change point test.On the one hand,we determine the relevant variance change point of the data as a standard to measure the changes in market volatility that can detect the 2008 financial crisis.On the other hand,we analyze the impact of the policy and financial crisis on the Chinese securities market.Although the classic change point test can capture any subtle changes in market volatility,and can identify all possible change point location.It is too sensitive in the process of exploring market stability and it is not conducive to macro-control.