Testing For Changes In Time Series Based On Local Polynomial Estimation

Most existing works on change-point analysis deal with parametric time series, and the series is usually directly observable. In practice, however, the process of inter-est is often not observable, and explicit modeling form makes it less possible to study more underlying information about the problem. Therefore, we consider change-point detection in autocovariance of time series with nonparametric trend. Local polynomi-al fitting has many exciting statistical properties, so we try to fit the trend by local polynomial estimation, and then detect changes based on this. In section 2, we intro-duce cumulative sum(CUSUM) statistic and some propositions and conclusions under the GMC condition. In section 3, we deduce formulas in local polynomial fitting of time series, and prove change-point detection theory after removing the trend, such as the functional central limit theorem, asymptotic distribution theorem, and asymptotic power 1 theorem.In simulation studies, we use local polynomial of order 0-5 to fit the trend of model with AR(1) error, and carry out simulations to detect change-point in autocovariance of the error. As for different parameters, we carry out 3000 random simulations re-spectively to calculate their size and empirical power. In addition, we use Bartlett kernel, Parzen kernel and Tukey-Hanning kernel to estimate σ2(k) respectively, which is a long variance produced during the test. Then we calculate and compare their size and power. According to power analysis, local linear regression and Bartlett kernel are suggested.