Time Series Structure Change Point Test Via Support Vector Regression And Self-Normalization Method

The generation mechanism of many actual observations can be changed by many factors such as unexpected events,leading to possible changes in the statistical characteristics of the time series one observes,i.e.,containing change points.Testing these change points can not only prevent some potential risks,but also provide a reference basis for decision making,which makes change point testing a hot research topic in many disciplines such as statistics and econometrics.In the study of time series change-point tests,the construction of the test statistic is one of the important tasks,and the commonly used test statistic usually comes with unknown long-term variance,which is more difficult to estimate consistently.The Self-Normalization(SN)method has become an important method to study the change-point test because it can avoid estimating the long-term variance.On the other hand,the accuracy of model fitting has an important impact on the efficacy of the test statistic.Compared with traditional model fitting methods,Support Vector Regression(SVR)methods are often used to fit various time series models in recent years because of the advantages of wide range of applicable models and no need for a large number of tuning parameters.In this paper,we examine the structural change points of several types of time series models based on support vector regression and self-normalization methods,and the main research contents are summarized as follows:(1)Based on support vector regression and self-normalization methods to test the structural change points in the autoregressive sliding average(ARMA)model.An ARMA(7)11(8),model is first fitted to the first k and the remaining n-k observations,respectively,then support vector regression is performed by fitting the residuals,and finally the self-normalization statistic is constructed based on the residuals obtained from support vector regression.The limiting distribution of the test statistic is derived under the null hypothesis,and the consistency of the test statistic is proved under the alternative hypothesis.The numerical simulation results show that the proposed method not only controls the empirical size well and obtains satisfactory empirical power,but also outperforms some methods in the literature in terms of test efficacy when the change point occurs in the middle of the time series.Finally,the effectiveness of the self-normalization test method based on support vector regression is illustrated by an empirical analysis of a set of annual Nile runoff data and a set of monthly log-return data of Nekki225 index.(2)The self-normalization test based on support vector regression is further extended to the long memory time series model,and the long memory time series mean change point and variance change point test problems are investigated.The numerical simulation results show that the support vector regression-based self-normalization test is also applicable to the long-memory time series model,and the test efficacy is better than some methods in the literature in most cases.Finally,the validity and feasibility of the proposed test method is verified by analyzing a set of monthly data of S&P500 index and a set of weekly data of OPEC crude oil prices.(3)A new self-normalization test statistic is proposed based on support vector regression and the self-normalization method to test the structural change points in the GARCH(Generalized Autoregressive Conditional Heteroskedastic)time series model.First,a first-order difference is performed on the original observation series,and a GARCH(1,1)model is fitted using the first-order difference data,then a support vector regression is done based on the fitted residuals,and finally a new self-normalization statistic is constructed based on the residuals obtained from the support vector regression.The limiting distribution of the test statistic is derived under the null hypothesis,and the consistency of the test statistic is proved under the alternative hypothesis.In the numerical simulation section,structural change point tests in several different GARCH models are investigated based on the proposed test method,and the results show that the new method controls the empirical size well in most cases and satisfactory empirical power can be obtained.Finally,the effectiveness of the proposed method is illustrated by an empirical analysis of a set of GS stock data.