The Spurious Regression Research Of Heavy-tailed Sequence In The Presence Of Structural Breaks

Because of the broad use in industry, the research of change-points have attracted much attention of researchers and also become one of the mainstreams of modern statistics since1970. An important difference between the economic cycle model and traditional Keynesian model is whether there is a persistence component of output volatility, thus persistence change-point is important for policymakers to make good decisions. Heavy-tailed with infinite variance sequences have been increasingly popular in financial time series since they have a good additive and can well describe the financial data in the peak and fat-tail characteristics. Hence, the persistence change-point is significant in both theoretical and practical applications. The innovations of the thesis are as follows:With help of modified ratio statistics, hypothesis test and estimation about changes in persistence with heavy-tailed processes are considered. The modified variance ratio statistic is designed for the case where the direction of these changes is unknown and can overcome the unreliability, viz., low power. The asymptotic limiting distribution of the test under null hypothesis is present and the consistency is also given under alternative hypothesis. The numerical simulation affirms the performance of the tests.The procedures about estimation of changes in persistence with heavy-tailed sequences are proposed. An important feature of heavy-tailed with infinite variance processes is the "outlines", and the estimated results are seriously sensitive to them. In order to overcome the default, the residual cumulative sum test is proposed to detect changes and obtain its consistency and convergence rate of estimator. The results of simulation study support the validity of methods.As the modified ratio statistic depends on the unknown heavy-tailed indexes K under the null hypothesis, the Subsampling method is adopted to detect changes in persistence. If the sample size b satisfy the general conditions, these empirical distributions of Subsampling statistics converge in probability to that of modified ratio statistics under the null hypothesis. Simulation study and real data analysis assess the performance of these tests in finite sample.