厚尾相依序列持久性變點(diǎn)的統(tǒng)計(jì)推斷

1、 Subject: Subject: Subject: Subject: The The The The spurious spurious spurious spurious regression regression regression regression research research research research of of of of heavy-tailed heavy-tailed heavy-tailed

2、 heavy-tailed sequence sequence sequence sequence in in in in the the the thepresence presence presence presence of of of of structural structural structural structural breaks breaks breaks breaksSpecialty: Specialty: Sp

3、ecialty: Specialty: Applied Applied Applied Applied Mathematics Mathematics Mathematics MathematicsName: Name: Name: Name: Zhang Zhang Zhang Zhang Si Si Si Si (Signature) (Signature) (Signature) (Signature)Instructor: In

4、structor: Instructor: Instructor: Qiao Qiao Qiao Qiao Baoming Baoming Baoming Baoming (Signature) (Signature) (Signature) (Signature)Jin Jin Jin Jin Hao Hao Hao Hao (Signature) (Signature) (Signature) (Signature)ABSTRACT

5、 ABSTRACT ABSTRACT ABSTRACTBecause of the broad use in industry, the research of change-points have attracted muchattention of researchers and also become one of the mainstreams of modern statistics since1970. An importa

6、nt difference between the economic cycle model and traditional Keynesianmodel is whether there is a persistence component of output volatility, thus persistencechange-point is important for policymakers to make good deci

7、sions. Heavy-tailed withinfinite variance sequences have been increasingly popular in financial time series since theyhave a good additive and can well describe the financial data in the peak and fat-tailcharacteristics.

8、 Hence, the persistence change-point is significant in both theoretical andpractical applications. The innovations of the thesis are as follows:With help of modified ratio statistics, hypothesis test and estimation about

9、 changes inpersistence with heavy-tailed processes are considered. The modified variance ratio statistic isdesigned for the case where the direction of these changes is unknown and can overcome theunreliability, viz., lo

10、w power. The asymptotic limiting distribution of the test under nullhypothesis is present and the consistency is also given under alternative hypothesis. Thenumerical simulation affirms the performance of the tests.The p

11、rocedures about estimation of changes in persistence with heavy-tailed sequencesare proposed. An important feature of heavy-tailed with infinite variance processes is the“outlines”, and the estimated results are seriousl

12、y sensitive to them. In order to overcome thedefault, the residual cumulative sum test is proposed to detect changes and obtain itsconsistency and convergence rate of estimator. The results of simulation study support th