MAXIMUM LIKELIHOOD ESTIMATION OF HAWKES SELF-EXCITING POINT PROCESSES

被引：172

作者：

OZAKI, T

机构：

来源：

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS | 1979年 / 31卷 / 01期

关键词：

D O I：

10.1007/BF02480272

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

A maximum likelihood estimation procedure of Hawkes' self-exciting point process model is proposed with explicit presentations of the log-likelihood of the model and its gradient and Hessian. A simulation method of the process is also presented. Some numerical results are given. © 1979 Kluwer Academic Publishers.

引用

收藏

页码：145 / 155

页数：11

相关论文

共 13 条

[1]

DAVIDON WC, 1959, 5990 ARG NAT LAB REP

[2] A RAPIDLY CONVERGENT DESCENT METHOD FOR MINIMIZATION [J].

FLETCHER, R ;

POWELL, MJD .

COMPUTER JOURNAL, 1963, 6 (02) :163-&

[3]

HAWKES AG, 1971, J ROY STAT SOC B, V33, P438

[4] SPECTRA OF SOME SELF-EXCITING AND MUTUALLY EXCITING POINT PROCESSES [J].

HAWKES, AG .

BIOMETRIKA, 1971, 58 (01) :83-&

[5] CLUSTER PROCESS REPRESENTATION OF A SELF-EXCITING PROCESS [J].

HAWKES, AG ;

OAKES, D .

JOURNAL OF APPLIED PROBABILITY, 1974, 11 (03) :493-503

[6]

HOOKE R, 1961, J ACM, V8, P212, DOI 10.1145/321062.321069

[7] REMARKS ON THEORY, COMPUTATION AND APPLICATION OF SPECTRAL ANALYSIS OF SERIES OF EVENTS [J].

LEWIS, PAW .

JOURNAL OF SOUND AND VIBRATION, 1970, 12 (03) :353-+

[8] EFFICIENT METHOD FOR FINDING MINIMUM OF FUNCTION OF SEVERAL-VARIABLES WITHOUT CALCULATING DERIVATIVES [J].

POWELL, MJD .

COMPUTER JOURNAL, 1964, 7 (02) :155-&

[9] AN AUTOMATIC METHOD FOR FINDING THE GREATEST OR LEAST VALUE OF A FUNCTION [J].

ROSENBROCK, HH .

COMPUTER JOURNAL, 1960, 3 (03) :175-184

[10] REGULAR POINT PROCESSES AND THEIR DETECTION [J].

RUBIN, I .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1972, 18 (05) :547-+