ARMA Model for Random Periodic Processes_Yujia Liu.pdf (2.73 MB)

ARMA model for random periodic processes

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thesis
posted on 11.07.2019, 11:10 by Yujia Liu
In this thesis, we construct ARMA model for random periodic processes. We stress on the mixed periodicity and randomness of the model and redefined the definition of sample autocovariance function. We prove the asymptotic normality of Yule-Walker estimation and innovation estimation for coefficients in causal and invertible case. We also prove the central limit theorem for random periodic processes. Under this and ergodic theorem, we prove the asymptotic normality of maximum likelihood estimation for non-causal autoregressive model for random periodic processes. We simulate ARMA model for random
periodic processes to two examples and compare the results with classical ARMA model.

History

School

  • Science

Department

  • Mathematical Sciences

Publisher

Loughborough University

Rights holder

© Yujia Liu

Publication date

2018

Notes

A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of the degree of Doctor of Philosophy at Loughborough University.

Language

en

Supervisor(s)

Huaizhong Zhao ; Chunrong Feng

Qualification name

PhD

Qualification level

Doctoral

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