ARMA model for random periodic processes
thesisposted on 11.07.2019 by Yujia Liu
In order to distinguish essays and pre-prints from academic theses, we have a separate category. These are often much longer text based documents than a paper.
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.
- Mathematical Sciences