Estimation of a Digitised Gaussian ARMA model by Monte Carlo Expectation Maximisation
- Resource Type
- Authors
- Jingsong Yuan; Hannah Lennon
- Source
- Lennon, H & Yuan, J 2019, ' Estimation of a Digitised Gaussian ARMA model by Monte Carlo Expectation Maximisation ', Computational Statistics and Data Analysis, vol. 133, pp. 277-284 . https://doi.org/10.1016/j.csda.2018.10.015
- Subject
- Statistics and Probability
Computer science
Gaussian
Monte Carlo method
01 natural sciences
010104 statistics & probability
symbols.namesake
Operator (computer programming)
0502 economics and business
Expectation–maximization algorithm
Applied mathematics
Autoregressive–moving-average model
0101 mathematics
ARMA model
EM algorithm
050205 econometrics
Series (mathematics)
Applied Mathematics
05 social sciences
Markov chain Monte Carlo
Conditional probability distribution
Monte Carlo EM
Computational Mathematics
Computational Theory and Mathematics
Gaussian copula
symbols
Integer-valued time series
Maximum likelihood
- Language
- English
Dependence modelling of integer-valued stationary time series has gained considerable interest. A generalisation of the ARMA model has been previously provided using the binomial operator and its estimation carried out using Markov Chain Monte Carlo methods. There are also various models that make use of a latent process. The time series is considered now as a digitised version of a Gaussian ARMA process, which is equivalent to assuming a Gaussian copula with ARMA dependence. Naturally this becomes an incomplete data problem and an EM algorithm can be used for maximum likelihood estimation. Due to the complexity of the conditional distribution given the observed data, a Monte Carlo E-step is implemented. Details of the MCEM algorithm are provided and standard errors of the parameter estimates are considered. Examples with real and simulated data are provided.