MCEM: Monte Carlo EM algorithm
In hlennon/copulaIVTS: Dependence modelling of a digitised Gaussian ARMA(p,q) copula model for Integer-Valued Time Series

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Use: Computes the MLEs of the Gaussian copula model using the Monte Carlo EM algorithm

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MCEM(obs.data, Monte_Carlo_samples, p, q, initial,  num_iterations,
                prec=0.01,  marginal_dist="negbin",
                optim_method="nmkb", compute_stderrors=TRUE)

`obs.data`	Observed Data
`Monte_Carlo_samples`	The number of Monte Carlo samples, m, to approximate the conditional expectation, if m is a vector it repeats num_iterations with each numbr in the vector
`p`	order of the ar parameters in ARMA(p,q)
`q`	order of the ma parameters in ARMA(p,q)
`initial`	initial parameter values for the EM algorithm
`prec`	precision for stopping criteria
`num_iterations`	Number of iterations
`marginal_dist`	Marginal distributions
`optim_method`	Default is "nmkb" from the R package dfoptim, however "CG", "BFGS" or "nlm" can be used. optimx() from the optimx R package suggests all 4 can be used but in practice only "L-BFGS-B" have provided a good optimisation routine
`compute_stderrors`	TRUE or FALSE

Default is "L-BFGS-B", however "CG", "BFGS" or "nlm" can be used. optimx() from the optimx R package suggests all 4 can be used but in practice only "L-BFGS-B" have provided a good optimisation routine.

There are two types of optimisation: function minimisation and mathematical programming. Most optimisers in R are function minimisers. method="L-BFGS-B" is the method of Bryd et al. (1995) which is a modification of BFGS quasi-newton method. "Dela_lx" for change in log-likelihood of observed data, as following Chen and Ledolter (1995)

Iterations for the MCEM algorithm which converge to the MLE estimates of the ARMA(1,1) parameters

Produces pdf plots

Hannah Lennon <drhannahlennon@gmail.com>

Lennon H., & Yuan J., Estimation of a digitised Gaussian ARMA model by Monte Carlo Expectation Maximisation, Computational Statistics & Data Analysis 2018;8:e020683

Lennon, H., 2016. Gaussian copula modelling for integer-valued time series (Doctoral Thesis, University of Manchester).

First and Second Year Transfer Reports

library(numDeriv)
library(MASS)
library(VGAM)
library(dfoptim)
library(polynom)
library(dfoptim)
ls()

set.seed(1)
obs.data <- generate_data(10, 0.2, 0.1, "nbinom", c(3, 0.4))$x