FitARMA: Fit ARMA/ARIMA using fast MLE algorithm
In FitARMA: Fit ARMA or ARIMA Using Fast MLE Algorithm

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

Fits an ARIMA(p,d,q) model using the algorithm given in McLeod and Zhang (2007).

1	FitARMA(z, order = c(0, 0, 0), demean = TRUE, MeanMLEQ = FALSE, pApprox = 30, MaxLag = 30)

`z`	time series
`order`	model order, c(p,d,q)
`demean`	if TRUE, mean parameter included otherwise assumed zero
`MeanMLEQ`	exact MLE for mean, ignored unless demean=TRUE
`pApprox`	order of approximation to be used
`MaxLag`	maximum number of lags for portmanteau test

See McLeod and Ying (2007).

A list with class name "FitARMA" and components:

`loglikelihood`	value of the loglikelihood
`phiHat`	AR coefficients
`thetaHat`	MA coefficients
`sigsqHat`	innovation variance estimate
`muHat`	estimate of the mean
`covHat`	covariance matrix of the coefficient estimates
`racf`	residual autocorrelations
`LjungBox`	table of Ljung-Box portmanteau test statistics
`res`	innovation residuals, same length as z
`fits`	fitted values, same length as z
`demean`	TRUE if mean estimated otherwise assumed zero
`IterationCount`	number of iterations in mean mle estimation
`convergence`	value returned by optim – should be 0
`MLEMeanQ`	TRUE if mle for mean algorithm used
`tsp`	tsp(z)
`call`	result from match.call() showing how the function was called
`ModelTitle`	description of model
`DataTitle`	returns attr(z,"title")

When d>0 and demean=TRUE, the mean of the differenced series is estimated. This corresponds to including a polynomial of degree d.

When d>0, the AIC/BIC are computed for the differenced series and so they are not comparable to the values obtained for models with d=0.

A.I. McLeod, aimcleod@uwo.ca

A.I. McLeod andY. Zhang (2008), Faster ARMA maximum likelihood estimation, Computational Statistics & Data Analysis, 52-4, 2166-2176. DOI link: http://dx.doi.org/10.1016/j.csda.2007.07.020

GetFitARMA, print.FitARMA, coef.FitARMA, residuals.FitARMA, fitted.FitARMA, arima

data(SeriesA) #in datasets()
out1<-FitARMA(SeriesA, c(1,0,1))
out1
coef(out1)
out2<-FitARMA(SeriesA, c(0,1,1))
out2
coef(out2)

Loading required package: FitAR
Loading required package: lattice
Loading required package: leaps
Loading required package: ltsa
Loading required package: bestglm
Chemical process concentrations
ARIMA(1,0,1)
length of series = 197 ,  number of parameters = 3
loglikelihood = 228.79 ,  aic = -451.6 ,  bic =  -441.7
                MLE           sd     Z-ratio
phi(1)    0.9086651   0.04260981 21.32525596
theta(1)  0.5758000   0.08343768  6.90095818
mu       17.0624365 319.55196104  0.05339487
Chemical process concentrations
ARIMA(0,1,1)
length of series = 196 ,  number of parameters = 2
loglikelihood = 224.73 ,  aic = -445.5 ,  bic =  -438.9
                 MLE         sd     Z-ratio
theta(1) 0.703101044 0.05079214 13.84271366
mu       0.002040816 0.02261138  0.09025615