FitAR {FitAR}R Documentation

Fit AR, ARp and ARz

Description

Exact MLE for full AR as well as subset AR. Both subset ARp and subset ARz models are implemented. For subset ARp models the R function arima is used. For full AR and subset ARz models, algorithm of McLeod & Zhang (2006) is implemented. The LS algorithm for subset ARp is also available as an option.

Usage

FitAR(z, p, lag.max = "default", ARModel = "ARz", ...)

Arguments

z time series, vector or ts object.
p p specifies the model. If length(p) is 1, an AR(p) is assumed and if p has length greater than 1, a subset ARp or ARz is assumed - the default is ARz. For example, to fit a subset model with lags 1 and 4 present, set p to c(1,4) or equivalently c(1,0,0,4). To fit a subset model with just lag 4, you must use p=c(0,0,0,4) since p=4 will fit a full AR(4).
lag.max the residual autocorrelations are tabulated for lags 1, ..., lag.max. Also lag.max is used for the Ljung-Box portmanteau test.
ARModel which subset model, ARz or ARp
... optional arguments which are passed to FitARz or FitARp

Details

The exact MLE for AR(p) and subset ARz use methods described in McLeod and Zhang (2006). In addition the exact MLE for the mean can be computed using an iterative backfitting approach described in McLeod and Zhang (2008).

The subset ARp model can be fit by exact MLE using the R function arima or by least-squares.

The default for lag.max is min(300, ceiling(length(z)/5))

Value

A list with class name "FitAR" and components:

loglikelihood value of the loglikelihood
phiHat coefficients in AR(p) – including 0's
sigsqHat innovation variance estimate
muHat estimate of the mean
covHat covariance matrix of the coefficient estimates
zetaHat transformed parameters, length(zetaHat) = # coefficients estimated
RacfMatrix residual autocorrelations and sd for lags 1, ..., lag.max
LjungBox table of Ljung-Box portmanteau test statistics
SubsetQ parameters in AR(p) – including 0's
res innovation residuals, same length as z
fits fitted values, same length as z
pvec lags used in AR model
demean TRUE if mean estimated otherwise assumed zero
FitMethod "MLE" or "LS"
IterationCount number of iterations in mean mle estimation
convergence value returned by optim – should be 0
MLEMeanQ TRUE if mle for mean algorithm used
ARModel "ARp" if FitARp used, otherwise "ARz"
tsp tsp(z)
call result from match.call() showing how the function was called
ModelTitle description of model
DataTitle returns attr(z,"title")
z time series data input

Note

There are generic print, summary, coef and resid functions for class "FitAR".

Author(s)

A.I. McLeod

References

McLeod, A.I. and Zhang, Y. (2006). Partial Autocorrelation Parameterization for Subset Autoregression. Journal of Time Series Analysis, 27, 599-612.

McLeod, A.I. and Zhang, Y. (2008a). Faster ARMA Maximum Likelihood Estimation, Computational Statistics and Data Analysis, 52-4, 2166-2176. DOI link: http://dx.doi.org/10.1016/j.csda.2007.07.020.

McLeod, A.I. and Zhang, Y. (2008b, Submitted). Improved Subset Autoregression: With R Package. Journal of Statistical Software.

See Also

FitARp, FitARz, GetFitARz, FitARp, GetFitARpMLE, RacfPlot

Examples

#First example: fit exact MLE to AR(4) 
set.seed(3323)
phi<-c(2.7607,-3.8106,2.6535,-0.9238)
z<-SimulateGaussianAR(phi,1000)
ans<-FitAR(z,4,MeanMLEQ=TRUE)
ans
coef(ans)

#Second example: compare with sample mean result
ans<-FitAR(z,4)
coef(ans)

#Third example: fit subset ARz and ARp models
z<-log(lynx)
FitAR(z, c(1,2,4,7,10,11))
#now obtain exact MLE for Mean as well
FitAR(z, c(1,2,4,7,10,11), MeanMLE=TRUE)
#subset ARp using exact MLE
FitAR(z, c(1,2,4,7,10,11), ARModel="ARp", MLEQ=TRUE)
#subset ARp using LS
FitAR(z, c(1,2,4,7,10,11), ARModel="ARp", MLEQ=FALSE)
#or
FitAR(z, c(1,2,4,7,10,11), ARModel="ARp")

#Fourth example: use UBIC model selection to fit subset models
z<-log(lynx)
#ARz case
p<-SelectModel(z,ARModel="ARz")[[1]]$p
ans1<-FitAR(z, p)
ans1
ans1$ARModel

#ARp case
p<-SelectModel(z,ARModel="ARp")[[1]]$p
ans2<-FitAR(z, p, ARModel="ARp")
ans2
ans2$ARModel

#Fifth example: fit a full AR(p) using AIC/BIC methods
z<-log(lynx)
#BIC
p<-SelectModel(z,ARModel="AR")[1,1]
ans1<-FitAR(z, p)
ans1
#AIC
p<-SelectModel(z, ARModel="AR", Criterion="AIC")[1,1]
ans2<-FitAR(z, p)
ans2

[Package FitAR version 1.74 Index]