FitAR (version 1.94)

FitAR: 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

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

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))

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)

## Not run:  #save time building package!
# #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
# ## End(Not run)

#Sixth Example: Subset autoregression depends on lag.max!
#Because least-squares is used, P=lag.max observations are
#  are deleted. This causes different results depending on lag.max.
#This phenomenon does not happen with "ARz" subset models
#ARp models depend on lag.max
SelectModel(z,lag.max=15,ARModel="ARp", Criterion="BIC", Best=1)
SelectModel(z,lag.max=20,ARModel="ARp", Criterion="BIC", Best=1)
#ARz models do NOT depend in this way on lag.max.
#Obviously if some lags beyond the initial value of lag.max are
# found to be important, then there is a dependence but this
# is not a problem!
SelectModel(z,lag.max=15,ARModel="ARz", Criterion="BIC", Best=1)
SelectModel(z,lag.max=20,ARModel="ARz", Criterion="BIC", Best=1)