| IARloglik {iAR} | R Documentation |
Maximum Likelihood Estimation of the IAR Model
Description
Maximum Likelihood Estimation of the IAR Model.
Usage
IARloglik(y, st, delta = 0, zero.mean = TRUE, standardized = TRUE)
Arguments
y |
Array with the time series observations. |
st |
Array with the irregular observational times. |
delta |
Array with the measurements error standard deviations. |
zero.mean |
logical; if TRUE, the array y has zero mean; if FALSE, y has a mean different from zero. |
standardized |
logical; if TRUE, the array y is standardized; if FALSE, y contains the raw time series. |
Value
A list with the following components:
phi MLE of the phi parameter of the IAR model.
ll Value of the negative log likelihood evaluated in phi.
References
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311–4322. ISSN 0035-8711, doi: 10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
See Also
gentime, IARsample, arima, IARphiloglik
Examples
#Generating IAR sample
set.seed(6714)
st<-gentime(n=100)
y<-IARsample(phi=0.99,st=st,n=100)
y<-y$series
#Compute Phi
phi=IARloglik(y=y,st=st)$phi
print(phi)
#Compute the standard deviation of innovations
n=length(y)
d=c(0,diff(st))
phi1=phi**d
yhat=phi1*as.vector(c(0,y[1:(n-1)]))
plot(st,y,type='l')
lines(st,yhat,col='red')
sigma=var(y)
nu=c(sigma,sigma*(1-phi1**(2))[-1])
tau<-nu/sigma
sigmahat<-mean(c((y-yhat)**2/tau))
nuhat<-sigmahat*(1-phi1**(2))
nuhat2<-sqrt(nuhat)
#Equally spaced models
require(arfima)
fit2<-arfima(y,order=c(1,0,0))
fit<-arima(y,order=c(1,0,0),include.mean=FALSE)
syarf<-tacvfARFIMA(phi=fit2$modes[[1]]$phi,dfrac=fit2$modes[[1]]$dfrac,
sigma2=fit2$modes[[1]]$sigma,maxlag=20)[1]
syar<-fit$sigma/(1-fit$coef[1]**2)
print(sigmahat)
print(syar)
print(syarf)
carf<-fit2$modes[[1]]$sigma/syarf
car<-(1-fit$coef[1]**2)
ciar<-(1-phi1**(2))
#Compute the standard deviation of innovations (regular case)
sigma=var(y)
nuhat3=sqrt(sigma*ciar)
searf<-sqrt(sigma*carf)
sear<-sqrt(sigma*car)
#Plot the standard deviation of innovations
plot(st[-1], nuhat3[-1], t="n", axes=FALSE,xlab='Time',ylab='Standard Deviation of Innovations')
axis(1)
axis(2)
segments(x0=st[-1], y0=nuhat3[-1], y1=0, col=8)
points(st, nuhat3, pch=20, col=1, bg=1)
abline(h=sd(y),col='red',lwd=2)
abline(h=sear,col='blue',lwd=2)
abline(h=searf,col='green',lwd=2)
abline(h=mean(nuhat3[-1]),col='black',lwd=2)