BIARkalman {iAR}

Maximum Likelihood Estimation of the BIAR Model via Kalman Recursions

Description

Maximum Likelihood Estimation of the BIAR model parameters phiR and phiI. The estimation procedure uses the Kalman Filter to find the maximum of the likelihood.

Usage

BIARkalman(
  y1,
  y2,
  t,
  delta1 = 0,
  delta2 = 0,
  zero.mean = "TRUE",
  niter = 10,
  seed = 1234
)

Arguments

y1

Array with the observations of the first time series of the BIAR process.

y2

Array with the observations of the second time series of the BIAR process.

t

Array with the irregular observational times.

delta1

Array with the measurements error standard deviations of the first time series of the BIAR process.

delta2

Array with the measurements error standard deviations of the second time series of the BIAR process.

zero.mean

logical; if true, the array y has zero mean; if false, y has a mean different from zero.

niter

Number of iterations in which the function nlminb will be repeated.

seed

a single value, interpreted as the seed of the random process.

Value

A list with the following components:

• phiR MLE of the autocorrelation coefficient of BIAR model (phiR).

• phiI MLE of the cross-correlation coefficient of the BIAR model (phiI).

• ll Value of the negative log likelihood evaluated in phiR and phiI.

References

Elorrieta F, Eyheramendy S, Palma W, Ojeda C (2021). “A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series.” Monthly Notices of the Royal Astronomical Society, 505(1), 1105–1116. ISSN 0035-8711, doi: 10.1093/mnras/stab1216, https://academic.oup.com/mnras/article-pdf/505/1/1105/38391762/stab1216.pdf.

See Also

gentime, BIARsample, BIARphikalman

Examples

n=80
set.seed(6714)
st<-gentime(n)
x=BIARsample(n=n,phiR=0.9,phiI=0,st=st,rho=0)
y=x$y
y1=y/apply(y,1,sd)
biar=BIARkalman(y1=y1[1,],y2=y1[2,],t=st,delta1 = rep(0,length(y[1,])),
delta2=rep(0,length(y[1,])))
biar