CIARkalman {iAR}

Maximum Likelihood Estimation of the CIAR Model via Kalman Recursions

Description

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

Usage

CIARkalman(
  y,
  t,
  delta = 0,
  zero.mean = TRUE,
  standardized = TRUE,
  c = 1,
  niter = 10,
  seed = 1234
)

Arguments

y

Array with the time series observations.

t

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.

c

Nuisance parameter corresponding to the variance of the imaginary part.

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 Real part of the coefficient of CIAR model (phiR).

• phiI MLE of the Imaginary part of the coefficient of the CIAR model (phiI).

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

References

Elorrieta, F, Eyheramendy, S, Palma, W (2019). “Discrete-time autoregressive model for unequally spaced time-series observations.” A&A, 627, A120. doi: 10.1051/0004-6361/201935560, https://doi.org/10.1051/0004-6361/201935560.

See Also

gentime, CIARsample, CIARphikalman

Examples

n=100
set.seed(6714)
st<-gentime(n)
x=CIARsample(n=n,phiR=0.9,phiI=0,st=st,c=1)
y=x$y
y1=y/sd(y)
ciar=CIARkalman(y=y1,t=st)
ciar
Mod(complex(real=ciar$phiR,imaginary=ciar$phiI))