# CIARkalman: Maximum Likelihood Estimation of the CIAR Model via Kalman... In iAR: Irregularly Observed Autoregressive Models

 CIARkalman R Documentation

## 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

\insertRef

Elorrieta_2019iAR

`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))
```

iAR documentation built on Nov. 25, 2022, 1:06 a.m.