# CIARinterpolation: Interpolation from CIAR model In iAR: Irregularly Observed Autoregressive Models

 CIARinterpolation R Documentation

## Interpolation from CIAR model

### Description

Interpolation of missing values from models fitted by `CIARkalman`

### Usage

```CIARinterpolation(
x,
y,
t,
delta = 0,
yini = 0,
zero.mean = TRUE,
standardized = TRUE,
c = 1,
seed = 1234
)
```

### Arguments

 `x` An array with the parameters of the CIAR model. The elements of the array are, in order, the real (phiR) and the imaginary (phiI) part of the coefficient of CIAR model. `y` Array with the time series observations. `t` Array with the irregular observational times. `delta` Array with the measurements error standard deviations. `yini` a single value, initial value for the estimation of the missing value of the time series. `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. `seed` a single value, interpreted as the seed of the random process.

### Value

A list with the following components:

• fitted Estimation of a missing value of the CIAR process.

• ll Value of the negative log likelihood evaluated in the fitted missing values.

### References

\insertRef

Elorrieta_2019iAR

`gentime`, `CIARsample`, `CIARkalman`

### 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
napos=10
y0=y1
y1[napos]=NA
xest=c(ciar\$phiR,ciar\$phiI)
yest=CIARinterpolation(xest,y=y1,t=st)
yest\$fitted
mse=(y0[napos]-yest\$fitted)^2
print(mse)
plot(st,y,type='l',xlim=c(st[napos-5],st[napos+5]))
points(st,y,pch=20)
points(st[napos],yest\$fitted*sd(y),col="red",pch=20)
```

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