# BIARinterpolation: Interpolation from BIAR model In iAR: Irregularly Observed Autoregressive Models

 BIARinterpolation R Documentation

## Interpolation from BIAR model

### Description

Interpolation of missing values from models fitted by `BIARkalman`

### Usage

```BIARinterpolation(
x,
y1,
y2,
t,
delta1 = 0,
delta2 = 0,
yini1 = 0,
yini2 = 0,
zero.mean = TRUE,
niter = 10,
seed = 1234,
nsmooth = 1
)
```

### Arguments

 `x` An array with the parameters of the BIAR model. The elements of the array are, in order, the real (phiR) and the imaginary (phiI) part of the coefficient of BIAR model. `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. `yini1` a single value, initial value of the estimation of the missing value of the first time series of the BIAR process. `yini2` a single value, initial value of the estimation of the missing value 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. `nsmooth` a single value; If 1, only one time series of the BIAR process has a missing value. If 2, both time series of the BIAR process have a missing value.

### Value

A list with the following components:

• fitted Estimation of the missing values of the BIAR process.

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

### References

\insertRef

Elorrieta_2021iAR

`gentime`, `BIARsample`, `BIARphikalman`

### Examples

```
set.seed(6713)
n=100
st<-gentime(n)
x=BIARsample(n=n,phiR=0.9,phiI=0.3,st=st,rho=0.9)
y=x\$y
y1=y/apply(y,1,sd)
yerr1=rep(0,n)
yerr2=rep(0,n)
biar=BIARkalman(y1=y1[1,],y2=y1[2,],t=st,delta1 = yerr1,delta2=yerr2)
biar
napos=10
y0=y1
y1[1,napos]=NA
xest=c(biar\$phiR,biar\$phiI)
yest=BIARinterpolation(xest,y1=y1[1,],y2=y1[2,],t=st,delta1=yerr1,
delta2=yerr2,nsmooth=1)
yest\$fitted
mse=(y0[1,napos]-yest\$fitted)^2
print(mse)
par(mfrow=c(2,1))
plot(st,x\$y[1,],type='l',xlim=c(st[napos-5],st[napos+5]))
points(st,x\$y[1,],pch=20)
points(st[napos],yest\$fitted*apply(y,1,sd)[1],col="red",pch=20)
plot(st,x\$y[2,],type='l',xlim=c(st[napos-5],st[napos+5]))
points(st,x\$y[2,],pch=20)

```

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