iAR (version 1.3.2)

interpolation: Interpolation for iAR, CiAR, and BiAR Classes

Description

This method performs imputation of missing values in a time series using an autoregressive model. The imputation is done iteratively for each missing value, utilizing available data and model coefficients. Depending on the model family, the interpolation is performed differently: - For norm: A standard autoregressive model for normally distributed data. - For t: A model for time series with t-distributed errors. - For gamma: A model for time series with gamma-distributed errors. - For CiAR: A complex irregular autoregressive model. - For BiAR: A bivariate autoregressive model.

Usage

interpolation(x, ...)

Value

An object of the same class as x with interpolated time series.

Arguments

x

An object of class iAR, CiAR, or BiAR, containing the model specification and parameters:

• For iAR:

  • family: The distribution family of the iAR model (one of "norm", "t", or "gamma").

  • series: A numeric vector representing the time series to interpolate.

  • coef: The coefficients of the iAR model.

  • zero_mean: Logical, whether the model assumes a zero-mean series.

  • standardized: Logical, whether the model uses standardized data (only for "norm" family).

  • mean: The mean parameter (only for "gamma" family).

• For CiAR:

  • coef: The coefficients of the CiAR model.

  • series_esd: The series of error standard deviations for the CiAR model.

  • zero_mean: Logical, whether the model assumes a zero-mean series.

  • standardized: Logical, whether the model uses standardized data.

  • seed: Optional seed for random number generation.

• For BiAR:

  • coef: The coefficients of the BiAR model.

  • series_esd: The series of error standard deviations for the BiAR model.

  • zero_mean: Logical, whether the model assumes a zero-mean series.

  • yini1: Initial value for the first time series (for BiAR models).

  • yini2: Initial value for the second time series (for BiAR models).

  • seed: Optional seed for random number generation.

...

Additional arguments (unused).

Details

Performs interpolation on time series with missing values. This method is implemented for: 1. Irregular Autoregressive models (iAR) 2. Complex Irregular Autoregressive models (CiAR) 3. Bivariate Autoregressive models (BiAR)

The method handles missing values (NA) in the time series by imputing them iteratively. For each missing value, the available data is used to fit the autoregressive model, and the missing value is imputed based on the model's output. For the CiAR and BiAR models, the error standard deviations and initial values are also considered during imputation.

References

Eyheramendy_2018iAR,Elorrieta_2019iAR,Elorrieta_2021iAR

See Also

forecast for forecasting methods for these models.

Examples

# Interpolation for iAR model
library(iAR)
n=100
set.seed(6714)
o=iAR::utilities()
o<-gentime(o, n=n)
times=o@times
model_norm <- iAR(family = "norm", times = times, coef = 0.9)  
model_norm <- sim(model_norm)
y=model_norm@series
y1=y/sd(y)
model_norm@series=y1
model_norm@series_esd=rep(0,n)
model_norm <- kalman(model_norm) 
print(model_norm@coef)
napos=10
model_norm@series[napos]=NA
model_norm <- interpolation(model_norm)
interpolation=na.omit(model_norm@interpolated_values)
mse=as.numeric(y1[napos]-interpolation)^2
print(mse)
plot(times,y,type='l',xlim=c(times[napos-5],times[napos+5]))
points(times,y,pch=20)
points(times[napos],interpolation*sd(y),col="red",pch=20)

# Interpolation for CiAR model
model_CiAR <- CiAR(times = times,coef = c(0.9, 0))
model_CiAR <- sim(model_CiAR)
y=model_CiAR@series
y1=y/sd(y)
model_CiAR@series=y1
model_CiAR@series_esd=rep(0,n)
model_CiAR <- kalman(model_CiAR)
print(model_CiAR@coef)
napos=10
model_CiAR@series[napos]=NA
model_CiAR <- interpolation(model_CiAR)
interpolation=na.omit(model_CiAR@interpolated_values)
mse=as.numeric(y1[napos]-interpolation)^2
print(mse)
plot(times,y,type='l',xlim=c(times[napos-5],times[napos+5]))
points(times,y,pch=20)
points(times[napos],interpolation*sd(y),col="red",pch=20)
# Interpolation for BiAR model
model_BiAR <- BiAR(times = times,coef = c(0.9, 0.3), rho = 0.9)
model_BiAR <- sim(model_BiAR)
y=model_BiAR@series
y1=y/apply(y,2,sd)
model_BiAR@series=y1
model_BiAR@series_esd=matrix(0,n,2)
model_BiAR <- kalman(model_BiAR)
print(model_BiAR@coef) 
napos=10
model_BiAR@series[napos,1]=NA
model_BiAR@series_esd[napos,1]=NA
model_BiAR <- interpolation(model_BiAR)
interpolation=na.omit(model_BiAR@interpolated_values[,1])
mse=as.numeric(y1[napos,1]-interpolation)^2
print(mse)
par(mfrow=c(2,1))
plot(times,y[,1],type='l',xlim=c(times[napos-5],times[napos+5]))
points(times,y[,1],pch=20)
points(times[napos],interpolation*apply(y,1,sd)[1],col="red",pch=20)
plot(times,y[,2],type='l',xlim=c(times[napos-5],times[napos+5]))
points(times,y[,2],pch=20)