iAR (version 1.3.2)

fit: Fitted Values for iAR, CiAR, and BiAR Classes

Description

Fitted Values for the provided data. This method is implemented for: 1. Irregular Autoregressive models (`iAR`) 2. Complex Irregular Autoregressive models (`CiAR`) 3. Bivariate Autoregressive models (`BiAR`)

Usage

fit(x, ...)

Value

An updated object of class iAR, CiAR, or BiAR, where the fitted_values property contains the fitted time series values.

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 be fitted.

  • coef: The coefficient(s) of the iAR model.

  • times: A numeric vector specifying the time points of the series.

  • zero_mean: Logical, whether to fit a zero-mean model.

  • standardized: Logical, whether the model output should be standardized (for "norm" family).

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

• For CiAR:

  • coef: The real and imaginary parts of the CiAR model's coefficients.

  • series: A numeric vector representing the time series to be fitted.

  • times: A numeric vector specifying the time points of the series.

  • zero_mean: Logical, whether to fit a zero-mean model.

  • standardized: Logical, whether the model output should be standardized.

  • c: A scaling parameter for the CiAR model.

• For BiAR:

  • coef: The coefficients of the BiAR model (real and imaginary parts).

  • series: A numeric matrix with two columns representing the bivariate time series to be fitted.

  • times: A numeric vector specifying the time points of the series.

  • series_esd: A numeric matrix for the error structure (optional, used internally).

  • zero_mean: Logical, whether to fit a zero-mean model.

...

Additional arguments (unused).

Details

This method fits the specified time series model to the data contained in the object. Depending on the class of the input object:

• For iAR, the function supports three distribution families:

• "norm" for normal distribution.

• "t" for t-distribution.

• "gamma" for gamma distribution.

• For CiAR, the function uses complex autoregressive processes.

• For BiAR, the function fits a bivariate autoregressive process.

All required parameters (e.g., coefficients, time points) must be set before calling this method.

References

Eyheramendy_2018iAR,Elorrieta_2019iAR,Elorrieta_2021iAR

Examples

# Example 1: Fitting a normal 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)
model_norm <- kalman(model_norm) 
model_norm <- fit(model_norm)
plot(model_norm@times, model_norm@series, type = "l", main = "Original Series")
lines(model_norm@times, model_norm@fitted_values, col = "red", lwd = 2)
plot_fit(model_norm)

# Example 2: Fitting a CiAR model
set.seed(6714)
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)
model_CiAR <- fit(model_CiAR)
yhat=model_CiAR@fitted_values

# Example 3: Fitting a BiAR model
n=80
set.seed(6714)
o=iAR::utilities()
o<-gentime(o, n=n)
times=o@times
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) 
model_BiAR <- fit(model_BiAR)
print(model_BiAR@rho)
yhat=model_BiAR@fitted_values