# Fitted Values for iAR, CiAR, and BiAR Classes 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`) ```r fit(x, ...) ``` ## 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). ## Returns An updated object of class `iAR`, `CiAR`, or `BiAR`, where the `fitted_values` property contains the fitted time series values. ## 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. ## Examples ```r # 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 ``` ## References \insertRef Eyheramendy_2018iAR,\insertRef Elorrieta_2019iAR,\insertRef Elorrieta_2021iAR

fit function