# Forecast for iAR, CiAR, and BiAR Classes Generates forecasts for the specified time series model. This method is implemented for: 1. Irregular Autoregressive models (`iAR`) 2. Complex Irregular Autoregressive models (`CiAR`) 3. Bivariate Autoregressive models (`BiAR`) ```r forecast(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 forecast. * `coef`: The coefficient(s) 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). * `tAhead`: Integer, the number of steps ahead to forecast. * For `CiAR`: * `coef`: The real and imaginary parts of the CiAR model's coefficients. * `series`: A numeric vector representing the time series to forecast. * `times`: A numeric vector specifying the time points of the series. * `zero_mean`: Logical, whether the model assumes a zero-mean series. * `standardized`: Logical, whether the model output should be standardized. * `tAhead`: Integer, the number of steps ahead to forecast. * 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 forecast. * `times`: A numeric vector specifying the time points of the series. * `tAhead`: Integer, the number of steps ahead to forecast. - `...`: Additional arguments (unused). ## Returns An updated object of class `iAR`, `CiAR`, or `BiAR`, where the `forecast` property contains the forecasted values. ## Details This method generates forecasts for the specified time series model. 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 generates forecasts for a bivariate autoregressive process. All required parameters (e.g., coefficients, time points) must be set before calling this method. ## Examples ```r # Example 1: Forecasting with 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@tAhead=1.3 model_norm <- forecast(model_norm) plot(times, model_norm@series, type = "l", main = "Original Series with Forecast") points(max(times)+ model_norm@tAhead, model_norm@forecast, col = "blue", pch = 16) plot_forecast(model_norm) # Example 2: Forecasting with 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@tAhead=1.3 model_CiAR <-forecast(model_CiAR) model_CiAR@forecast # Example 3: Forecasting with 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@tAhead=1.3 model_BiAR <-forecast(model_BiAR) model_BiAR@forecast ``` ## References \insertRef Eyheramendy_2018iAR,\insertRef Elorrieta_2019iAR,\insertRef Elorrieta_2021iAR

forecast function