Package dev.nm.stat.timeseries.linear.multivariate.stationaryprocess.arma

Class Summary

Class	Description
VARFit	This class construct a VAR model by estimating the coefficients using OLS regression.
VARLinearRepresentation	The linear representation of an Autoregressive Moving Average (ARMA) model is a (truncated) infinite sum of AR terms.
VARMAAutoCorrelation	Compute the Auto-Correlation Function (ACF) for a vector AutoRegressive Moving Average (ARMA) model, assuming that \(EX_{t} = 0\).
VARMAAutoCovariance	Compute the Auto-CoVariance Function (ACVF) for a vector AutoRegressive Moving Average (ARMA) model, assuming that \(EX_{t} = 0\).
VARMAForecastOneStep	This is an implementation, adapted for an ARMA process, of the innovation algorithm, which is an efficient way of obtaining a one step least square linear predictor.
VARMAModel	A multivariate ARMA model, \(X_{t}\), takes this form. \[ X_t = \mu + \Sigma \phi_i X_{t-i} + \Sigma \theta_j \epsilon_{t-j} + \epsilon_t, \]
VARMAXModel	The VARMAX model (ARMA model with eXogenous inputs) is a generalization of the ARMA model by incorporating exogenous variables.
VARModel	This class represents a VAR model.
VARXModel	A VARX (Vector AutoRegressive model with eXogeneous inputs) model, \(X_{t}\), takes this form. \[ Y_t = \mu + \Sigma \phi_i * Y_{t-i} + \Psi * D_t + \epsilon_t \] where \(Y_{t}\), μ and \(\epsilon _{t}\) are n-dimensional vectors.
VECM	A Vector Error Correction Model (VECM(p)) has one of the following specifications: Transitory: \[ \Delta Y_t = \mu + \Pi Y_{t-1} + \sum \left ( \Gamma_i Y_{t-1} \right ) + \Psi D_t + \epsilon_t, i = 1, 2, ..., p-1 \] or Long-run: \[ \Delta Y_t = \mu + \Pi Y_{t-p} + \sum \left ( \Gamma_i Y_{t-1} \right ) + \Psi D_t + \epsilon_t, i = 1, 2, ..., p-1 \] \(Y_{t}\), μ and \(\epsilon _{t}\) are n-dimensional vectors.
VECMLongrun	The long-run Vector Error Correction Model (VECM(p)) takes this form. \[ \Delta Y_t = \mu + \Pi Y_{t-p} + \sum \left ( \Gamma_i Y_{t-1} \right ) + \Psi D_t + \epsilon_t, i = 1, 2, ..., p-1 \] \(Y_{t}\), μ and \(\epsilon _{t}\) are n-dimensional vectors.
VECMTransitory	A transitory Vector Error Correction Model (VECM(p)) takes this form. \[ \Delta Y_t = \mu + \Pi Y_{t-1} + \Sigma \left ( \Gamma_i Y_{t-1} \right ) + \Psi D_t + \epsilon_t, i = 1, 2, ..., p-1 \] \(Y_{t}\), μ and \(\epsilon _{t}\) are n-dimensional vectors.
VMAInvertibility	The inverse representation of an Autoregressive Moving Average (ARMA) model is a (truncated) infinite sum of the Moving Averages.
VMAModel	This class represents a multivariate MA model.