Class VARIMAXModel
- java.lang.Object
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- dev.nm.stat.timeseries.linear.multivariate.arima.VARIMAXModel
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- Direct Known Subclasses:
VARIMAModel,VARMAXModel
public class VARIMAXModel extends Object
The ARIMAX model (ARIMA model with eXogenous inputs) is a generalization of the ARIMA model by incorporating exogenous variables. Letting L be the lag operator, the d-th difference of a multivariate ARIMAX(p, d, q) process Yt is \[ X_t = (1 - L)^d Y_t \] where Xt is an ARMAX(p, q) process, for which \[ X_t = \mu + \Sigma \phi_i X_{t-i} + \Sigma \theta_j \epsilon_{t-j} + \psi' D_t + \epsilon_t, \] Xt, μ and εt are n-dimensional vectors. The (n * n) matrices \({\phi_i}\) and \({\theta_j}\) are the AR and MA coefficients respectively. Dt is an (m * 1) vector which contains all exogenous variables at time t (excluding the intercept term), and its coefficients are represented by an (n * m) matrix ψ.
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Constructor Summary
Constructors Constructor Description VARIMAXModel(Matrix[] phi, int d, Matrix[] theta, Matrix psi)Construct a multivariate ARIMAX model with unit variance and zero-intercept (mu).VARIMAXModel(Matrix[] phi, int d, Matrix[] theta, Matrix psi, Matrix sigma)Construct a multivariate ARIMAX model with zero-intercept (mu).VARIMAXModel(Vector mu, Matrix[] phi, int d, Matrix[] theta, Matrix psi)Construct a multivariate ARIMAX model with unit variance.VARIMAXModel(Vector mu, Matrix[] phi, int d, Matrix[] theta, Matrix psi, Matrix sigma)Construct a multivariate ARIMAX model.VARIMAXModel(VARIMAXModel that)Copy constructor.VARIMAXModel(ARIMAXModel model)Construct a multivariate ARIMAX model from a univariate ARIMAX model.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description ImmutableMatrixAR(int i)Get the i-th AR coefficient; AR(0) = 1.intd()Get the order of integration.intdimension()Get the dimension of multivariate time series.VARMAXModelgetVARMAX()Get the ARMAX part of this ARIMAX model, essentially ignoring the differencing.ImmutableMatrixMA(int i)Get the i-th MA coefficient; MA(0) = 1.intmaxPQ()Get the maximum of AR length or MA length.ImmutableVectormu()Get the intercept (constant) vector.intp()Get the number of AR terms.ImmutableMatrix[]phi()Get all the AR coefficients.ImmutableMatrixpsi()Get the coefficients of the deterministic terms.intq()Get the number of MA terms.ImmutableMatrixsigma()Get the white noise covariance matrix.ImmutableMatrix[]theta()Get all the MA coefficients.
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Constructor Detail
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VARIMAXModel
public VARIMAXModel(Vector mu, Matrix[] phi, int d, Matrix[] theta, Matrix psi, Matrix sigma)
Construct a multivariate ARIMAX model.- Parameters:
mu- the intercept (constant) vectorphi- the AR coefficients (excluding the initial 1);nullif no AR coefficientd- the order of integrationtheta- the MA coefficients (excluding the initial 1);nullif no MA coefficientpsi- the coefficients of the deterministic terms (excluding the intercept term)sigma- the white noise covariance matrix
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VARIMAXModel
public VARIMAXModel(Vector mu, Matrix[] phi, int d, Matrix[] theta, Matrix psi)
Construct a multivariate ARIMAX model with unit variance.- Parameters:
mu- the intercept (constant) vectorphi- the AR coefficients (excluding the initial 1);nullif no AR coefficientd- the order of integrationtheta- the MA coefficients (excluding the initial 1);nullif no MA coefficientpsi- the coefficients of the deterministic terms (excluding the intercept term)
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VARIMAXModel
public VARIMAXModel(Matrix[] phi, int d, Matrix[] theta, Matrix psi, Matrix sigma)
Construct a multivariate ARIMAX model with zero-intercept (mu).- Parameters:
phi- the AR coefficients (excluding the initial 1);nullif no AR coefficientd- the order of integrationtheta- the MA coefficients (excluding the initial 1);nullif no MA coefficientpsi- the coefficients of the deterministic terms (excluding the intercept term)sigma- the white noise covariance matrix
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VARIMAXModel
public VARIMAXModel(Matrix[] phi, int d, Matrix[] theta, Matrix psi)
Construct a multivariate ARIMAX model with unit variance and zero-intercept (mu).- Parameters:
phi- the AR coefficients (excluding the initial 1);nullif no AR coefficientd- the order of integrationtheta- the MA coefficients (excluding the initial 1);nullif no MA coefficientpsi- the coefficients of the deterministic terms (excluding the intercept term)
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VARIMAXModel
public VARIMAXModel(VARIMAXModel that)
Copy constructor.- Parameters:
that- a multivariate ARIMAX model
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VARIMAXModel
public VARIMAXModel(ARIMAXModel model)
Construct a multivariate ARIMAX model from a univariate ARIMAX model.- Parameters:
model- a univariate ARIMAX model
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Method Detail
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mu
public ImmutableVector mu()
Get the intercept (constant) vector.- Returns:
- the intercept (constant) vector
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AR
public ImmutableMatrix AR(int i)
Get the i-th AR coefficient; AR(0) = 1.- Parameters:
i- an index- Returns:
- the i-th AR coefficient
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phi
public ImmutableMatrix[] phi()
Get all the AR coefficients.- Returns:
- all the AR coefficients
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MA
public ImmutableMatrix MA(int i)
Get the i-th MA coefficient; MA(0) = 1.- Parameters:
i- an index- Returns:
- the i-th MA coefficient
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theta
public ImmutableMatrix[] theta()
Get all the MA coefficients.- Returns:
- all the MA coefficients
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psi
public ImmutableMatrix psi()
Get the coefficients of the deterministic terms.- Returns:
- the coefficients of the deterministic terms; could be
null
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d
public int d()
Get the order of integration.- Returns:
- the order of integration
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dimension
public int dimension()
Get the dimension of multivariate time series.- Returns:
- the dimension of multivariate time series
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p
public int p()
Get the number of AR terms.- Returns:
- the number of AR terms
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q
public int q()
Get the number of MA terms.- Returns:
- the number of MA terms
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maxPQ
public int maxPQ()
Get the maximum of AR length or MA length.- Returns:
- max(# AR terms, # MA terms)
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sigma
public ImmutableMatrix sigma()
Get the white noise covariance matrix.- Returns:
- the white noise covariance matrix
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getVARMAX
public VARMAXModel getVARMAX()
Get the ARMAX part of this ARIMAX model, essentially ignoring the differencing.- Returns:
- the ARMAX part
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