Package dev.nm.stat.timeseries.linear.multivariate.arima

Class VARIMAXModel

java.lang.Object

dev.nm.stat.timeseries.linear.multivariate.arima.VARIMAXModel

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 Y_t is \[ X_t = (1 - L)^d Y_t \] where X_t is an ARMAX(p, q) process, for which \[ X_t = \mu + \Sigma \phi_i X_{t-i} + \Sigma \theta_j \epsilon_{t-j} + \psi' D_t + \epsilon_t, \] X_t, μ and ε_t are n-dimensional vectors. The (n * n) matrices \({\phi_i}\) and \({\theta_j}\) are the AR and MA coefficients respectively. D_t 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.

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.

Method Summary

Modifier and Type	Method	Description
ImmutableMatrix	AR(int i)	Get the i-th AR coefficient; AR(0) = 1.
int	d()	Get the order of integration.
int	dimension()	Get the dimension of multivariate time series.
VARMAXModel	getVARMAX()	Get the ARMAX part of this ARIMAX model, essentially ignoring the differencing.
ImmutableMatrix	MA(int i)	Get the i-th MA coefficient; MA(0) = 1.
int	maxPQ()	Get the maximum of AR length or MA length.
ImmutableVector	mu()	Get the intercept (constant) vector.
int	p()	Get the number of AR terms.
ImmutableMatrix[]	phi()	Get all the AR coefficients.
ImmutableMatrix	psi()	Get the coefficients of the deterministic terms.
int	q()	Get the number of MA terms.
ImmutableMatrix	sigma()	Get the white noise covariance matrix.
ImmutableMatrix[]	theta()	Get all the MA coefficients.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

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) vector

phi - the AR coefficients (excluding the initial 1); null if no AR coefficient

d - the order of integration

theta - the MA coefficients (excluding the initial 1); null if no MA coefficient

psi - the coefficients of the deterministic terms (excluding the intercept term)

sigma - the white noise covariance matrix

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) vector

phi - the AR coefficients (excluding the initial 1); null if no AR coefficient

d - the order of integration

theta - the MA coefficients (excluding the initial 1); null if no MA coefficient

psi - the coefficients of the deterministic terms (excluding the intercept term)

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); null if no AR coefficient

d - the order of integration

theta - the MA coefficients (excluding the initial 1); null if no MA coefficient

psi - the coefficients of the deterministic terms (excluding the intercept term)

sigma - the white noise covariance matrix

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); null if no AR coefficient

d - the order of integration

theta - the MA coefficients (excluding the initial 1); null if no MA coefficient

psi - the coefficients of the deterministic terms (excluding the intercept term)

VARIMAXModel

public VARIMAXModel(VARIMAXModel that)

Copy constructor.

Parameters:

that - a multivariate ARIMAX model

VARIMAXModel

public VARIMAXModel(ARIMAXModel model)

Construct a multivariate ARIMAX model from a univariate ARIMAX model.

Parameters:

model - a univariate ARIMAX model

Method Detail

mu

public ImmutableVector mu()

Get the intercept (constant) vector.

Returns:

the intercept (constant) vector

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

phi

public ImmutableMatrix[] phi()

Get all the AR coefficients.

Returns:

all the AR coefficients

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

theta

public ImmutableMatrix[] theta()

Get all the MA coefficients.

Returns:

all the MA coefficients

psi

public ImmutableMatrix psi()

Get the coefficients of the deterministic terms.

Returns:

the coefficients of the deterministic terms; could be null

d

public int d()

Get the order of integration.

Returns:

the order of integration

dimension

public int dimension()

Get the dimension of multivariate time series.

Returns:

the dimension of multivariate time series

p

public int p()

Get the number of AR terms.

Returns:

the number of AR terms

q

public int q()

Get the number of MA terms.

Returns:

the number of MA terms

maxPQ

public int maxPQ()

Get the maximum of AR length or MA length.

Returns:

max(# AR terms, # MA terms)

sigma

public ImmutableMatrix sigma()

Get the white noise covariance matrix.

Returns:

the white noise covariance matrix

getVARMAX

public VARMAXModel getVARMAX()

Get the ARMAX part of this ARIMAX model, essentially ignoring the differencing.

Returns:

the ARMAX part