com.numericalmethod.suanshu.stats.timeseries.linear.univariate.arima

Class ARIMAXModel

java.lang.Object

com.numericalmethod.suanshu.stats.timeseries.linear.univariate.arima.ARIMAXModel

All Implemented Interfaces:

java.io.Serializable

Direct Known Subclasses:

ARIMAModel, ARMAXModel

public class ARIMAXModel
extends java.lang.Object
implements java.io.Serializable

This class represents a univariate ARIMAX (ARIMA model with eXogenous inputs) model.

The ARIMAX model incorporates exogenous variables and it can be considered as a generalization of the ARIMA model. Letting L be lag operator, the d-th difference of an 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 = μ + Σ φ_i * X_{t-i} + Σ θ_j * ε_{t-j} + ψ' * D_t + ε_t,

\[ X_t = \mu + \Sigma \phi_i X_{t-i} + \Sigma \theta_j \epsilon_{t-j} + \psi' D_t + \epsilon_t, \] where D_t is an (m * 1) vector which contains all exogenous variables at time t (excl. the intercept term), and its coefficients are represented by an m-dimensional vector ψ.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected double[]	AR the AR coefficients
protected double[]	MA the MA coefficients
protected double	mu the intercept (constant) term
protected double[]	psi the coefficients of the deterministic terms (excluding the intercept term)
protected double	sigma the white noise variance

Constructor Summary

Constructors

Constructor and Description
ARIMAXModel(ARIMAXModel that) Copy constructor.
ARIMAXModel(double[] AR, int d, double[] MA, double[] psi) Construct a zero-intercept (mu) univariate ARIMAX model with unit variance.
ARIMAXModel(double[] AR, int d, double[] MA, double[] psi, double sigma) Construct a zero-intercept (mu) univariate ARIMAX model.
ARIMAXModel(double mu, double[] AR, int d, double[] MA, double[] psi) Construct a univariate ARIMAX model with unit variance.
ARIMAXModel(double mu, double[] AR, int d, double[] MA, double[] psi, double sigma) Construct a univariate ARIMAX (ARIMA model with eXogenous inputs) model.

Method Summary

Modifier and Type	Method and Description
double[]	AR() Get the AR coefficients, excluding the initial 1.
double	AR(int i) Get the i-th AR coefficient; AR(0) = 1.
int	d() Get the order of integration.
ARMAXModel	getArmax() Get the ARMAX specification of this ARIMAX model, essentially ignoring the differencing.
double[]	MA() Get the MA coefficients, excluding the initial 1.
double	MA(int i) Get the i-th MA coefficient; MA(0) = 1.
int	maxPQ() Get the maximum of AR length or MA length.
double	mu() Get the intercept term.
int	p() Get the number of AR terms.
double[]	psi() Get the coefficients of the deterministic terms.
int	q() Get the number of MA terms.
double	sigma() Get the white noise variance.
java.lang.String	toString()

Methods inherited from class java.lang.Object

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

Field Detail

mu

protected final double mu

the intercept (constant) term

AR

protected final double[] AR

the AR coefficients

MA

protected final double[] MA

the MA coefficients

psi

protected final double[] psi

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

sigma

protected final double sigma

the white noise variance

Constructor Detail

ARIMAXModel

public ARIMAXModel(double mu,
                   double[] AR,
                   int d,
                   double[] MA,
                   double[] psi,
                   double sigma)

Construct a univariate ARIMAX (ARIMA model with eXogenous inputs) model.

Parameters:

mu - the intercept (constant) term

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

d - the order of integration

MA - 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 variance

ARIMAXModel

public ARIMAXModel(double mu,
                   double[] AR,
                   int d,
                   double[] MA,
                   double[] psi)

Construct a univariate ARIMAX model with unit variance.

Parameters:

mu - the intercept (constant) term

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

d - the order of integration

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

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

ARIMAXModel

public ARIMAXModel(double[] AR,
                   int d,
                   double[] MA,
                   double[] psi,
                   double sigma)

Construct a zero-intercept (mu) univariate ARIMAX model.

Parameters:

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

d - the order of integration

MA - 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 variance

ARIMAXModel

public ARIMAXModel(double[] AR,
                   int d,
                   double[] MA,
                   double[] psi)

Construct a zero-intercept (mu) univariate ARIMAX model with unit variance.

Parameters:

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

d - the order of integration

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

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

ARIMAXModel

public ARIMAXModel(ARIMAXModel that)

Copy constructor.

Parameters:

that - a univariate ARIMAX model

Method Detail

mu

public double mu()

Get the intercept term.

Returns:

the intercept (constant) term

AR

public double AR(int i)

Get the i-th AR coefficient; AR(0) = 1.

Parameters:

i - an index

Returns:

the i-th AR coefficient

AR

public double[] AR()

Get the AR coefficients, excluding the initial 1.

Returns:

the AR coefficients; could be null

MA

public double MA(int i)

Get the i-th MA coefficient; MA(0) = 1.

Parameters:

i - an index

Returns:

the i-th MA coefficient

MA

public double[] MA()

Get the MA coefficients, excluding the initial 1.

Returns:

the MA coefficients; could be null

psi

public double[] 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

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 double sigma()

Get the white noise variance.

Returns:

the white noise variance

getArmax

public ARMAXModel getArmax()

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

Returns:

the ARMAX specification

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object