com.numericalmethod.suanshu.stats.dlm.multivariate

Class StateEquation

java.lang.Object

com.numericalmethod.suanshu.stats.dlm.multivariate.StateEquation

All Implemented Interfaces:

java.io.Serializable

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

This is the state equation in a controlled dynamic linear model.

x_t = G_t * x_t-1 + H_t * u_t + w_t,

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
StateEquation(Matrix G, Matrix W) Construct a time-invariant state equation without control variables.
StateEquation(Matrix G, Matrix H, Matrix W, NormalRvg rmvnorm) Construct a time-invariant state equation.
StateEquation(R1toMatrix G, R1toMatrix W) Construct a state equation without control variables.
StateEquation(R1toMatrix G, R1toMatrix H, R1toMatrix W) Construct a state equation.
StateEquation(R1toMatrix G, R1toMatrix H, R1toMatrix W, NormalRvg rmvnorm) Construct a state equation.
StateEquation(StateEquation states) Construct a multivariate state equation from a univariate state equation.
StateEquation(StateEquation that) Copy constructor.

Method Summary

Modifier and Type	Method and Description
int	dimension() Get the dimension of state xt.
Matrix	G(int t) Get G(t), the coefficient matrix of xt - 1.
Matrix	H(int t) Get H(t), the covariance matrix of ut.
Matrix	W(int t) Get W(t), the covariance matrix of wt.
Vector	xt_mean(int t, Vector xt_1) Predict the next state without control variable.
Vector	xt_mean(int t, Vector xt_1, Vector ut) Predict the next state.
ImmutableMatrix	xt_var(int t, Matrix var_tlag_tlag) Get the variance of the apriori prediction for the next state.
ImmutableVector	xt(int t, Vector xt_1) Evaluate the state equation without the control variable.
ImmutableVector	xt(int t, Vector xt_1, Vector ut) Evaluate the state equation.

Methods inherited from class java.lang.Object

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

Constructor Detail

StateEquation

public StateEquation(R1toMatrix G,
                     R1toMatrix H,
                     R1toMatrix W,
                     NormalRvg rmvnorm)

Construct a state equation.

Parameters:

G - the coefficient matrix function of x_{t - 1}

H - the coefficient matrix function of control variables u_t; use null if there isn't any

W - the covariance matrix function of w_t

rmvnorm - a p-dimensional standard multivariate Gaussian random vector generator (for seeding); p = the dimension of W or x_t

StateEquation

public StateEquation(R1toMatrix G,
                     R1toMatrix H,
                     R1toMatrix W)

Construct a state equation.

Parameters:

G - the coefficient matrix function of x_{t - 1}

H - the coefficient matrix function of control variables u_t; use null if there isn't any

W - the covariance matrix function of w_t

StateEquation

public StateEquation(R1toMatrix G,
                     R1toMatrix W)

Construct a state equation without control variables.

Parameters:

G - the coefficient matrix function of x_{t - 1}

W - the covariance matrix function of w_t

StateEquation

public StateEquation(Matrix G,
                     Matrix H,
                     Matrix W,
                     NormalRvg rmvnorm)

Construct a time-invariant state equation.

Parameters:

G - the coefficient matrix function of x_{t - 1}

H - the coefficient matrix function of control variables u_t; use null if there isn't any

W - the covariance matrix function of w_t

rmvnorm - a p-dimensional standard multivariate Gaussian random vector generator; p = the dimension of W or x_t

StateEquation

public StateEquation(Matrix G,
                     Matrix W)

Construct a time-invariant state equation without control variables.

Parameters:

G - the coefficient matrix function of x_{t - 1}

W - the covariance matrix function of w_t

StateEquation

public StateEquation(StateEquation states)

Construct a multivariate state equation from a univariate state equation.

Parameters:

states - a univariate state equation

StateEquation

public StateEquation(StateEquation that)

Copy constructor.

Parameters:

that - a StateEquation

Method Detail

dimension

public int dimension()

Get the dimension of state x_t.

Returns:

the dimension of states

G

public Matrix G(int t)

Get G(t), the coefficient matrix of x_{t - 1}.

Parameters:

t - time

Returns:

G(t)

H

public Matrix H(int t)

Get H(t), the covariance matrix of u_t.

Parameters:

t - time

Returns:

H(t)

W

public Matrix W(int t)

Get W(t), the covariance matrix of w_t.

Parameters:

t - time

Returns:

W(t)

xt_mean

public Vector xt_mean(int t,
                      Vector xt_1,
                      Vector ut)

Predict the next state.

E(x_t) = G_t * x_{t - 1} + H_t * u_t

Parameters:

t - time

xt_1 - x lag x_{t - 1}

ut - the control variable u_t

Returns:

x_t

xt_mean

public Vector xt_mean(int t,
                      Vector xt_1)

Predict the next state without control variable.

E(x_t) = G_t * x_{t - 1} + H_t * u_t

Parameters:

t - time

xt_1 - x lag x_{t - 1}

Returns:

x_t

xt_var

public ImmutableMatrix xt_var(int t,
                              Matrix var_tlag_tlag)

Get the variance of the apriori prediction for the next state.

Var(x_{t | t - 1}) = G_t * Var(x_{t - 1| t - 1}) * G_t' + W_t

Parameters:

t - time

var_tlag_tlag - Var(x_{t - 1 | t - 1}), the covariance of the posterior update

Returns:

Var(x_{t | t - 1})

xt

public ImmutableVector xt(int t,
                          Vector xt_1,
                          Vector ut)

Evaluate the state equation.

x_t = G_t * x_{t - 1} + H_t * u_t + w_t

Parameters:

t - time

xt_1 - x lag x_{t - 1}

ut - the control variable u_t

Returns:

x_t

xt

public ImmutableVector xt(int t,
                          Vector xt_1)

Evaluate the state equation without the control variable.

x_t = G_t * x_{t - 1} + H_t * u_t + w_t

Parameters:

t - time

xt_1 - x lag x_{t - 1}

Returns:

x_t