dev.nm.stat.dlm.multivariate

Class MultivariateStateEquation

java.lang.Object

dev.nm.stat.dlm.multivariate.MultivariateStateEquation

public class MultivariateStateEquation
extends Object

This is the state equation in a controlled dynamic linear model. \[ x_{t} = G_{t} \cdot x_{t-1} + H_{t} \cdot u_{t} + w_{t}, \]

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
int	dimension() Gets the dimension of state \(x_{t}\).
Matrix	G(int t) Gets G(t), the coefficient matrix of \(x_{t - 1}\).
Matrix	H(int t) Gets H(t), the covariance matrix of \(u_{t}\).
Matrix	W(int t) Gets W(t), the covariance matrix of \(w_{t}\).
Vector	xt_mean(int t, Vector xt_1) Predicts the next state without control variable. \[ E(x_t) = G_t \cdot x_\{t - 1\} + H_t \cdot u_t \]
Vector	xt_mean(int t, Vector xt_1, Vector ut) Predicts the next state. \[ E(x_t) = G_t \cdot x_\{t - 1\} + H_t \cdot u_t \]
ImmutableMatrix	xt_var(int t, Matrix var_tlag_tlag) Gets the variance of the apriori prediction for the next state. \[ \operatorname{Var}(x_\{t | t - 1\}) = G_t \cdot \operatorname{Var}(x_\{t - 1| t - 1\}) \cdot G_t' + W_t \]
ImmutableVector	xt(int t, Vector xt_1) Evaluates the state equation without the control variable. \[ x_t = G_t \cdot x_\{t - 1\} + H_t \cdot u_t + w_t \]
ImmutableVector	xt(int t, Vector xt_1, Vector ut) Evaluates the state equation. \[ x_t = G_t \cdot x_\{t - 1\} + H_t \cdot u_t + w_t \]

Methods inherited from class java.lang.Object

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

Constructor Detail

MultivariateStateEquation

public MultivariateStateEquation(R1toMatrix G,
                                 R1toMatrix H,
                                 R1toMatrix W,
                                 NormalRVG rmvnorm)

Constructs 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 \(x_{t}\)

MultivariateStateEquation

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

Constructs 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 \(w_{t}\)

MultivariateStateEquation

public MultivariateStateEquation(R1toMatrix G,
                                 R1toMatrix W)

Constructs a state equation without control variables.

Parameters:

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

W - the covariance matrix function of \(w_{t}\)

MultivariateStateEquation

public MultivariateStateEquation(Matrix G,
                                 Matrix H,
                                 Matrix W,
                                 NormalRVG rmvnorm)

Constructs 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 \(x_{t}\)

MultivariateStateEquation

public MultivariateStateEquation(Matrix G,
                                 Matrix W)

Constructs a time-invariant state equation without control variables.

Parameters:

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

W - the covariance matrix function of \(w_{t}\)

MultivariateStateEquation

public MultivariateStateEquation(StateEquation states)

Constructs a multivariate state equation from a univariate state equation.

Parameters:

states - a univariate state equation

MultivariateStateEquation

public MultivariateStateEquation(MultivariateStateEquation that)

Copy constructor.

Parameters:

that - a StateEquation

Method Detail

dimension

public int dimension()

Gets the dimension of state \(x_{t}\).

Returns:

the dimension of states

G

public Matrix G(int t)

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

Parameters:

t - time

Returns:

G(t)

H

public Matrix H(int t)

Gets H(t), the covariance matrix of \(u_{t}\).

Parameters:

t - time

Returns:

H(t)

W

public Matrix W(int t)

Gets 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)

Predicts the next state. \[ E(x_t) = G_t \cdot x_\{t - 1\} + H_t \cdot u_t \]

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)

Predicts the next state without control variable. \[ E(x_t) = G_t \cdot x_\{t - 1\} + H_t \cdot u_t \]

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)

Gets the variance of the apriori prediction for the next state. \[ \operatorname{Var}(x_\{t | t - 1\}) = G_t \cdot \operatorname{Var}(x_\{t - 1| t - 1\}) \cdot G_t' + W_t \]

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)

Evaluates the state equation. \[ x_t = G_t \cdot x_\{t - 1\} + H_t \cdot u_t + w_t \]

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)

Evaluates the state equation without the control variable. \[ x_t = G_t \cdot x_\{t - 1\} + H_t \cdot u_t + w_t \]

Parameters:

t - time

xt_1 - x lag \(x_{t - 1}\)

Returns:

\(x_{t}\)