dev.nm.stat.dlm.univariate

Class StateEquation

java.lang.Object

dev.nm.stat.dlm.univariate.StateEquation

public class StateEquation
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
StateEquation(double G, double W) Construct a time-invariant state equation without control variables.
StateEquation(double G, double H, double W, RandomStandardNormalGenerator rnorm) Construct a time-invariant state equation.
StateEquation(StateEquation that) Copy constructor.
StateEquation(UnivariateRealFunction G, UnivariateRealFunction W) Construct a state equation without control variables.
StateEquation(UnivariateRealFunction G, UnivariateRealFunction H, UnivariateRealFunction W) Construct a state equation.
StateEquation(UnivariateRealFunction G, UnivariateRealFunction H, UnivariateRealFunction W, RandomStandardNormalGenerator rnorm) Construct a state equation.

Method Summary

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

StateEquation

public StateEquation(UnivariateRealFunction G,
                     UnivariateRealFunction H,
                     UnivariateRealFunction W,
                     RandomStandardNormalGenerator rnorm)

Construct a state equation.

Parameters:

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

H - the coefficient function of control variables \(u_{t}\)

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

rnorm - a standard Gaussian random number generator (for seeding)

StateEquation

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

Construct a state equation.

Parameters:

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

H - the coefficient function of control variables \(u_{t}\)

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

StateEquation

public StateEquation(UnivariateRealFunction G,
                     UnivariateRealFunction W)

Construct a state equation without control variables.

Parameters:

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

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

StateEquation

public StateEquation(double G,
                     double H,
                     double W,
                     RandomStandardNormalGenerator rnorm)

Construct a time-invariant state equation.

Parameters:

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

H - the coefficient of control variables \(u_{t}\)

W - the variance of \(w_{t}\)

rnorm - a standard Gaussian random number generator

StateEquation

public StateEquation(double G,
                     double W)

Construct a time-invariant state equation without control variables.

Parameters:

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

W - the variance of \(w_{t}\)

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 double G(int t)

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

Parameters:

t - time

Returns:

G(t)

H

public double H(int t)

Get H(t), the variance of \(u_{t}\).

Parameters:

t - time

Returns:

H(t)

W

public double W(int t)

Get W(t), the variance of \(w_{t}\).

Parameters:

t - time

Returns:

W(t)

xt_mean

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

Predict 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 double xt_mean(int t,
                      double xt_1)

Predict 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 double xt_var(int t,
                     double var_tlag_tlag)

Get 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 variance of the posterior update

Returns:

Var(x_{t | t - 1})

xt

public double xt(int t,
                 double xt_1,
                 double ut)

Evaluate 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 double xt(int t,
                 double xt_1)

Evaluate 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:

\(x_{t}\)