dev.nm.stat.dlm.univariate

Class ObservationEquation

java.lang.Object

dev.nm.stat.dlm.univariate.ObservationEquation

public class ObservationEquation
extends Object

This is the observation equation in a controlled dynamic linear model. \[ y_{t} = F_{t} \cdot x_{t} + v_{t} \]

Constructor Summary

Constructors

Constructor and Description
ObservationEquation(double F, double V) Construct a time-invariant an observation equation.
ObservationEquation(double F, double V, RandomStandardNormalGenerator rnorm) Construct a time-invariant an observation equation.
ObservationEquation(ObservationEquation that) Copy constructor.
ObservationEquation(UnivariateRealFunction F, UnivariateRealFunction V) Construct an observation equation.
ObservationEquation(UnivariateRealFunction F, UnivariateRealFunction V, RandomStandardNormalGenerator rnorm) Construct an observation equation.

Method Summary

Modifier and Type	Method and Description
int	dimension() Get the dimension of observation \(y_{t}\).
double	F(int t) Get F(t), the coefficient of \(x_{t}\).
double	V(int t) Get V(t), the variance of \(v_{t}\).
double	yt_mean(int t, double xt) Predict the next observation. \[ E(y_t) = F_t \cdot x_t \]
double	yt_var(int t, double var_t_tlag) Get the variance of the apriori prediction for the next observation. \[ \operatorname{Var}(y_\{t | t - 1\}) = F_t \cdot \operatorname{Var}(x_\{t | t - 1\}) \cdot F_t' + V_t \]
double	yt(int t, double xt) Evaluate the observation equation. \[ y_t = F_t \cdot x_t + v_t \]

Methods inherited from class java.lang.Object

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

Constructor Detail

ObservationEquation

public ObservationEquation(UnivariateRealFunction F,
                           UnivariateRealFunction V,
                           RandomStandardNormalGenerator rnorm)

Construct an observation equation.

Parameters:

F - the coefficient function of \(x_{t}\), a function of time

V - the variance function of \(v_{t}\), a function of time

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

ObservationEquation

public ObservationEquation(UnivariateRealFunction F,
                           UnivariateRealFunction V)

Construct an observation equation.

Parameters:

F - the coefficient function of \(x_{t}\), a function of time

V - the variance function of \(v_{t}\), a function of time

ObservationEquation

public ObservationEquation(double F,
                           double V,
                           RandomStandardNormalGenerator rnorm)

Construct a time-invariant an observation equation.

Parameters:

F - the coefficient of \(x_{t}\)

V - the variance of \(v_{t}\)

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

ObservationEquation

public ObservationEquation(double F,
                           double V)

Construct a time-invariant an observation equation.

Parameters:

F - the coefficient of \(x_{t}\)

V - the variance of \(v_{t}\)

ObservationEquation

public ObservationEquation(ObservationEquation that)

Copy constructor.

Parameters:

that - a ObservationEquation

Method Detail

dimension

public int dimension()

Get the dimension of observation \(y_{t}\).

Returns:

the dimension of observations

F

public double F(int t)

Get F(t), the coefficient of \(x_{t}\).

Parameters:

t - time

Returns:

F(t)

V

public double V(int t)

Get V(t), the variance of \(v_{t}\).

Parameters:

t - time

Returns:

V(t)

yt_mean

public double yt_mean(int t,
                      double xt)

Predict the next observation. \[ E(y_t) = F_t \cdot x_t \]

Parameters:

t - time

xt - state \(x_{t}\)

Returns:

the mean observation

yt_var

public double yt_var(int t,
                     double var_t_tlag)

Get the variance of the apriori prediction for the next observation. \[ \operatorname{Var}(y_\{t | t - 1\}) = F_t \cdot \operatorname{Var}(x_\{t | t - 1\}) \cdot F_t' + V_t \]

Parameters:

t - time

var_t_tlag - Var(y_{t | t - 1}), the variance of the apriori prediction

Returns:

Var(y_{t | t - 1})

yt

public double yt(int t,
                 double xt)

Evaluate the observation equation. \[ y_t = F_t \cdot x_t + v_t \]

Parameters:

t - time

xt - state \(x_{t}\)

Returns:

the mean observation