dev.nm.stat.dlm.multivariate

Class MultivariateDLM

java.lang.Object

dev.nm.stat.dlm.multivariate.MultivariateDLM

public class MultivariateDLM
extends Object

This is the multivariate controlled DLM (controlled Dynamic Linear Model) specification. A controlled DLM, for (t ≥ 1), is described by two equations: the observation and state equations.

Observation Equation: \[ y_{t} = F_{t} \cdot x_{t} + v_{t}, \] State Equation: \[ x_{t} = G_{t} \cdot x_{t-1} + H_{t} \cdot u_{t} + w_{t}, \] \(\{y_{t}\}\) are the observation vectors; \(\{x_{t}\}\) are the state vectors. \(F_{t}\) and \(G_{t}\) are known matrices of dimension (number of observations * number of states) and (number of states * number of states) respectively. \(\{v_{t}\}\) and \(\{w_{t}\}\) are two independent sequences of independent normal random vectors with mean zero and known variance matrices \(\{V_{t}\}\) and \(\{W_{t}\}\), respectively; Furthermore, it is assumed that \(x_{0}\) is independent of \(\{v_{t}\}\) and \(\{w_{t}\}\) and is normally distributed with mean \(m_{0}\) and covariance matrix \(C_{0}\), where \(m_{0}\) is a vector of length the same as the number of states and \(C_{0}\) is a matrix of dimension (number of states * number of states); \(u_{t}\) is an m-dimensional vector of control variables, i.e., the variables whose values can be regulated by the user, in order to obtain a desired level of the state \(x_{t}\). \(H_{t}\) is a known matrix of coefficients, with dimension of (number of states * m).

See Also:

• G. Petris et al., "ch. 2, pp. 31-84," Dynamic Linear Models with R, New York, Springer, 2009.
• Wikipedia: Kalman filter - Underlying dynamic system model

Constructor Summary

Constructors

Constructor and Description
MultivariateDLM(MultivariateDLM that) Copy constructor.
MultivariateDLM(Vector m0, Matrix C0, MultivariateObservationEquation Yt, MultivariateStateEquation Xt) Construct a (multivariate) controlled dynamic linear model.

Method Summary

Modifier and Type	Method and Description
ImmutableMatrix	C0() Get the covariance matrix of \(x_{0}\).
int	getObsDimension() Get the dimension of the observations.
MultivariateObservationEquation	getObservationModel() Get the observation model.
int	getStateDimension() Get the dimension of states.
MultivariateStateEquation	getStateModel() Get the state model.
ImmutableVector	m0() Get the the mean of \(x_{0}\).

Methods inherited from class java.lang.Object

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

Constructor Detail

MultivariateDLM

public MultivariateDLM(Vector m0,
                       Matrix C0,
                       MultivariateObservationEquation Yt,
                       MultivariateStateEquation Xt)

Construct a (multivariate) controlled dynamic linear model.

Parameters:

m0 - the mean of \(x_{0}\)

C0 - the covariance matrix of \(x_{0}\)

Yt - the observation equation for the model

Xt - the state equation for the model

MultivariateDLM

public MultivariateDLM(MultivariateDLM that)

Copy constructor.

Parameters:

that - a (multivariate) controlled dynamic linear model

Method Detail

m0

public ImmutableVector m0()

Get the the mean of \(x_{0}\).

Returns:

m0, the mean of \(x_{0}\)

C0

public ImmutableMatrix C0()

Get the covariance matrix of \(x_{0}\).

Returns:

C0, the covariance matrix of \(x_{0}\)

getObsDimension

public int getObsDimension()

Get the dimension of the observations.

Returns:

the dimension of the observations

getStateDimension

public int getStateDimension()

Get the dimension of states.

Returns:

the dimension of states

getObservationModel

public MultivariateObservationEquation getObservationModel()

Get the observation model.

Returns:

the observation model

getStateModel

public MultivariateStateEquation getStateModel()

Get the state model.

Returns:

the state model