Class MultivariateObservationEquation


  • public class MultivariateObservationEquation
    extends Object
    This is the observation equation in a controlled dynamic linear model.
    yt = Ft * xt + vt
    • Constructor Detail

      • MultivariateObservationEquation

        public MultivariateObservationEquation​(R1toMatrix F,
                                               R1toMatrix V,
                                               NormalRVG rmvnorm)
        Constructs an observation equation.
        Parameters:
        F - the coefficient matrix function of xt, a function of time
        V - the covariance matrix function of vt, a function of time
        rmvnorm - a d-dimensional standard multivariate Gaussian random vector generator (for seeding); d = the dimension of V or yt
      • MultivariateObservationEquation

        public MultivariateObservationEquation​(R1toMatrix F,
                                               R1toMatrix V)
        Constructs an observation equation.
        Parameters:
        F - the coefficient matrix function of xt, a function of time
        V - the covariance matrix function of vt, a function of time
      • MultivariateObservationEquation

        public MultivariateObservationEquation​(Matrix F,
                                               Matrix V,
                                               NormalRVG rmvnorm)
        Constructs a time-invariant an observation equation.
        Parameters:
        F - the coefficient matrix of xt
        V - the covariance matrix of vt
        rmvnorm - a d-dimensional standard multivariate Gaussian random vector generator (for seeding); d = the dimension of V or yt
      • MultivariateObservationEquation

        public MultivariateObservationEquation​(Matrix F,
                                               Matrix V)
        Constructs a time-invariant an observation equation.
        Parameters:
        F - the coefficient matrix of xt
        V - the covariance matrix of vt
      • MultivariateObservationEquation

        public MultivariateObservationEquation​(ObservationEquation obs)
        Constructs a multivariate observation equation from a univariate observation equation.
        Parameters:
        obs - a univariate observation equation
      • MultivariateObservationEquation

        public MultivariateObservationEquation​(MultivariateObservationEquation that)
        Copy constructor.
        Parameters:
        that - a ObservationEquation
    • Method Detail

      • dimension

        public int dimension()
        Gets the dimension of observation yt.
        Returns:
        the dimension of observations
      • F

        public ImmutableMatrix F​(int t)
        Gets F(t), the coefficient matrix of xt.
        Parameters:
        t - time
        Returns:
        F(t)
      • V

        public ImmutableMatrix V​(int t)
        Gets V(t), the covariance matrix of vt.
        Parameters:
        t - time
        Returns:
        V(t)
      • yt_mean

        public ImmutableVector yt_mean​(int t,
                                       Vector xt)
        Predicts the next observation.
        E(y_t) = F_t * x_t
        Parameters:
        t - time
        xt - state xt
        Returns:
        the mean observation
      • yt_var

        public ImmutableMatrix yt_var​(int t,
                                      Matrix var_t_tlag)
        Gets the covariance of the apriori prediction for the next observation.
        Var(y_{t | t - 1}) = F_t * Var(x_{t | t - 1}) * 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 ImmutableVector yt​(int t,
                                  Vector xt)
        Evaluates the observation equation.
        y_t = F_t * x_t + v_t
        Parameters:
        t - time
        xt - state xt
        Returns:
        the mean observation