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Steady-State Covariance Matrix for the Observed Variables in the Linear Stochastic Differential Equation Model

Source: R/simStateSpace-lin-sde-cov-y.R
LinSDECovY.Rd

The steady-state covariance matrix for the observed variables in the linear stochastic differential equation model \(\mathrm{Cov} \left( \mathbf{y} \right)\) is given by $$ \mathrm{Cov} \left( \mathbf{y} \right) = \boldsymbol{\Lambda} \mathrm{Cov} \left( \boldsymbol{\eta} \right) \boldsymbol{\Lambda}^{\prime} + \boldsymbol{\Theta} $$ where \(\boldsymbol{\Lambda}\) is the matrix of factor loadings, \(\boldsymbol{\Theta}\) is the covariance matrix of the measurement error, and \(\mathrm{Cov} \left( \boldsymbol{\eta} \right)\) is the steady-state covariance matrix for the latent variables.

Usage

LinSDECovY(lambda, theta, cov_eta)

Arguments

lambda

Numeric matrix. Factor loading matrix linking the latent variables to the observed variables (\(\boldsymbol{\Lambda}\)).

theta

Numeric matrix. The covariance matrix of the measurement error (\(\boldsymbol{\Theta}\)).

cov_eta

Numeric matrix. The steady-state covariance matrix for the latent variables in the linear stochastic differential equation model

See also

Other Simulation of State Space Models Data Functions: LinSDE2SSM(), LinSDECovEta(), LinSDEMeanEta(), LinSDEMeanY(), SSMCovEta(), SSMCovY(), SSMMeanEta(), SSMMeanY(), SimAlphaN(), SimBetaN(), SimCovDiagN(), SimCovN(), SimIotaN(), SimPhiN(), SimSSMFixed(), SimSSMIVary(), SimSSMLinGrowth(), SimSSMLinGrowthIVary(), SimSSMLinSDEFixed(), SimSSMLinSDEIVary(), SimSSMOUFixed(), SimSSMOUIVary(), SimSSMVARFixed(), SimSSMVARIVary(), TestPhi(), TestStability(), TestStationarity()

Author

Ivan Jacob Agaloos Pesigan

Examples

phi <- matrix(
  data = c(
    -0.357, 0.771, -0.450,
    0.0, -0.511, 0.729,
    0.0, 0.0, -0.693
  ),
  nrow = 3
)
sigma <- matrix(
  data = c(
    0.24455556, 0.02201587, -0.05004762,
    0.02201587, 0.07067800, 0.01539456,
    -0.05004762, 0.01539456, 0.07553061
  ),
  nrow = 3
)
lambda <- diag(3)
theta <- diag(3)
cov_eta <- LinSDECovEta(
  phi = phi,
  sigma = sigma
)
LinSDECovY(
  lambda = lambda,
  theta = theta,
  cov_eta = cov_eta
)
#>           [,1]      [,2]      [,3]
#> [1,] 1.3425148 0.3296023 0.0343817
#> [2,] 0.3296023 1.5664625 0.2545955
#> [3,] 0.0343817 0.2545955 1.2999909