Steady-State Mean Vector for the Latent Variables in the Linear Stochastic Differential Equation Model

The steady-state mean vector for the latent variables in the linear stochastic differential equation model \(\mathrm{Mean} \left( \boldsymbol{\eta} \right)\) is given by $$ \mathrm{Mean} \left( \boldsymbol{\eta} \right) = -\boldsymbol{\Phi}^{-1} \boldsymbol{\iota} $$ where \(\boldsymbol{\Phi}\) is the drift matrix, and \(\boldsymbol{\iota}\) is an unobserved term that is constant over time.

Usage

LinSDEMeanEta(phi, iota)

Arguments

phi

Numeric matrix. The drift matrix which represents the rate of change of the solution in the absence of any random fluctuations (\(\boldsymbol{\Phi}\)).

iota

Numeric vector. An unobserved term that is constant over time (\(\boldsymbol{\iota}\)).

See also

Other Simulation of State Space Models Data Functions: LinSDE2SSM(), LinSDECovEta(), LinSDECovY(), LinSDEMeanY(), ProjectToHurwitz(), ProjectToStability(), SSMCovEta(), SSMCovY(), SSMMeanEta(), SSMMeanY(), SimAlphaN(), SimBetaN(), SimBetaN2(), SimCovDiagN(), SimCovN(), SimIotaN(), SimNuN(), SimPhiN(), SimPhiN2(), SimSSMFixed(), SimSSMIVary(), SimSSMLinGrowth(), SimSSMLinGrowthIVary(), SimSSMLinSDEFixed(), SimSSMLinSDEIVary(), SimSSMOUFixed(), SimSSMOUIVary(), SimSSMVARFixed(), SimSSMVARIVary(), SpectralRadius(), TestPhi(), TestPhiHurwitz(), 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
)
iota <- rep(x = 1, times = 3)
LinSDEMeanEta(
  phi = phi,
  iota = iota
)
#> [1] 2.801120 6.183295 6.128597