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Intercept from Steady-State Mean Vector for the Latent Variables in the State Space Model

Source: R/simStateSpace-ssm-intercept-eta.R
SSMInterceptEta.Rd

The intercept vector for the latent variables in the state space model \(\boldsymbol{\alpha}\) is given by $$ \boldsymbol{\alpha} = \mathrm{Mean} \left( \boldsymbol{\eta} \right) - \boldsymbol{\beta} \mathrm{Mean} \left( \boldsymbol{\eta} \right) $$ where \(\boldsymbol{\beta}\) is the transition matrix relating the values of the latent variables at the previous to the current time point, \(\mathrm{Mean} \left( \boldsymbol{\eta} \right)\) is the steady-state mean vector for the latent variables.

Usage

SSMInterceptEta(beta, mean_eta)

Arguments

beta

Numeric matrix. Transition matrix relating the values of the latent variables at the previous to the current time point (\(\boldsymbol{\beta}\)).

mean_eta

Numeric vector. Steady-state mean vector of the latent variables \(\mathrm{Mean} \left( \boldsymbol{\eta} \right)\).

See also

Other Simulation of State Space Models Data Functions: LinSDE2SSM(), LinSDECovEta(), LinSDECovY(), LinSDEMeanEta(), LinSDEMeanY(), ProjectToHurwitz(), ProjectToStability(), SSMCovEta(), SSMCovY(), SSMInterceptY(), SSMMeanEta(), SSMMeanY(), SimAlphaN(), SimBetaN(), SimBetaN2(), SimBetaNCovariate(), SimCovDiagN(), SimCovN(), SimIotaN(), SimNuN(), SimPhiN(), SimPhiN2(), SimPhiNCovariate(), SimSSMFixed(), SimSSMIVary(), SimSSMLinGrowth(), SimSSMLinGrowthIVary(), SimSSMLinSDEFixed(), SimSSMLinSDEIVary(), SimSSMOUFixed(), SimSSMOUIVary(), SimSSMVARFixed(), SimSSMVARIVary(), SpectralRadius(), TestPhi(), TestPhiHurwitz(), TestStability(), TestStationarity()

Author

Ivan Jacob Agaloos Pesigan

Examples

beta <- matrix(
  data = c(
    0.7, 0.5, -0.1,
    0.0, 0.6, 0.4,
    0.0, 0.0, 0.5
  ),
  nrow = 3
)
alpha <- rep(x = 1, times = 3)
mean_eta <- SSMMeanEta(
  beta = beta,
  alpha = alpha
)
SSMInterceptEta(
  beta = beta,
  mean_eta = mean_eta
)
#> [1] 1 1 1