LinSDECov {simStateSpace}R Documentation

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

Description

The steady-state covariance matrix is the solution to the Sylvester equation, i.e.

\mathbf{A} \mathbf{X} + \mathbf{X} \mathbf{B} + \mathbf{C} = \mathbf{0} ,

where \mathbf{X} is unknown, \mathbf{A} = \boldsymbol{\Phi}, \mathbf{B} = \boldsymbol{\Phi}^{\prime}, and \mathbf{C} = \boldsymbol{\Sigma}.

Usage

LinSDECov(phi, sigma)

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}).

sigma

Numeric matrix. The covariance matrix of volatility or randomness in the process (\boldsymbol{\Sigma}).

Author(s)

Ivan Jacob Agaloos Pesigan

See Also

Other Simulation of State Space Models Data Functions: LinSDE2SSM(), LinSDEMean(), SimBetaN(), SimPhiN(), SimSSMFixed(), SimSSMIVary(), SimSSMLinGrowth(), SimSSMLinGrowthIVary(), SimSSMLinSDEFixed(), SimSSMLinSDEIVary(), SimSSMOUFixed(), SimSSMOUIVary(), SimSSMVARFixed(), SimSSMVARIVary(), TestPhi(), TestStability(), TestStationarity()

Examples

phi <- matrix(
  data = c(
    -0.10,
    0.05,
    0.05,
    -0.10
  ),
  nrow = 2
)
sigma <- matrix(
  data = c(
    2.79,
    0.06,
    0.06,
    3.27
  ),
  nrow = 2
)
LinSDECov(phi = phi, sigma = sigma)


[Package simStateSpace version 1.2.10 Index]