data.gen.LGSS {synthesis}

Linear Gaussian state-space model

Description

Generates data from a specific linear Gaussian state space model of the form x_{t} = \phi x_{t-1} + \sigma_v v_t and y_t = x_t + \sigma_e e_t , where v_t and e_t denote independent standard Gaussian random variables, i.e. N(0,1).

Usage

data.gen.LGSS(
  theta,
  nobs,
  start = runif(n = 1, min = -1, max = 1),
  do.plot = TRUE
)

Arguments

theta

The parameters \theta=\{\phi,\sigma_v,\sigma_e\} of the LGSS model.

nobs

The data length to be generated.

start

A numeric value indicating the starting value for the time series. If the starting point is not specified, it is generated randomly.

do.plot

Logical value. If TRUE (default value), a plot of the generated LGSS system is shown.

Value

A list of two variables, state and response.

References

#Dahlin, J. & Schon, T. B. 'Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models.' Journal of Statistical Software, Code Snippets, 88(2): 1–41, 2019.

Examples

data.LGSS <- data.gen.LGSS(theta=c(0.75,1.00,0.10), nobs=500, start=0)