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. \(N(0,1)\).
generateData(theta, noObservations, initialState)The parameters \(\theta=\{\phi,\sigma_v,\sigma_e\}\) of the LGSS model. The parameter \(\phi\) that scales the current state in the state dynamics is restricted to [-1,1] to obtain a stable model. The standard deviations of the state process noise \(\sigma_v\) and the observation process noise \(\sigma_e\) must be positive.
The number of time points to simulate.
The initial state.
The function returns a list with the elements:
x: The latent state for \(t=0,...,T\).
y: The observation for \(t=0,...,T\).
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.