generateSPASM: Generate data from an additive state space model

In dajmcdon/spasm: Implements the Laplace-Gaussian filter for sparse, additive, state-space models

Description

This function generates data and returns components so as to easily test the Laplace-Gaussian filter and the sparse spline additive models. Data is generated as

y_{t} = Z sin(z * x_{t} / 2π) + σ_{y} * N(0, I)

x_{t+1} = Tt x_t + σ_x * N(0,I)

where Z is a dxp matrix of standard uniform random variables and z=[1 ... p].

Usage

generateSPASM(N, p, d, sig.x = 0.1, sig.y = 0.1)

Arguments

N	the number of observed time points
p	the dimension of the hidden state vector
d	the dimension of the observation vector
sig.x	scalar which multiplies the hidden standard normal noise
sig.y	scalar which multiplies the standard normal noise added to the observations

Value

a list with components

y

the observations, nxd

x

the hidden states, nxp

Tt

the state transition matrix, pxp

HHt

the observation noise variance, dxd

GGt

the hidden noise variance, pxp

Examples

generateSPASM(100,3,4)

dajmcdon/spasm documentation built on May 6, 2019, 1:31 a.m.