ou2: Two-dimensional discrete-time Ornstein-Uhlenbeck process

In kidusasfaw/pomp: Statistical Inference for Partially Observed Markov Processes

Description

ou2() constructs a ‘pomp’ object encoding a bivariate discrete-time Ornstein-Uhlenbeck process with noisy observations.

Usage

ou2(alpha_1 = 0.8, alpha_2 = -0.5, alpha_3 = 0.3, alpha_4 = 0.9,
  sigma_1 = 3, sigma_2 = -0.5, sigma_3 = 2, tau = 1, x1_0 = -3,
  x2_0 = 4, times = 1:100, t0 = 0)

Arguments

alpha_1, alpha_2, alpha_3, alpha_4	entries of the alpha matrix, in column-major order. That is, alpha_2 is in the lower-left position.
sigma_1, sigma_2, sigma_3	entries of the lower-triangular sigma matrix. sigma_2 is the entry in the lower-left position.
tau	measurement error s.d.
x1_0, x2_0	latent variable values at time t0
times	vector of observation times
t0	the zero time

Details

If the state process is X(t) = (x_{1}(t),x_{2}(t)), then

X(t+1) = α X(t) + σ ε(t),

where α and σ are 2x2 matrices, σ is lower-triangular, and ε(t) is standard bivariate normal. The observation process is Y(t) = (y_1(t),y_2(t)), where y_i(t) \sim \mathrm{normal}(x_i(t),τ).

Value

A ‘pomp’ object with simulated data.

See Also

Other pomp examples: blowflies, dacca, gompertz, measles, ricker, rw2, sir_models, verhulst

Examples

plot(ou2())
coef(ou2())
x <- simulate(ou2())
plot(x)
pf <- pfilter(ou2(),Np=1000)
logLik(pf)

kidusasfaw/pomp documentation built on May 20, 2019, 2:59 p.m.