pomp (version 0.39-3)

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

Description

ou2 is a pomp object encoding a bivariate discrete-time Ornstein-Uhlenbeck process.

Usage

data(ou2)

Details

If the state process is $X(t) = (x_{1}(t),x_{2}(t))$, then $$X(t+1) = \alpha X(t) + \sigma \epsilon(t),$$ where $\alpha$ and $\sigma$ are 2x2 matrices, $\sigma$ is lower-triangular, and $\epsilon(t)$ is standard bivariate normal. The observation process is $Y(t) = (y_1(t),y_2(t))$, where $y_i(t) \sim \mathrm{normal}(x_i(t),\tau)$. The functions rprocess, dprocess, rmeasure, dmeasure, and skeleton are implemented using compiled C code for computational speed: see the source code for details. This object is demonstrated in the vignette "Advanced topics in pomp".

See Also

pomp and the vignettes

Examples

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