pomp (version 1.19)

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

Description

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

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.

See Also

pomp

Examples

# NOT RUN {
pompExample(ou2)
plot(ou2)
coef(ou2)
x <- simulate(ou2)
plot(x)
pf <- pfilter(ou2,Np=1000)
logLik(pf)
# }