ou2 {pomp} | R Documentation |
Two-dimensional discrete-time Ornstein-Uhlenbeck process
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 |
sigma_1 , sigma_2 , sigma_3 |
entries of the lower-triangular |
tau |
measurement error s.d. |
x1_0 , x2_0 |
latent variable values at time |
times |
vector of observation times |
t0 |
the zero time |
Details
If the state process is , then
where and
are 2x2 matrices,
is lower-triangular, and
is standard bivariate normal.
The observation process is
, where
.
Value
A ‘pomp’ object with simulated data.
See Also
More examples provided with pomp:
blowflies
,
childhood_disease_data
,
compartmental_models
,
dacca()
,
ebola
,
gompertz()
,
pomp_examples
,
ricker()
,
rw2()
,
verhulst()
Examples
po <- ou2()
plot(po)
coef(po)
x <- simulate(po)
plot(x)
pf <- pfilter(po,Np=1000)
logLik(pf)