MCMC initialization.

Specifies the observed SDE data, interobservation times, initial parameter and missing data values to be supplied to sde.post().

sde.init(model, x, dt, m = 1, nvar.obs, theta)

Arguments

model	An sde.model object.
x	An nobs x ndims matrix of data.
dt	A scalar or length nobs-1 vector of interobservations times.
m	Positive integer, such that m-1 evenly-spaced missing data time points are placed between observations. See Details.
nvar.obs	A scalar or length nobs vector of integers between 0 and ndims denoting the number of observed SDE variables in each row of data. Defaults to ndims. See Details.
theta	A length nparams vector of parameter values.

Value

An sde.init object, corresponding to a list with elements:

data

An ncomp x ndims matrix of complete data, where ncomp = N_m = m * (nobs-1)+1.

dt.m

The complete data interobservation time, dt_m = dt/m.

nvar.obs.m

The number of variables observed per row of data. Note that nvar.obs.m[(i-1)*m+1] == nvar.obs[ii], and that nvar.obs.m[i-1] == 0 if i is not a multiple of m.

params

Parameter initial values.

Examples

# load Heston's model
hmod <- sde.examples("hest")

# generate some observed data
nObs <- 5
x0 <- c(X = log(1000), Z = 0.1)
X0 <- apply(t(replicate(nObs, x0)), 2, jitter)
dT <- .6
theta <- c(alpha = 0.1, gamma = 1, beta = 0.8, sigma = 0.6, rho = -0.8)

# no missing data
sde.init(model = hmod, x = X0, dt = dT, theta = theta)
#> $data
#>             X          Z
#> [1,] 6.819487 0.09819872
#> [2,] 6.872264 0.09881696
#> [3,] 6.929321 0.10138062
#> [4,] 6.849917 0.10131988
#> [5,] 6.897041 0.09930631
#> 
#> $dt.m
#> [1] 0.6 0.6 0.6 0.6
#> 
#> $nvar.obs.m
#> [1] 2 2 2 2 2
#> 
#> $params
#> alpha gamma  beta sigma   rho 
#>   0.1   1.0   0.8   0.6  -0.8 
#> 
#> attr(,"class")
#> [1] "sde.init"

# all but endpoint volatilities are missing
sde.init(model = hmod, x = X0, dt = dT, m = 1,
         nvar.obs = c(2, rep(1, nObs-2), 2), theta = theta)
#> $data
#>             X          Z
#> [1,] 6.819487 0.09819872
#> [2,] 6.872264 0.09881696
#> [3,] 6.929321 0.10138062
#> [4,] 6.849917 0.10131988
#> [5,] 6.897041 0.09930631
#> 
#> $dt.m
#> [1] 0.6 0.6 0.6 0.6
#> 
#> $nvar.obs.m
#> [1] 2 1 1 1 2
#> 
#> $params
#> alpha gamma  beta sigma   rho 
#>   0.1   1.0   0.8   0.6  -0.8 
#> 
#> attr(,"class")
#> [1] "sde.init"

# all volatilities missing,
# two completely missing SDE timepoints between observations
m <- 3 # divide each observation interval into m equally spaced timepoints
sde.init(model = hmod, x = X0, dt = dT,
         m = m, nvar.obs = 1, theta = theta)
#> $data
#>              X          Z
#>  [1,] 6.819487 0.09819872
#>  [2,] 6.837079 0.09840480
#>  [3,] 6.854672 0.09861088
#>  [4,] 6.872264 0.09881696
#>  [5,] 6.891283 0.09967151
#>  [6,] 6.910302 0.10052606
#>  [7,] 6.929321 0.10138062
#>  [8,] 6.902853 0.10136037
#>  [9,] 6.876385 0.10134012
#> [10,] 6.849917 0.10131988
#> [11,] 6.865625 0.10064869
#> [12,] 6.881333 0.09997750
#> [13,] 6.897041 0.09930631
#> 
#> $dt.m
#>  [1] 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
#> 
#> $nvar.obs.m
#>  [1] 1 0 0 1 0 0 1 0 0 1 0 0 1
#> 
#> $params
#> alpha gamma  beta sigma   rho 
#>   0.1   1.0   0.8   0.6  -0.8 
#> 
#> attr(,"class")
#> [1] "sde.init"