The `tsprofile`

method allows one to specify a model with
given parameters, simulate data from that model under different lengths,
and then estimate the parameters given the simulated data, thus enabling
the creation of parameter distributions under different size
assumptions. The goal of the exercise is to understand how much
variation under the true specified parameters we should expect given
each data size given the algorithms for estimation implemented in this
package.

When choosing **n** paths to generate for
**sizes** of [400, 800, 1000], for instance, we simply
simulate n x max(sizes), creating a (max size) x nsim matrix
**S**, and then for each path (i) and size (j) we estimate
S[1:j, i]. Thus the simulated data in size 1000 will include the
simulated data for sizes 400 and 800 for each path (i).

The demonstration code below is illustrative of how to create a
specification with fixed parameters which can then be passed to the
tsprofile method. In real world applications, one should set nsim quite
high and the sizes guided by problem specific considerations. The method
can take advantage of parallel functionality using the
`future`

package as well as tracing using the
`progressr`

package.

```
library(tsdistributions)
library(future)
library(progressr)
plan(list(
tweak(sequential),
tweak(multisession, workers = 1)
))
# tracing using the progressr package
# handlers(global = TRUE)
# handlers("progress")
# set up some dummy data to establish the specification
spec <- distribution_modelspec(rnorm(100), distribution = "std")
# make sure to set all parameter values. The mu and sigma are otherwise defaulted
# to the mean and standard deviation of the data input.
spec$parmatrix[parameter %in% c("mu","sigma","shape"), value := c(0.0, 1.0, 5.0)]
sim <- tsprofile(spec, nsim = 100, sizes = c(400, 1000, 2000), seed = 100, trace = FALSE)
plan("sequential")
summary(sim)
#>
#> RMSE Profile Summary : STD
#>
#> actual 400 1000 2000
#> mu 0 0.04499 0.02755 0.01964
#> sigma 1 0.06008 0.03501 0.02531
#> shape 5 2.93846 0.87897 0.62052
#> skewness 0 0.00000 0.00000 0.00000
#> kurtosis 9 290.36839 72.09854 12.34290
```

Note that inspection of the returned object should be conducted to observe whether any NA values are present. If the estimation was no successful for a particular set of data, then NA values are returned. These are not excluded from the returned table, but the summary statistics table removes the NA’s (na.rm) in the calculation of the different measures.