This function simulates a time series from the distribution estimated by the given vlmc object.
Usage
# S3 method for vlmc
simulate(object, nsim = 1L, seed = NULL, init = NULL, burnin = 0L, ...)Arguments
- object
a fitted vlmc object.
- nsim
length of the simulated time series (defaults to 1).
- seed
an optional random seed (see the dedicated section).
- init
an optional initial sequence for the time series.
- burnin
number of initial observations to discard or
"auto"(see the dedicated section).- ...
additional arguments.
Value
a simulated discrete time series of the same type as the one used to
build the vlmc with a seed attribute (see the Random seed section). The
results has also the dts class to hide the seed attribute when using
print or similar function.
Burn in (Warm up) period
When using a VLMC for simulation purposes, we are generally interested in
the stationary distribution of the corresponding Markov chain. To reduce
the dependence of the samples from the initial values and get closer to
this stationary distribution (if it exists), it is recommended to discard
the first samples which are produced in a so-called "burn in" (or "warm
up") period. The burnin parameter can be used to implement this approach.
The VLMC is used to produce a sample of size burnin + nsim but the first
burnin values are discarded. Notice that this burn in values can be
partially given by the init parameter if it is specified.
If burnin is set to "auto", the burnin period is set to 64 * context_number(object), following the heuristic proposed in Mächler and
Bühlmann (2004).
Random seed
This function reproduce the behaviour of stats::simulate(). If seed is
NULL the function does not change the random generator state and returns
the value of .Random.seed as a seed attribute in the return value. This
can be used to reproduce exactly the simulation results by setting
.Random.seed to this value. Notice that if the random seed has not be
initialised by R so far, the function issues a call to runif(1) to
perform this initialisation (as is done in stats::simulate()).
It seed is an integer, it is used in a call to set.seed() before the
simulation takes place. The integer is saved as a seed attribute in the
return value. The integer seed is completed by an attribute kind which
contains the value as.list([RNGkind()]) exactly as with
stats::simulate(). The random generator state is reset to its original
value at the end of the call.
Extended contexts
As explained in details in loglikelihood.vlmc() documentation and in the
dedicated vignette("likelihood", package = "mixvlmc"), the first initial
values of a time series do not in general have a proper context for a VLMC
with a non zero order. In order to simulate something meaningful for those
values when init is not provided, we rely on the notion of extended
context defined in the documents mentioned above. This follows the same
logic as using loglikelihood.vlmc() with the parameter
initial="extended". All vlmc functions that need to manipulate initial
values with no proper context use the same approach.
References
Mächler, M. and Bühlmann, P. (2004) "Variable Length Markov Chains: Methodology, Computing, and Software" Journal of Computational and Graphical Statistics, 13 (2), 435-455, doi:10.1198/1061860043524
See also
stats::simulate() for details and examples on the random number
generator setting
Examples
pc <- powerconsumption[powerconsumption$week == 5, ]
dts <- cut(pc$active_power, breaks = c(0, quantile(pc$active_power, probs = c(0.25, 0.5, 0.75, 1))))
model <- vlmc(dts, min_size = 5)
new_dts <- simulate(model, 500, seed = 0)
new_dts_2 <- simulate(model, 500, seed = 0, init = dts[1:5])
new_dts_3 <- simulate(model, 500, seed = 0, burnin = 500)