This function fits a Variable Length Markov Chain with Covariates (coVLMC) to a discrete time series coupled with a time series of covariates by optimizing an information criterion (BIC or AIC).
tune_covlmc(
x,
covariate,
criterion = c("BIC", "AIC"),
initial = c("truncated", "specific", "extended"),
alpha_init = NULL,
min_size = 5,
max_depth = 100,
verbose = 0,
save = c("best", "initial", "all"),
trimming = c("full", "partial", "none"),
best_trimming = c("none", "partial", "full")
)a list with the following components:
best_model: the optimal COVLMC
criterion: the criterion used to select the optimal VLMC
initial: the likelihood function used to select the optimal VLMC
results: a data frame with details about the pruning process
saved_models: a list of intermediate COVLMCs if save="initial" or
save="all". It contains an initial component with the large coVLMC
obtained first and an all component with a list of all the other coVLMC
obtained by pruning the initial one.
a discrete time series; can be numeric, character, factor and logical.
a data frame of covariates.
criterion used to select the best model. Either "BIC"
(default) or "AIC" (see details).
specifies the likelihood function, more precisely the way the
first few observations for which contexts cannot be calculated are
integrated in the likelihood. See loglikelihood() for details.
if non NULL used as the initial cut off parameter (in
quantile scale) to build the initial VLMC
integer >= 1 (default: 5). Tune the minimum number of
observations for a context in the growing phase of the context tree (see
covlmc() for details).
integer >= 1 (default: 100). Longest context considered in growing phase of the initial context tree (see details).
integer >= 0 (default: 0). Verbosity level of the pruning process.
specify which BIC models are saved during the pruning process.
The default value "best" asks the function to keep only the best model
according to the criterion. When save="initial" the function keeps in
addition the initial (complex) model which is then pruned during the
selection process. When save="all", the function returns all the models
considered during the selection process. See details for memory occupation.
specify the type of trimming used when saving the intermediate models, see details.
specify the type of trimming used when saving the best model and the initial one (see details).
covlmc objects tend to be large and saving all the models during the
search for the optimal model can lead to an unreasonable use of memory. To
avoid this problem, models are kept in trimmed form only using
trim.covlmc() with keep_model=FALSE. Both the initial model and the
best one are saved untrimmed. This default behaviour corresponds to
trimming="full". Setting trimming="partial" asks the function to use
keep_model=TRUE in trim.covlmc() for intermediate models. Finally,
trimming="none" turns off trimming, which is discouraged expected for
small data sets.
In parallel processing contexts (e.g. using foreach::%dopar%), the memory
occupation of the results can become very large as models tend to keep
environments attached to the formulas. In this situation, it is highly
recommended to trim all saved models, including the best one and the
initial one. This can be done via the best_trimming parameter whose
possible values are identical to the ones of trimming.
This function automates the process of fitting a large coVLMC to a discrete
time series with covlmc() and of pruning the tree (with cutoff() and
prune()) to get an optimal with respect to an information criterion. To
avoid missing long term dependencies, the function uses the max_depth
parameter as an initial guess but then relies on an automatic increase of the
value to make sure the initial context tree is only limited by the min_size
parameter. The initial value of the alpha parameter of covlmc() is also
set to a conservative value (0.5) to avoid prior simplification of the
context tree. This can be overridden by setting the alpha_init parameter to
a more adapted value.
Once the initial coVLMC is obtained, the cutoff() and prune() functions
are used to build all the coVLMC models that could be generated using smaller
values of the alpha parameter. The best model is selected from this
collection, including the initial complex tree, as the one that minimizes the
chosen information criterion.
covlmc(), cutoff() and prune()
pc <- powerconsumption[powerconsumption$week %in% 6:7, ]
dts <- cut(pc$active_power, breaks = c(0, quantile(pc$active_power, probs = c(0.5, 1))))
dts_cov <- data.frame(day_night = (pc$hour >= 7 & pc$hour <= 17))
dts_best_model_tune <- tune_covlmc(dts, dts_cov)
draw(as_covlmc(dts_best_model_tune))
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