Fit an optimal Variable Length Markov Chain with Covariates (coVLMC)

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).

Usage

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")
)

Arguments

x: a discrete time series; can be numeric, character, factor and logical.
covariate: a data frame of covariates.
criterion: criterion used to select the best model. Either "BIC" (default) or "AIC" (see details).
initial: 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.
alpha_init: if non NULL used as the initial cut off parameter (in quantile scale) to build the initial VLMC
min_size: 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).
max_depth: integer >= 1 (default: 100). Longest context considered in growing phase of the initial context tree (see details).
verbose: integer >= 0 (default: 0). Verbosity level of the pruning process.
save: 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.
trimming: specify the type of trimming used when saving the intermediate models, see details.
best_trimming: specify the type of trimming used when saving the best model and the initial one (see details).

Value

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.

Details

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.

Memory occupation

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.

Examples

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))
#> *
#> +-- (0,1.26] (collapsing: 0.0003608)
#> |   +-- (0,1.26] (0.0117 [ -2.603 ])
#> |   '-- (1.26,6.48] (1 [ -1.52 ])
#> '-- (1.26,6.48]
#>     +-- (0,1.26] (0.4311 [ 1.705 ])
#>     '-- (1.26,6.48]
#>         +-- (0,1.26] (0.5816 [ 1.609 ])
#>         '-- (1.26,6.48] (collapsing: 7.999e-05)
#>             +-- (0,1.26] (0.0006256 [ 0.47 2.862 ])
#>             '-- (1.26,6.48] (0.9555 [ 2.856 ])