Extreme Granger-causal graph parallelized estimate — Extreme_causality_graph

This function estimates the causal graph (path diagram) between a set of time series, using doFuture parallellization for computational efficiency. It does the same as Extreme_causality_graph(), but potentially faster if appropriate parallelization is used.

Usage

Extreme_causality_graph_parallel(
  w,
  max_causal_lag = 1,
  max_confounder_lag = 0,
  nu_x = 0.3,
  q_y = 0.2,
  q_z = 0.1,
  instant = FALSE,
  both_tails = TRUE,
  p_value_based = FALSE,
  p_value_cutoff = 0.05,
  strategy = c("sequential", "multisession", "multicore", "mixed"),
  n_workers = NULL
)

Arguments

w: A data.frame of all time series, which should be numeric and of the same length.
max_causal_lag: The time delay for the effect from x to y. This is the coefficient 'p' in Appendix A of the manuscript.
max_confounder_lag: The lag from $Z$ to $(X, Y)$. If the common cause has different lags to $X$ and $Y$, it may cause spurious causality between $X$ and $Y$. Ensure max_confounder_lag is larger than this lag.
nu_x: The coefficient $\tau_X$ or $k_n$ in the manuscript, defined as $k_n = \lfloor n^{\nu_x} \rfloor$. If strong hidden confounding is expected, set nu_x to 0.4 or 0.5.
q_y: The coefficient $\tau_y = q_y \times n$, describing the conditioning on $Y_t$. For large auto-correlation in $Y$, set q_y to 0.1 or less. Note that in the manuscript, $q_y$ is defined as 1 - q_y.
q_z: The coefficient $\tau_z = q_z \times n$, describing the conditioning on $Z_t$. This is irrelevant if z is NULL. For strong confounding effects, set q_z to 0.2 or 0.3. Note that in the manuscript, $q_z$ is defined as 1 - q_z.
instant: Whether instantaneous effects should be captured; defaults to FALSE.
both_tails: Set to TRUE to consider both large and extremely negative values. For example, in GARCH models, both tails are of interest, while in VAR models, only large values might be relevant.
p_value_based: If FALSE, Algorithm 1 is used for inferring the edges. If TRUE, the testing procedure with a cut-off p-value of p_value_cutoff is used for detecting the presence of an edge. These procedures typically output similar results, but the testing procedure is significantly slower.
p_value_cutoff: P-value cut-off level to reject the absence of an edge in the estimated graph.
strategy: One of "sequential" (default), "multisession", "multicore", or "mixed".
n_workers: A positive numeric scalar or a function specifying the maximum number of parallel futures that can be active at the same time before blocking. If a function, it is called without arguments when the future is created and its value is used to configure the workers. The function should return a numeric scalar. Defaults to future::availableCores()-1 if NULL (default), with "multicore" constraint in the relevant case. Ignored if strategy=="sequential".

Value

A named list containing:

G: A graph defined by its edges. Each row corresponds to an edge from the first column pointing to the second column. Use graph <- graph_from_edgelist(G$G) from the igraph package to obtain the graph environment;
weights: Weights corresponding to each edge, representing how close the coefficient $\hat{\Gamma}_{X\rightarrow Y | Z}$ is to 1. If $\hat{\Gamma}_{X\rightarrow Y | Z} = 1$, the weight is 1. The weight is 0 if $\hat{\Gamma}_{X\rightarrow Y | Z} = (1 + \hat{\Gamma}^{baseline}_{X\rightarrow Y | Z}) / 2$.