Extreme Granger-causal graph estimate — Extreme_causality

This function estimates the causal graph (path diagram) between a set of time series. Use Extreme_causality_graph_parallel() instead, for faster parallel computations.

Usage

Extreme_causality_graph(
  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
)

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.

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 $\hat{\Gamma}_{X\rightarrow Y | Z} = (1 + \hat{\Gamma}^{baseline}_{X\rightarrow Y | Z}) / 2$.