simplex {rEDM} | R Documentation |
simplex
uses time delay embedding on a single time series to
generate an attractor reconstruction, and then applies the simplex
projection algorithm to make forecasts.
s_map
is similar to simplex
, but uses the S-map algorithm to
make forecasts.
simplex(time_series, lib = c(1, NROW(time_series)), pred = lib, norm_type = c("L2 norm", "L1 norm", "P norm"), P = 0.5, E = 1:10, tau = 1, tp = 1, num_neighbors = "e+1", stats_only = TRUE, exclusion_radius = NULL, epsilon = NULL, silent = FALSE) s_map(time_series, lib = c(1, NROW(time_series)), pred = lib, norm_type = c("L2 norm", "L1 norm", "P norm"), P = 0.5, E = 1, tau = 1, tp = 1, num_neighbors = 0, theta = c(0, 1e-04, 3e-04, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 0.5, 0.75, 1, 1.5, 2, 3, 4, 6, 8), stats_only = TRUE, exclusion_radius = NULL, epsilon = NULL, silent = FALSE, save_smap_coefficients = FALSE)
time_series |
either a vector to be used as the time series, or a data.frame or matrix with at least 2 columns (in which case the first column will be used as the time index, and the second column as the time series) |
lib |
a 2-column matrix (or 2-element vector) where each row specifes the first and last *rows* of the time series to use for attractor reconstruction |
pred |
(same format as lib), but specifying the sections of the time series to forecast. |
norm_type |
the distance function to use. see 'Details' |
P |
the exponent for the P norm |
E |
the embedding dimensions to use for time delay embedding |
tau |
the lag to use for time delay embedding |
tp |
the prediction horizon (how far ahead to forecast) |
num_neighbors |
the number of nearest neighbors to use (any of "e+1", "E+1", "e + 1", "E + 1" will peg this parameter to E+1 for each run, any value < 1 will use all possible neighbors.) |
stats_only |
specify whether to output just the forecast statistics or the raw predictions for each run |
exclusion_radius |
excludes vectors from the search space of nearest neighbors if their *time index* is within exclusion_radius (NULL turns this option off) |
epsilon |
excludes vectors from the search space of nearest neighbors if their *distance* is farther away than epsilon (NULL turns this option off) |
silent |
prevents warning messages from being printed to the R console |
theta |
the nonlinear tuning parameter (note that theta = 0 is equivalent to an autoregressive model of order E.) |
save_smap_coefficients |
specifies whether to include the s_map coefficients with the output (and forces the full output as if stats_only were set to FALSE) |
simplex
is typically applied, and the embedding dimension
varied, to find an optimal embedding dimension for the data. Thus, the
default parameters are set so that passing a time series as the only argument
will run over E = 1:10 (embedding dimension), using leave-one-out
cross-validation over the whole time series, and returning just the forecast
statistics.
s_map
is typically applied, with fixed embedding dimension, and theta
varied, to test for nonlinear dynamics in the data. Thus, the default
parameters are set so that passing a time series as the only argument will
run over a default list of thetas (0, 0.0001, 0.0003, 0.001, 0.003, 0.01,
0.03, 0.1, 0.3, 0.5, 0.75, 1.0, 1.5, 2, 3, 4, 6, and 8), using E = 1,
leave-one-out cross-validation over the whole time series, and returning just
the forecast statistics.
norm_type "L2 norm" (default) uses the typical Euclidean distance:
distance(a, b) := √(∑(a_i - b_i)^2)
norm_type "L1 norm" uses the Manhattan distance:
distance(a, b) := ∑|a_i - b_i|
norm type "P norm" uses the LP norm, generalizing the L1 and L2 norm to use $p$ as the exponent:
distance(a, b) := (∑(a_i - b_i)^p)^(1/p)
For simplex
, if stats_only = TRUE
, then a data.frame
with components for the parameters and forecast statistics:
E | embedding dimension |
tau | time lag |
tp | prediction horizon |
nn | number of neighbors |
num_pred | number of predictions |
rho | correlation coefficient between observations and predictions |
mae | mean absolute error |
rmse | root mean square error |
perc | percent correct sign |
p_val | p-value that rho is significantly greater than 0 using Fisher's z-transformation |
const_rho | same as rho, but for the constant predictor |
const_mae | same as mae, but for the constant predictor |
const_rmse | same as rmse, but for the constant predictor |
const_perc | same as perc, but for the constant predictor |
const_p_val | same as p_val, but for the constant predictor |
Otherwise, a list where the number of elements is equal to the number of runs (unique parameter combinations). Each element is a list with the following components:
params | data.frame of parameters (E, tau, tp, nn) |
model_output | data.frame with columns for the time index, observations, and predictions |
stats | data.frame of forecast statistics |
For s_map
, the same as for simplex
, but with an additional
column for the value of theta. If stats_only = FALSE
and
save_smap_coefficients = TRUE
, then a matrix of S-map coefficients
will appear in the full output.
data("two_species_model") ts <- two_species_model$x[1:200] simplex(ts, lib = c(1, 100), pred = c(101, 200)) data("two_species_model") ts <- two_species_model$x[1:200] #' simplex(ts, stats_only = FALSE) data("two_species_model") ts <- two_species_model$x[1:200] s_map(ts, E = 2) data("two_species_model") ts <- two_species_model$x[1:200] s_map(ts, E = 2, theta = 1, save_smap_coefficients = TRUE)