simplex: Perform univariate forecasting
In ha0ye/rEDM: Applications of Empirical Dynamic Modeling from Time Series

Description Usage Arguments Details Value Examples

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 = 2, 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 = 2, 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 specifies 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`	the distance measure to use. see 'Details'
`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. Note that the default value will change depending on the method selected. (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 (theta is only relevant if method == "s-map")
`save_smap_coefficients`	specifies whether to include the s_map coefficients with the output (and forces stats_only = FALSE, as well)

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 = 2 (default) uses the "L2 norm", Euclidean distance:

distance(a, b) := √(∑(a_i - b_i)^2)

norm = 1 uses the "L1 norm", Manhattan distance:

distance(a, b) := ∑|a_i - b_i|

Other values generalize the L1 and L2 norm to use the given argument as the exponent, P, as:

distance(a, b) := (∑(a_i - b_i)^P)^(1/P)

For simplex, 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_pred_rho`	same as `rho`, but for the constant predictor
`const_pred_mae`	same as `mae`, but for the constant predictor
`const_pred_rmse`	same as `rmse`, but for the constant predictor
`const_pred_perc`	same as `perc`, but for the constant predictor
`const_p_val`	same as `p_val`, but for the constant predictor
`model_output`	data.frame with columns for the time index, observations, predictions, and estimated prediction variance (if `stats_only == FALSE`)

For s_map, the same as for simplex, but with additional columns:

`theta`	the nonlinear tuning parameter
`smap_coefficients`	data.frame with columns for the s-map coefficients (if `save_smap_coefficients == TRUE`)
`smap_coefficient_covariances`	list of covariance matrices for the s-map coefficients (if `save_smap_coefficients == TRUE`)

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)