rEDM (version 0.4.7)

block_lnlp: Perform generalized forecasting using simplex projection or s-map

Description

block_lnlp uses multiple time series given as input to generate an attractor reconstruction, and then applies the simplex projection or s-map algorithm to make forecasts. This method generalizes the simplex and s-map routines, and allows for "mixed" embeddings, where multiple time series can be used as different dimensions of an attractor reconstruction.

Usage

block_lnlp(block, lib = c(1, NROW(block)), pred = lib, norm_type = c("L2 norm", "L1 norm", "P norm"), P = 0.5, method = c("simplex", "s-map"), tp = 1, num_neighbors = "e+1", columns = NULL, target_column = 1, stats_only = TRUE, first_column_time = FALSE, exclusion_radius = NULL, epsilon = NULL, theta = NULL, silent = FALSE, save_smap_coefficients = FALSE, short_output = FALSE)

Arguments

block

either a vector to be used as the time series, or a data.frame or matrix where each column is a 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

method

the prediction method to use. see 'Details'

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.)

columns

either a vector with the columns to use (indices or names), or a list of such columns

target_column

the index (or name) of the column to forecast

stats_only

specify whether to output just the forecast statistics or the raw predictions for each run

first_column_time

indicates whether the first column of the given block is a time column (and therefore excluded when indexing)

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)

theta

the nonlinear tuning parameter (theta is only relevant if method == "s-map")

silent

prevents warning messages from being printed to the R console

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)

short_output

specifies whether to return a truncated output data.frame whose rows only include the predictions made and not the whole input block

Value

If stats_only, then a data.frame with components for the parameters and forecast statistics:

cols

embedding

tp

prediction horizon

nn

number of neighbors

num_pred

number of predictions

rho

correlation coefficient between observations and predictions

mae

mean absolute error

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

smap_coefficients

matrix with the s_map coefficients (first E columns are for the E lags, and the (E+1)th column is the constant)

stats

data.frame of forecast statistics (num_pred, rho, mae, rmse)

Details

The default parameters are set so that passing a vector as the only argument will use that vector to predict itself one time step ahead. If a matrix or data.frame is given as the only argument, the first column will be predicted, using the remaining columns as the embedding. Rownames will be converted to numeric if possible to be used as the time index, otherwise 1:NROW will be used instead. The default lib and pred are for 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: $$distance(a,b) := \sqrt{\sum_i{(a_i - b_i)^2}}$$ norm_type "L1 norm" uses the Manhattan distance: $$distance(a,b) := \sum_i{|a_i - b_i|}$$ norm type "P norm" uses the P norm, generalizing the L1 and L2 norm to use $p$ as the exponent: $$distance(a,b) := \sum_i{(a_i - b_i)^p}^{1/p}$$

method "simplex" (default) uses the simplex projection forecasting algorithm

method "s-map" uses the s-map forecasting algorithm

Examples

data("two_species_model")
block <- two_species_model[1:200,]
block_lnlp(block, columns = c("x", "y"), first_column_time = TRUE)