tde_gp is used in the same vein as simplex or s_map to do time series forecasting using Gaussian processes. Here, the default parameters are set so that passing a time series as the only argument will run over E = 1:10 (embedding dimension) to created a lagged block, and passing in that block and all remaining arguments into block_gp.

tde_gp(time_series, lib = c(1, NROW(time_series)), pred = lib,
  E = 1:10, tau = 1, tp = 1, phi = 0, v_e = 0, eta = 0,
  fit_params = TRUE, stats_only = TRUE,
  save_covariance_matrix = FALSE, silent = FALSE, ...)

Arguments

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.

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)

phi

length-scale parameter. see 'Details'

v_e

noise-variance parameter. see 'Details'

eta

signal-variance parameter. see 'Details'

fit_params

specify whether to use MLE to estimate params over the lib

stats_only

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

save_covariance_matrix

specifies whether to include the full covariance matrix with the output (and forces the full output as if stats_only were set to FALSE)

silent

prevents warning messages from being printed to the R console

...

other parameters. see 'Details'

Value

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

E
embedding dimension
tau
time lag
tp
prediction horizon
phi
length-scale parameter
v_e
noise-variance parameter
eta
signal-variance parameter
fit_params
whether params were fitted or not
num_pred
number of predictions
rho
correlation coefficient between observations andpredictions
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
model_output
data.frame with columns for the time index,
observations, mean-value for predictions, and independent variance forpredictions (if
stats_only == FALSEor
save_covariance_matrix == TRUE
)
covariance_matrix
the full covariance matrix for predictions
(ifsave_covariance_matrix == TRUE
)

Details

See block_gp for implementation details of the Gaussian process regression.

Examples

data("two_species_model") ts <- two_species_model$x[1:200] tde_gp(ts, lib = c(1, 100), pred = c(101, 200), E = 5)
#> E tau embedding tp phi v_e eta fit_params num_pred #> 1 5 1 1, 2, 3, 4, 5 1 0.4597587 -5.685457 6.904747 TRUE 99 #> rho mae rmse perc p_val #> 1 0.9977515 0.01071626 0.01289583 1 6.917437e-243