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, ...)
| 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' |
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 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 |
model_output | data.frame with columns for the time index,
observations, mean-value for predictions, and independent variance for
predictions (if stats_only == FALSE or
save_covariance_matrix == TRUE) |
covariance_matrix | the full covariance matrix for predictions
(if save_covariance_matrix == TRUE) |
See block_gp for implementation details of the Gaussian process
regression.
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