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 = NULL, pred = NULL, norm = 2, E = 1:10,
tau = -1, tp = 1, num_neighbors = "e+1", stats_only = TRUE,
exclusion_radius = NULL, epsilon = NULL, silent = TRUE)s_map(time_series, lib = NULL, pred = NULL, norm = 2, E = 1,
tau = -1, tp = 1, num_neighbors = 0, theta = NULL, stats_only = TRUE,
exclusion_radius = NULL, epsilon = NULL, silent = TRUE,
save_smap_coefficients = FALSE)
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)
a 2-column matrix, data.frame, 2-element vector or string of row indice pairs, where each pair specifies the first and last *rows* of the time series to create the library. If not specified, all available rows are used
(same format as lib), but specifying the sections of the time series to forecast. If not specified, set equal to lib
the distance measure to use. see 'Details'
the embedding dimensions to use for time delay embedding
the time-delay offset to use for time delay embedding
the prediction horizon (how far ahead to forecast)
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 set this parameter to E+1.)
specify whether to output just the forecast statistics or the raw predictions for each run
excludes vectors from the search space of nearest neighbors if their *time index* is within exclusion_radius (NULL turns this option off)
Deprecated.
prevents warning messages from being printed to the R console
the nonlinear tuning parameter (theta is only relevant if method == "s-map")
specifies whether to include the s_map coefficients with the output
For simplex, if stats_only = TRUE: a data.frame with components for the parameters and forecast statistics:
| E | embedding dimension |
| tau | embedding time offset |
| 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 |
For simplex, if stats_only = FALSE: a named list with
data.frame "stats" specified above, and named list "model_output":
| model_output | named list with data.frames for each model. Columns include the time index, observations, predictions, and estimated prediction variance |
For s_map, if stats_only = TRUE,
the same data.frame as for simplex, but with additional column:
| theta | the nonlinear tuning parameter |
For s_map, if save_smap_coefficients = TRUE, a named list with
data.frame "stats" specified above and the following list items:
| smap_coefficients | data.frame with columns for the s-map coefficients |
| smap_coefficient_covariances | list of covariance matrices for the s-map coefficients |
For s_map, if stats_only = FALSE, a named list with
data.frame "stats" specified above, and named list "model_output":
| model_output | named list with data.frames for each model. Columns include the time index, observations, predictions, and estimated prediction variance |
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 (only option currently available) uses the "L2 norm",
Euclidean distance:
$$distance(a,b) := \sqrt{\sum_i{(a_i - b_i)^2}}
$$
# NOT RUN {
ts <- block_3sp$x_t
simplex(ts, lib = c(1, 100), pred = c(101, 190))
ts <- block_3sp$x_t
simplex(ts, stats_only = FALSE)
ts <- block_3sp$x_t
s_map(ts, E = 2)
ts <- block_3sp$x_t
s_map(ts, E = 2, theta = 1, save_smap_coefficients = TRUE)
# }
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