multiview applies the method described in Ye & Sugihara (2016) for
forecasting, wherein multiple attractor reconstructions are tested, and a
single nearest neighbor is selected from each of the top k
reconstructions to produce final forecasts.
multiview(block, lib = c(1, floor(NROW(block)/2)), pred = c(floor(NROW(block)/2) + 1, NROW(block)), norm = 2, E = 3, tau = 1, tp = 1, max_lag = 3, num_neighbors = "e+1", k = "sqrt", na.rm = FALSE, target_column = 1, stats_only = TRUE, save_lagged_block = FALSE, first_column_time = FALSE, exclusion_radius = NULL, silent = FALSE)
| 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 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) |
| max_lag | the maximum number of lags to use for variable combinations. So if max_lag == 3, a variable X will appear with lags X[t], X[t - tau], X[t - 2*tau] |
| 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.) |
| k | the number of embeddings to use ("sqrt" will use k = floor(sqrt(m)), "all" or values less than 1 will use k = m) |
| na.rm | logical. Should missing values (including `NaN`` be omitted from the calculations?) |
| 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 |
| save_lagged_block | specify whether to output the lagged block that
is constructed as part of running |
| 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) |
| silent | prevents warning messages from being printed to the R console |
A data.frame with components for the parameters and forecast statistics:
| E | embedding dimension |
| tau | time lag |
| tp | prediction horizon |
| nn | number of neighbors |
| k | number of embeddings used |
E | embedding dimension |
tau | time lag |
tp | prediction horizon |
nn | number of neighbors |
k | number of embeddings used |
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, predictions, and estimated prediction variance
(if stats_only == FALSE) |
embeddings | list of the columns used in each of the embeddings
that comprise the model (if stats_only == FALSE) |
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.
The default parameters are set so that, given a matrix of time series, forecasts will be produced for the first column. By default, all possible combinations of the columns are used for the attractor construction, the k = sqrt(m) heuristic will be used, forecasts will be one time step ahead. 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 to use the first half of the data for the "library" and to predict over the second half of the data. Unless otherwise set, the output will be just the forecast statistics.
norm = 2 (default) uses the "L2 norm", Euclidean distance:
$$distance(a,b) := \sqrt{\sum_i{(a_i - b_i)^2}}
$$
norm = 1 uses the "L1 norm", Manhattan distance:
$$distance(a,b) := \sum_i{|a_i - b_i|}
$$
Other values generalize the L1 and L2 norm to use the given argument as the
exponent, P, as:
$$distance(a,b) := \sum_i{(a_i - b_i)^P}^{1/P}
$$
#> Warning: Found overlap between lib and pred. Enabling cross-validation with exclusion radius = 0.#> E tau tp nn k num_pred rho mae rmse perc p_val #> 1 3 1 1 4 1 99 0.8463247 0.3514340 0.4589715 0.8484848 2.000945e-34 #> 2 3 1 1 4 3 99 0.9023856 0.2720415 0.3535066 0.8989899 2.955477e-48 #> 3 3 1 1 4 8 99 0.9084469 0.2592693 0.3400605 0.9393939 2.262100e-50