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)

## 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 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 (same format as lib), but specifying the sections of the time series to forecast. the distance measure to use. see 'Details' the embedding dimensions to use for time delay embedding the lag to use for time delay embedding the prediction horizon (how far ahead to forecast) 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] 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.) the number of embeddings to use ("sqrt" will use k = floor(sqrt(m)), "all" or values less than 1 will use k = m) logical. Should missing values (including NaN be omitted from the calculations?) the index (or name) of the column to forecast specify whether to output just the forecast statistics or the raw predictions for each run specify whether to output the lagged block that is constructed as part of running multiview indicates whether the first column of the given block is a time column (and therefore excluded when indexing) excludes vectors from the search space of nearest neighbors if their *time index* is within exclusion_radius (NULL turns this option off) prevents warning messages from being printed to the R console

## Value

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 )

## Details

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: $$distance(a,b) := \sum_i{(a_i - b_i)^P}^{1/P}$$

## Examples

data("block_3sp")
block <- block_3sp[, c(2, 5, 8)]
multiview(block, k = c(1, 3, "sqrt"))#> 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
`