The rEDM
package is a collection of methods for Empirical Dynamic
Modeling (EDM). EDM is based on the mathematical theory of
reconstructing attractor manifolds from time series data, with
applications to forecasting, causal inference, and more. It is based on
research software developed for the Sugihara Lab (University
of California San Diego, Scripps Institution of Oceanography).
This package implements an R wrapper of EDM tools from the cppEDM library.
Functionality includes:
- Simplex projection (Sugihara and May 1990)
- Sequential Locally Weighted Global Linear Maps (S-map) (Sugihara 1994)
- Multivariate embeddings (Dixon et. al. 1999)
- Convergent cross mapping (Sugihara et. al. 2012)
- Multiview embedding (Ye and Sugihara 2016)
You can install rEDM from CRAN with:
install.packages("rEDM")
or the development version from github with:
install.packages("devtools")
devtools::install_github("SugiharaLab/rEDM")
We begin by looking at annual time series of sunspots:
df <- data.frame(yr = as.numeric(time(sunspot.year)),
sunspot_count = as.numeric(sunspot.year))
plot(df$yr, df$sunspot_count, type = "l",
xlab = "year", ylab = "sunspots")
First, we use EmbedDimension()
to determine the optimal embedding
dimension, E:
library(rEDM) # load the package
# If you're new to the rEDM package, please check out the tutorial:
# vignette("rEDM-tutorial")
E.opt = EmbedDimension( dataFrame = df, # input data
lib = "1 280", # portion of data to train
pred = "1 280", # portion of data to predict
columns = "sunspot_count",
target = "sunspot_count" )
E.opt
# E rho
# 1 1 0.7397
# 2 2 0.8930
# 3 3 0.9126
# 4 4 0.9133
# 5 5 0.9179
# 6 6 0.9146
# 7 7 0.9098
# 8 8 0.9065
# 9 9 0.8878
# 10 10 0.8773
Highest predictive skill is found between E = 3
and E = 6
. Since we
generally want a simpler model, if possible, we use E = 3
to forecast
the last 1/3 of data based on training (attractor reconstruction) from
the first 2/3.
simplex <- Simplex( dataFrame = df,
lib = "1 190", # portion of data to train
pred = "191 287", # portion of data to predict
columns = "sunspot_count",
target = "sunspot_count",
E = 3 )
plot( df$yr, df$sunspot_count, type = "l", lwd = 2,
xlab = "year", ylab = "sunspots")
lines( simplex$yr, simplex$Predictions, col = "red", lwd = 2)
legend( 'topleft', legend = c( "Observed", "Predicted (year + 1)" ),
fill = c( 'black', 'red' ), bty = 'n', cex = 1.3 )
Please see the package vignettes for more details:
browseVignettes("rEDM")
Sugihara G. and May R. 1990. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature, 344:734–741.
Sugihara G. 1994. Nonlinear forecasting for the classification of natural time series. Philosophical Transactions: Physical Sciences and Engineering, 348 (1688) : 477–495.
Dixon, P. A., M. Milicich, and G. Sugihara, 1999. Episodic fluctuations in larval supply. Science 283:1528–1530.
Sugihara G., May R., Ye H., Hsieh C., Deyle E., Fogarty M., Munch S., 2012. Detecting Causality in Complex Ecosystems. Science 338:496-500.