Research Article

Prediction after a Horizon of Predictability: Nonpredictable Points and Partial Multistep Prediction for Chaotic Time Series

Table 6

Abbreviations for the methods to identify nonpredictable points.

fpForced prediction. Forcing the algorithm to make a prediction at each intermediate point, ignoring nonpredictable points
cmClose motifs. Analyzing the number of “close motifs” of each intermediate point
enEntropy. Analyzing the entropy of the sets of possible predicted values of each intermediate point
apA priori. Using a priori information
lrLogistic regression. Using a logistic regression classifier
svmSupport vector machine. Using an SVM classifier employing polynomial kernel functions
dtDecision tree. Applying a decision tree employing an entropy criterion without any restriction on the tree depth to the features of the sets of possible predicted values
knnK-nearest-neighbors. Applying a k-nearest-neighbors classifier is applied to the features of the sets of possible predicted values; k-nearest-neighbors value is equal to 3
mlpMultilayer perceptron. Applying a multilayer perceptron containing 8 hidden layers and utilizes a sigmoidal activation function to the features of the sets of possible predicted values
adbAdaBoost. Assembling logistic regression classifiers using AdaBoost
adblrAdaBoost + logistic regression. Logistic regression classifiers are assembled with AdaBoost
adbsvmAdaBoost + SVM. Assembling SVM classifiers using AdaBoost
lrsLogistic regression, stacking. Stacking of logistic regression classifiers
lrvLogistic regression, voting. Assembling logistic regression classifiers by voting
dbscanDBSCAN. Clustering the sets of possible predicted values at each intermediate point using DBSCAN and calculating the growth rate of the total number of clusters over several consecutive points
wshrtWishart. Clustering the sets of possible predicted values at each intermediate point using Wishart clustering and calculating the growth rate of the total number of clusters over several consecutive points
cwatCompare weighted average, trajectories. Comparing the main predicted trajectory with a weighted average of other predicted trajectories
amdAverage modulus of difference. Calculating an average of modulus of a difference
wamdWeighted average modulus of difference. Calculating a weighted average of modulus of a difference
wamdtWeighted average modulus of difference, trajectory. Comparing a weighted average of modulus of a difference of the main trajectory to that of other trajectories
rgRapid growth. The spread grows monotonically over several consecutive points
rgdbscanRapid growth, DBSCAN. DBSCAN is used to obtain centers of clusters of possible predicted values
rgwshrtRapid growth, Wishart clustering. Wishart clustering is used to obtain centers of clusters of possible predicted values