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Title:

Variable-Lag Time Series Causality Inference Framework

Version:

0.1.5

Description:

A framework to infer causality on a pair of time series of real numbers based on variable-lag Granger causality and transfer entropy. Typically, Granger causality and transfer entropy have an assumption of a fixed and constant time delay between the cause and effect. However, for a non-stationary time series, this assumption is not true. For example, considering two time series of velocity of person A and person B where B follows A. At some time, B stops tying his shoes, then running to catch up A. The fixed-lag assumption is not true in this case. We propose a framework that allows variable-lags between cause and effect in Granger causality and transfer entropy to allow them to deal with variable-lag non-stationary time series. Please see Chainarong Amornbunchornvej, Elena Zheleva, and Tanya Berger-Wolf (2021) <doi:10.1145/3441452> when referring to this package in publications.

License:

GPL-3

URL:

https://github.com/DarkEyes/VLTimeSeriesCausality

BugReports:

https://github.com/DarkEyes/VLTimeSeriesCausality/issues

Language:

en-US

Encoding:

UTF-8

Depends:

R (≥ 3.5.0), dtw, tseries, RTransferEntropy

Imports:

ggplot2 (≥ 3.0)

Suggests:

knitr, rmarkdown, markdown

VignetteBuilder:

knitr

RoxygenNote:

7.3.1

NeedsCompilation:

Packaged:

2024-05-28 02:59:30 UTC; 006005

Author:

Chainarong Amornbunchornvej

[aut, cre]

Maintainer:

Chainarong Amornbunchornvej <grandca@gmail.com>

Repository:

CRAN

Date/Publication:

2024-05-28 04:20:02 UTC

GrangerFunc

Description

GrangerFunc is a Granger Causality function. It tests whether X Granger-causes Y.

Usage

GrangerFunc(
  Y,
  X,
  maxLag = 1,
  alpha = 0.05,
  autoLagflag = TRUE,
  gamma = 0.5,
  family = gaussian
)

Arguments

Y

is a numerical time series of effect

X

is a numerical time series of cause

maxLag

is a maximum possible time delay. The default is 1.

alpha

is a significance level of F-test to determine whether X Granger-causes Y. The default is 0.05.

autoLagflag

is a flag for enabling the automatic lag inference function. The default is true. If it is set to be true, then maxLag is set automatically using cross-correlation. Otherwise, if it is set to be false, then the function takes the maxLag value to infer Granger causality.

gamma

is a parameter to determine whether X Granger-causes Y using BIC difference ratio.

family

is a parameter of family of function for Generalized Linear Models function (glm). The default is gaussian.

Value

This function returns of whether X Granger-causes Y.

ftest

F-statistic of Granger causality.

p.val

A p-value from F-test.

BIC_H0

Bayesian Information Criterion (BIC) derived from Y regressing on Y past.

BIC_H1

Bayesian Information Criterion (BIC) derived from Y regressing on Y,X past.

XgCsY

The flag is true if X Granger-causes Y using BIC difference ratio where BICDiffRatio >= gamma.

XgCsY_ftest

The flag is true if X Granger-causes Y using F-test where p.val>=alpha.

XgCsY_BIC

The flag is true if X Granger-causes Y using BIC where BIC_H0>=BIC_H1.

maxLag

A maximum possible time delay.

H0

glm object of Y regressing on Y past.

H1

glm object of Y regressing on Y,X past.

BICDiffRatio

Bayesian Information Criterion difference ratio: (BIC_H0-BIC_H1)/BIC_H0.

Examples

# Generate simulation data
TS <- SimpleSimulationVLtimeseries()
# Run the function
out<-GrangerFunc(Y=TS$Y,X=TS$X)

MultipleSimulationVLtimeseries

Description

MultipleSimulationVLtimeseries is a support function for generating a set of time series TS[,1],...TS[,10]. TS[,1],TS[,2],TS[,3] are causes X time series that are generated independently. The rest of time series are Y time series that are effects of some causes TS[,1],TS[,2],TS[,3]. TS[,1] causes TS[,4],TS[,7],TS[,8], and TS[,10]. TS[,2] causes TS[,5],TS[,7],TS[,9], and TS[,10]. TS[,3] causes TS[,6],TS[,8],TS[,9], and TS[,10].

Usage

MultipleSimulationVLtimeseries(
  n = 200,
  lag = 5,
  YstFixInx = 110,
  YfnFixInx = 170,
  XpointFixInx = 100,
  arimaFlag = TRUE,
  seedVal = -1
)

Arguments

n

is length of time series.

lag

is a time lag between X and Y s.t. Y[t] is approximately X[t-lag].

YstFixInx

is the starting point of variable lag part.

YfnFixInx

is the end point of variable lag part.

XpointFixInx

is a point in X s.t. Y[YstFixInx:YfnFixInx]= X[XpointFixInx] .

arimaFlag

is ARMA model flag. If it is true, then X is generated by ARMA model. If it is false, then X is generated by sampling of the standard normal distribution.

seedVal

is a seed parameter for generating random noise.

Value

This function returns a list of time series TS.

Examples

# Generate simulation data
TS <- MultipleSimulationVLtimeseries()

SimpleSimulationVLtimeseries

Description

SimpleSimulationVLtimeseries is a support function for generating time series X,Y where X VL-Granger-causes Y.

Usage

SimpleSimulationVLtimeseries(
  n = 200,
  lag = 5,
  YstFixInx = 110,
  YfnFixInx = 170,
  XpointFixInx = 100,
  arimaFlag = TRUE,
  seedVal = -1,
  expflag = FALSE,
  causalFlag = TRUE
)

Arguments

n

is length of time series.

lag

is a time lag between X and Y s.t. Y[t] is approximately X[t-lag].

YstFixInx

is the starting point of variable lag part.

YfnFixInx

is the end point of variable lag part.

XpointFixInx

is a point in X s.t. Y[YstFixInx:YfnFixInx]= X[XpointFixInx] .

arimaFlag

is ARMA model flag. If it is true, then X is generated by ARMA model. If it is false, then X is generated by sampling of the standard normal distribution.

seedVal

is a seed parameter for generating random noise. If it is not -1, then the rnorm is set the random seed with seedVal.

expflag

is the flag to set the relation between Y[i+lag] and X[i]. If it is false Y,X has a linear relation, otherwise, they have an exponential relation.

causalFlag

is a flag. If it is true, then X causes Y. Otherwise, X,Y have no causal relation.

Value

This function returns a list of time series X,Y where X VL-Granger-causes Y.

Examples

# Generate simulation data
TS <- SimpleSimulationVLtimeseries()

TSNANNearestNeighborPropagation

Description

TSNANNearestNeighborPropagation is a function that fills NA values with nearest real values in the past ( or future if the first position of time series is NA), for time series X.

Usage

TSNANNearestNeighborPropagation(X)

Arguments

X

is a T-by-D matrix numerical time series

Value

This function returns a list of following relation variables below.

Xout

is a T-by-D matrix numerical time series that all NAN have been filled with nearest real values.

Examples

# Load example data

z<-1:20
z[2:5]<-NA
z<-TSNANNearestNeighborPropagation(z)

VLGrangerFunc

Description

VLGrangerFunc is a Variable-lag Granger Causality function. It tests whether X VL-Granger-causes Y.

Usage

VLGrangerFunc(
  Y,
  X,
  alpha = 0.05,
  maxLag,
  gamma = 0.5,
  autoLagflag = TRUE,
  family = gaussian
)

Arguments

Y

is a numerical time series of effect

X

is a numerical time series of cause

alpha

is a significance level of f-test to determine whether X Granger-causes Y. The default is 0.05.

maxLag

is a maximum possible time delay. The default is 0.2*length(Y).

gamma

is a parameter to determine whether X Granger-causes Y using BIC difference ratio. The default is 0.5.

autoLagflag

family

is a parameter of family of function for Generalized Linear Models function (glm). The default is gaussian.

Value

This function returns of whether X Granger-causes Y.

ftest

F-statistic of Granger causality.

p.val

A p-value from F-test.

BIC_H0

Bayesian Information Criterion (BIC) derived from Y regressing on Y past.

BIC_H1

Bayesian Information Criterion (BIC) derived from Y regressing on Y,X past.

XgCsY

The flag is true if X Granger-causes Y using BIC difference ratio where BICDiffRatio >= gamma.

XgCsY_ftest

The flag is true if X Granger-causes Y using f-test where p.val>=alpha.

XgCsY_BIC

The flag is true if X Granger-causes Y using BIC where BIC_H0>=BIC_H1.

maxLag

A maximum possible time delay.

H0

glm object of Y regressing on Y past.

H1

glm object of Y regressing on Y,X past.

follOut

is a list of variables from function followingRelation.

BICDiffRatio

Bayesian Information Criterion difference ratio: (BIC_H0-BIC_H1)/BIC_H0.

Examples

# Generate simulation data
TS <- SimpleSimulationVLtimeseries()
# Run the function
out<-VLGrangerFunc(Y=TS$Y,X=TS$X)

VLTransferEntropy

Description

VLTransferEntropy is a Variable-lag Transfer Entropy function. It tests whether X VL-Transfer-Entropy-causes Y.

Usage

VLTransferEntropy(
  Y,
  X,
  maxLag,
  nboot = 0,
  lx = 1,
  ly = 1,
  VLflag = TRUE,
  autoLagflag = TRUE,
  alpha = 0.05
)

Arguments

Y

is a numerical time series of effect

X

is a numerical time series of cause

maxLag

is a maximum possible time delay. The default is 0.2*length(Y).

nboot

is a number of times of bootstrapping for RTransferEntropy::transfer_entropy() function.

lx, ly

are lag parameters of RTransferEntropy::transfer_entropy().

VLflag

is a flag of Transfer Entropy choice: either VLflag=TRUE for VL-Transfer Entropy or VLflag=FALSE for Transfer Entropy.

autoLagflag

alpha

is a significant-level threshold for TE bootstrapping by Dimpfl and Peter (2013).

Value

This function returns of whether X (VL-)Transfer-Entropy-causes Y.

TEratio

is a Transfer Entropy ratio. If it is greater than one , then X causes Y.

res

is an object of output from RTransferEntropy::transfer_entropy()

follOut

is a list of variables from function followingRelation.

XgCsY_trns

The flag is true if X (VL-)Transfer-Entropy-causes Y using Transfer Entropy ratio ratio where TEratio >1 if X causes Y. Additionally, if nboot>1, the flag is true only when pval<=alpha.

pval

It is a p-value for TE bootstrapping by Dimpfl and Peter (2013).

Examples

# Generate simulation data
TS <- SimpleSimulationVLtimeseries()
# Run the function
out<-VLTransferEntropy(Y=TS$Y,X=TS$X)

checkMultipleSimulationVLtimeseries

Description

checkMultipleSimulationVLtimeseries is a support function that can compare two adjacency matrices: groundtruth and inferred matrices. It re

Usage

checkMultipleSimulationVLtimeseries(trueAdjMat, adjMat)

Arguments

trueAdjMat

a groundtruth matrix.

adjMat

an inferred matrix.

Value

This function returns a list of precision prec, recall rec, and F1 score F1 of inferred vs. groundtruth matrices.

Examples

## Generate simulation data
#G<-matrix(FALSE,10,10) # groundtruth
#G[1,c(4,7,8,10)]<-TRUE
#G[2,c(5,7,9,10)]<-TRUE
#G[3,c(6,8,9,10)]<-TRUE
#TS <- MultipleSimulationVLtimeseries()
#out<-multipleVLGrangerFunc(TS)
#checkMultipleSimulationVLtimeseries(trueAdjMat=G,adjMat=out$adjMat)

followingRelation

Description

followingRelation is a function that infers whether Y follows X.

Usage

followingRelation(Y, X, timeLagWindow, lagWindow = 0.2)

Arguments

Y

is a numerical time series of a follower

X

is a numerical time series of a leader

timeLagWindow

is a maximum possible time delay in the term of time steps.

lagWindow

is a maximum possible time delay in the term of percentage of length(X). If timeLagWindow is missing, then timeLagWindow=ceiling(lagWindow*length(X)). The default is 0.2.

Value

This function returns a list of following relation variables below.

follVal

is a following-relation value s.t. if follVal is positive, then Y follows X. If follVal is negative, then X follows Y. Otherwise, if follVal is zero, there is no following relation between X,Y.

nX

is a time series that is rearranged from X by applying the lags optIndexVec in order to imitate Y.

optDelay

is the optimal time delay inferred by cross-correlation of X,Y. It is positive if Y is simply just a time-shift of X (e.g. Y[t]=X[t-optDelay]).

optCor

is the optimal correlation of Y[t]=X[t-optDelay] for all t.

optIndexVec

is a time series of optimal warping-path from DTW that is corrected by cross correlation. It is approximately that Y[t]=X[t-optIndexVec[t]]).

VLval

is a percentage of elements in optIndexVec that is not equal to optDelay.

ccfout

is an output object of ccf function.

Examples

# Generate simulation data
TS <- SimpleSimulationVLtimeseries()
# Run the function
out<-followingRelation(Y=TS$Y,X=TS$X)

multipleVLGrangerFunc

Description

multipleVLGrangerFunc is a function that infers Variable-lag Granger Causality of all pairwises of m time series TS[,1],...TS[,m].

Usage

multipleVLGrangerFunc(
  TS,
  maxLag,
  alpha = 0.05,
  gamma = 0.3,
  autoLagflag = TRUE,
  causalFlag = 0,
  VLflag = TRUE,
  family = gaussian
)

Arguments

TS

is a numerical time series of effect where TS[t,k] is an element at time t of kth time series.

maxLag

is a maximum possible time delay. The default is 0.2*length(Y).

alpha

is a significance level of F-test to determine whether X Granger-causes Y. The default is 0.05.

gamma

is a parameter to determine whether X Granger-causes Y using BIC difference ratio. The default is 0.3.

autoLagflag

causalFlag

is a choice of criterion for inferring causality: causalFlag=0 for BIC difference ratio, causalFlag=1 for f-test, or causalFlag=2 for BIC.

VLflag

is a flag of Granger causality choice: either VLflag=TRUE for VL-Granger or VLflag=FALSE for Granger causality.

family

is a parameter of family of function for Generalized Linear Models function (glm). The default is gaussian.

Value

This function returns of a list of an adjacency matrix of causality where adjMat[i,j] is true if TS[,i] causes TS[,j].

Examples

## Generate simulation data
#TS <- MultipleSimulationVLtimeseries()
## Run the function
#out<-multipleVLGrangerFunc(TS)

multipleVLTransferEntropy

Description

multipleVLTransferEntropy is a function that infers Variable-lag Transfer Entropy of all pairwises of m time series TS[,1],...TS[,m].

Usage

multipleVLTransferEntropy(
  TS,
  maxLag,
  nboot = 0,
  lx = 1,
  ly = 1,
  VLflag = TRUE,
  autoLagflag = TRUE,
  alpha = 0.05
)

Arguments

TS

is a numerical time series of effect where TS[t,k] is an element at time t of kth time series.

maxLag

is a maximum possible time delay. The default is 0.2*length(Y).

nboot

is a number of times of bootstrapping for RTransferEntropy::transfer_entropy() function.

lx, ly

are lag parameters of RTransferEntropy::transfer_entropy().

VLflag

is a flag of Granger causality choice: either VLflag=TRUE for VL-Granger or VLflag=FALSE for Granger causality.

autoLagflag

alpha

is a significant-level threshold for TE bootstrapping by Dimpfl and Peter (2013).

Value

This function returns of a list of an adjacency matrix of causality where adjMat[i,j] is true if TS[,i] causes TS[,j].

Examples

## Generate simulation data
#out1<-SimpleSimulationVLtimeseries()
#TS<-cbind(out1$X,out1$Y)
## Run the function
#out2<-multipleVLTransferEntropy(TS,maxLag=1)

plotTimeSeries

Description

plotTimeSeries is a function for visualizing time series

Usage

plotTimeSeries(X, Y, strTitle = "Time Series Plot", TSnames)

Arguments

X

is a 1st numerical time series

Y

is a 2nd numerical time series. If it is not supplied, the function plots only X.

strTitle

is a string of the plot title

TSnames

is a list of legend of X,Y where TSnames[1] is a legend of X and TSnames[2] is a legend of Y.

Value

This function returns an object of ggplot class.

Examples

# Generate simulation data
TS <- SimpleSimulationVLtimeseries()
# Run the function
plotTimeSeries(Y=TS$Y,X=TS$X)