| Type: | Package |
| Title: | Models for Non Linear Causality Detection in Time Series |
| Version: | 1.4.5 |
| Date: | 2021-02-01 |
| Maintainer: | Youssef Hmamouche <hmamoucheyussef@gmail.com> |
| Description: | Models for non-linear time series analysis and causality detection. The main functionalities of this package consist of an implementation of the classical causality test (C.W.J.Granger 1980) <doi:10.1016/0165-1889(80)90069-X>, and a non-linear version of it based on feed-forward neural networks. This package contains also an implementation of the Transfer Entropy <doi:10.1103/PhysRevLett.85.461>, and the continuous Transfer Entropy using an approximation based on the k-nearest neighbors <doi:10.1103/PhysRevE.69.066138>. There are also some other useful tools, like the VARNN (Vector Auto-Regressive Neural Network) prediction model, the Augmented test of stationarity, and the discrete and continuous entropy and mutual information. |
| License: | GPL-2 | GPL-3 [expanded from: GNU General Public License] |
| Depends: | Rcpp |
| Imports: | methods, timeSeries, Rdpack |
| RdMacros: | Rdpack |
| LinkingTo: | Rcpp |
| SystemRequirements: | C++11 |
| NeedsCompilation: | yes |
| RoxygenNote: | 7.1.1 |
| Author: | Youssef Hmamouche [aut, cre] |
| Packaged: | 2021-02-01 15:52:25 UTC; youssef |
| Repository: | CRAN |
| Date/Publication: | 2021-02-02 01:20:05 UTC |
Models for non-linear causality detection in time series.
Description
Globally, this package focuses on non-linear time series analysis, especially on causality detection. To deal with non-linear dependencies between time series, we propose an extension of the Granger causality test using feed-forward neural networks. This package includes also an implementation of the Transfer Entropy, which can be also seen as a causality measure based on information theory. To do that, the package includes discrete and continuous Transfer entropy using the Kraskov approximation. The NlinTS package includes also some other useful tools, like the VARNN (Vector Auto-Regressive Neural Network) model, the Augmented Dickey-Fuller test of stationarity, and the discrete and continuous entropy and mutual information.
The Granger causality test
Description
The Granger causality test
Usage
causality.test(ts1, ts2, lag, diff = FALSE)
Arguments
ts1 |
Numerical dataframe containing one variable. |
ts2 |
Numerical dataframe containing one variable. |
lag |
The lag parameter. |
diff |
Logical argument for the option of making data stationary before making the test. |
Details
This is the classical Granger test of causality. The null hypothesis is that the second time series does not cause the first one
Value
gci: the Granger causality index.
Ftest: the statistic of the test.
pvalue: the p-value of the test.
summary (): shows the test results.
References
Granger CWJ (1980). “Testing for Causality.” Journal of Economic Dynamics and Control, 2, 329–352. ISSN 0165-1889, doi: 10.1016/0165-1889(80)90069-X.
Examples
library (timeSeries) # to extract time series
library (NlinTS)
data = LPP2005REC
model = causality.test (data[,1], data[,2], 2)
model$summary ()
Augmented Dickey_Fuller test
Description
Augmented Dickey_Fuller test
Usage
df.test(ts, lag)
Arguments
ts |
Numerical dataframe. |
lag |
The lag parameter. |
Details
Computes the stationarity test for a given univariate time series.
Value
df: returns the value of the test.
summary (): shows the test results.
References
Elliott G, Rothenberg TJ, Stock JH (1992). “Efficient tests for an autoregressive unit root.”
Examples
library (timeSeries)
library (NlinTS)
#load data
data = LPP2005REC
model = df.test (data[,1], 1)
model$summary ()
Continuous entropy
Description
Continuous entropy
Usage
entropy_cont(V, k = 3, log = "loge")
Arguments
V |
Interger vector. |
k |
Integer argument, the number of neighbors. |
log |
String argument in the set ("log2", "loge","log10"), which indicates the log function to use. The loge is used by default. |
Details
Computes the continuous entropy of a numerical vector using the Kozachenko approximation.
References
Kraskov A, Stogbauer H, Grassberger P (2004). “Estimating mutual information.” Phys. Rev. E, 69, 066138. doi: 10.1103/PhysRevE.69.066138.
Examples
library (timeSeries)
library (NlinTS)
#load data
data = LPP2005REC
print (entropy_cont (data[,1], 3))
Discrete Entropy
Description
Discrete Entropy
Usage
entropy_disc(V, log = "log2")
Arguments
V |
Integer vector. |
log |
String argument in the set ("log2", "loge","log10"), which indicates the log function to use. The log2 is used by default. |
Details
Computes the Shanon entropy of an integer vector.
Examples
library (NlinTS)
print (entropy_disc (c(3,2,4,4,3)))
Continuous Mutual Information
Description
Continuous Mutual Information
Usage
mi_cont(X, Y, k = 3, algo = "ksg1", normalize = FALSE)
Arguments
X |
Integer vector, first time series. |
Y |
Integer vector, the second time series. |
k |
Integer argument, the number of neighbors. |
algo |
String argument specifies the algorithm use ("ksg1", "ksg2"), as tow propositions of Kraskov estimation are provided. The first one ("ksg1") is used by default. |
normalize |
Logical argument (FALSE by default) for the option of normalizing the mutual information by dividing it by the joint entropy. |
Details
Computes the Mutual Information between two vectors using the Kraskov estimator.
References
Kraskov A, Stogbauer H, Grassberger P (2004). “Estimating mutual information.” Phys. Rev. E, 69, 066138. doi: 10.1103/PhysRevE.69.066138.
Examples
library (timeSeries)
library (NlinTS)
#load data
data = LPP2005REC
print (mi_cont (data[,1], data[,2], 3, 'ksg1'))
print (mi_cont (data[,1], data[,2], 3, 'ksg2'))
Discrete multivariate Mutual Information
Description
Discrete multivariate Mutual Information
Usage
mi_disc(df, log = "log2", normalize = FALSE)
Arguments
df |
Datafame of type Integer. |
log |
String argument in the set ("log2", "loge","log10"), which indicates the log function to use. The log2 is used by default. |
normalize |
Logical argument (FALSE by default) for the option of normalizing the mutual information by dividing it by the joint entropy. |
Details
Computes the Mutual Information between columns of a dataframe.
Examples
library (NlinTS)
df = data.frame (c(3,2,4,4,3), c(1,4,4,3,3))
mi = mi_disc (df)
print (mi)
Discrete bivariate Mutual Information
Description
Discrete bivariate Mutual Information
Usage
mi_disc_bi(X, Y, log = "log2", normalize = FALSE)
Arguments
X |
Integer vector. |
Y |
Integer vector. |
log |
String argument in the set ("log2", "loge","log10"), which indicates the log function to use. The log2 is used by default. |
normalize |
Logical argument (FALSE by default) for the option of normalizing the mutual information by dividing it by the joint entropy. |
Details
Computes the Mutual Information between two integer vectors.
Examples
library (NlinTS)
mi = mi_disc_bi (c(3,2,4,4,3), c(1,4,4,3,3))
print (mi)
A non linear Granger causality test
Description
A non linear Granger causality test
Usage
nlin_causality.test(
ts1,
ts2,
lag,
LayersUniv,
LayersBiv,
iters = 50,
learningRate = 0.01,
algo = "sgd",
batch_size = 10,
bias = TRUE,
seed = 0,
activationsUniv = vector(),
activationsBiv = vector()
)
Arguments
ts1 |
Numerical series. |
ts2 |
Numerical series. |
lag |
The lag parameter |
LayersUniv |
Integer vector that contains the size of hidden layers of the univariate model. The length of this vector is the number of hidden layers, and the i-th element is the number of neurons in the i-th hidden layer. |
LayersBiv |
Integer vector that contains the size of hidden layers of the bivariate model. The length of this vector is the number of hidden layers, and the i-th element is the number of neurons in the i-th hidden layer. |
iters |
The number of iterations. |
learningRate |
The learning rate to use, O.1 by default, and if Adam algorithm is used, then it is the initial learning rate. |
algo |
String argument, for the optimisation algorithm to use, in choice ["sgd", "adam"]. By default "sgd" (stochastic gradient descent) is used. The algorithm 'adam' is to adapt the learning rate while using "sgd". |
batch_size |
Integer argument for the batch size used in the back-propagation algorithm. |
bias |
Logical argument for the option of using the bias in the networks. |
seed |
Integer value for the random seed used in the random generation of the weights of the network (a value = 0 will use the clock as random generator seed). |
activationsUniv |
String vector for the activations functions to use (in choice ["sigmoid", "relu", "tanh"]) for the univariate model. The length of this vector is the number of hidden layers plus one (the output layer). By default, the relu activation function is used in hidden layers, and the sigmoid in the last layer. |
activationsBiv |
String vector for the activations functions to use (in choice ["sigmoid", "relu", "tanh"]) for the bivariate model. The length of this vector is the number of hidden layers plus one (the output layer). By default, the relu activation function is used in hidden layers, and the sigmoid in the last layer. |
Details
A non-linear test of causality using artificial neural networks. Two MLP artificial neural networks are evaluated to perform the test, one using just the target time series (ts1), and the second using both time series. The null hypothesis of this test is that the second time series does not cause the first one.
Value
gci: the Granger causality index.
Ftest: the statistic of the test.
pvalue: the p-value of the test.
summary (): shows the test results.
Examples
library (timeSeries) # to extract time series
library (NlinTS)
data = LPP2005REC
model = nlin_causality.test (data[,1], data[,2], 2, c(2), c(4), 50, 0.01, "sgd", 30, TRUE, 5)
model$summary ()
Continuous Transfer Entropy
Description
Continuous Transfer Entropy
Usage
te_cont(X, Y, p = 1, q = 1, k = 3, normalize = FALSE)
Arguments
X |
Integer vector, first time series. |
Y |
Integer vector, the second time series. |
p |
Integer, the lag parameter to use for the first vector, (p = 1 by default). |
q |
Integer the lag parameter to use for the first vector, (q = 1 by default). |
k |
Integer argument, the number of neighbors. |
normalize |
Logical argument for the option of normalizing value of TE (transfer entropy) (FALSE by default). This normalization is different from the discrete case, because, here the term H (X(t)| X(t-1), ..., X(t-p)) may be negative. Consequently, we use another technique, we divide TE by H0 - H (X(t)| X(t-1), ..., X(t-p), Yt-1), ..., Y(t-q)), where H0 is the max entropy (of uniform distribution). |
Details
Computes the continuous Transfer Entropy from the second time series to the first one using the Kraskov estimation
References
Kraskov A, Stogbauer H, Grassberger P (2004). “Estimating mutual information.” Phys. Rev. E, 69, 066138. doi: 10.1103/PhysRevE.69.066138.
Examples
library (timeSeries)
library (NlinTS)
#load data
data = LPP2005REC
te = te_cont (data[,1], data[,2], 1, 1, 3)
print (te)
Discrete Transfer Entropy
Description
Discrete Transfer Entropy
Usage
te_disc(X, Y, p = 1, q = 1, log = "log2", normalize = FALSE)
Arguments
X |
Integer vector, first time series. |
Y |
Integer vector, the second time series. |
p |
Integer, the lag parameter to use for the first vector (p = 1 by default). |
q |
Integer, the lag parameter to use for the first vector (q = 1 by default).. |
log |
String argument in the set ("log2", "loge","log10"), which indicates the log function to use. The log2 is used by default. |
normalize |
Logical argument for the option of normalizing the value of TE (transfer entropy) (FALSE by default). This normalization is done by deviding TE by H (X(t)| X(t-1), ..., X(t-p)), where H is the Shanon entropy. |
Details
Computes the Transfer Entropy from the second time series to the first one.
References
Schreiber T (2000). “Measuring Information Transfer.” Physical Review Letters, 85(2), 461-464. doi: 10.1103/PhysRevLett.85.461.
Examples
library (NlinTS)
te = te_disc (c(3,2,4,4,3), c(1,4,4,3,3), 1, 1)
print (te)
Artificial Neural Network VAR (Vector Auto-Regressive) model using a MultiLayer Perceptron, with the sigmoid activation function. The optimization algorithm is based on the stochastic gradient descent.
Description
Artificial Neural Network VAR (Vector Auto-Regressive) model using a MultiLayer Perceptron, with the sigmoid activation function. The optimization algorithm is based on the stochastic gradient descent.
Usage
varmlp(
df,
lag,
sizeOfHLayers,
iters = 50,
learningRate = 0.01,
algo = "sgd",
batch_size = 10,
bias = TRUE,
seed = 5,
activations = vector()
)
Arguments
df |
A numerical dataframe |
lag |
The lag parameter. |
sizeOfHLayers |
Integer vector that contains the size of hidden layers, where the length of this vector is the number of hidden layers, and the i-th element is the number of neurons in the i-th hidden layer. |
iters |
The number of iterations. |
learningRate |
The learning rate to use, O.1 by default, and if Adam algorithm is used, then it is the initial learning rate. |
algo |
String argument, for the optimisation algorithm to use, in choice ["sgd", "adam"]. By default "sgd" (stochastic gradient descent) is used. The algorithm 'adam' is to adapt the learning rate while using "sgd". |
batch_size |
Integer argument for the batch size used in the back-propagation algorithm. |
bias |
Logical, true if the bias have to be used in the network. |
seed |
Integer value for the seed used in the random generation of the weights of the network (a value = 0 will use the clock as random generator seed). |
activations |
String vector for the activations functions to use (in choice ["sigmoid", "relu", "tanh"]). The length of this vector is the number of hidden layers plus one (the output layer). By default, the relu activation function is used in hidden layers, and the sigmoid in the last layer. |
Details
This function builds the model, and returns an object that can be used to make forecasts and can be updated from new data.
Value
fit (df, iterations, batch_size): fit/update the weights of the model from the dataframe.
forecast (df): makes forecasts of an given dataframe. The forecasts include the forecasted row based on each previous "lag" rows, where the last one is the next forecasted row of df.
save (filename): save the model in a text file.
load (filename): load the model from a text file.
Examples
library (timeSeries) # to extract time series
library (NlinTS)
#load data
data = LPP2005REC
# Predict the last row of the data
train_data = data[1:(nrow (data) - 1), ]
model = varmlp (train_data, 1, c(10), 50, 0.01, "sgd", 30, TRUE, 0);
predictions = model$forecast (train_data)
print (predictions[nrow (predictions),])