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Showing content from http://cran.rstudio.com/web/packages/ggthemes/../patterncausality/readme/README.html below:

README

Pattern Causality

Overview

The patterncausality package implements a novel approach for detecting and analyzing causal relationships in complex systems. Key features include:

Core Capabilities

Pattern-based causality detection
State space reconstruction
Multi-dimensional causality analysis
Robust cross-validation methods

Applications

Financial market analysis
Climate system interactions
Medical diagnosis
Ecological system dynamics

Key Advantages

Detects nonlinear causal relationships
Quantifies causality strength
Identifies hidden patterns
Handles noisy data effectively

This algorithm has a lot of advantages.

You can find the hidden pattern in the complex system.
You can measure the causality in different fields.
You can search for the best parameters for the complex system.

Installation

You can install the development version of patterncausality from GitHub with:

# install.packages("devtools")
devtools::install_github("skstavroglou/pattern_causality")

You can also install the package from CRAN with:

install.packages("patterncausality")

Example Application in climate

We can import the existing data.

library(patterncausality)
data(climate_indices)
head(climate_indices)
#>         Date      AO    AAO   NAO   PNA
#> 1 1979-01-01 -2.2328 0.2088 -1.38 -0.69
#> 2 1979-02-01 -0.6967 0.3563 -0.67 -1.82
#> 3 1979-03-01 -0.8141 0.8992  0.78  0.38
#> 4 1979-04-01 -1.1568 0.6776 -1.71  0.09
#> 5 1979-05-01 -0.2501 0.7237 -1.03  1.35
#> 6 1979-06-01  0.9332 1.7000  1.60 -1.64

This dataset contains 4 famous time series of climate index, we can find the introduction of this dataset in the CRAN and R documment, we could use the patterncausality in this dataset to detect the hidden causality in this climate system.

The climate system is a typical complex system like lorenz system, which are both originating from the climate system, itâs a good example to show how to find the hidden causality in the complex system.

First of all, we need to determine the E and tao, it could be easy to complete by optimalParametersSearch function like this:

dataset <- climate_indices[, -1] # remove the date column
parameter <- optimalParametersSearch(Emax = 3, tauMax = 3, metric = "euclidean", dataset = dataset)
print(parameter)
#> Pattern Causality Parameter Optimization Results
#> ---------------------------------------------
#> Computation time: 5.272785 secs 
#> 
#> Parameters tested:
#>   Emax: 3 
#>   tauMax: 3 
#>   Metric: euclidean 
#> 
#> First few values:
#>         E tau     Total  Positive   Negative        Dark
#> Combo 1 2   1 0.6042453 0.6849813 0.31421642 0.000802264
#> Combo 2 2   2 0.6305240 0.7056670 0.29186182 0.002471206
#> Combo 3 2   3 0.6313371 0.7034166 0.29455531 0.002028052
#> Combo 4 3   1 0.3437698 0.4459306 0.10253491 0.451534540
#> Combo 5 3   2 0.3760357 0.4722030 0.07746789 0.450329129
#> Combo 6 3   3 0.3991651 0.4647719 0.07249595 0.462732182

Of course, we can also change the distance style to calculate the distance matrix or even custom distance function, we can find more inforation on our website. Then according the combo that produces the highest percentages collectively, we can choose the best parameters here.

After the parameters are confirmed, we could calculate the pattern causality.

X <- climate_indices$AO
Y <- climate_indices$AAO
pc <- pcLightweight(X, Y, E = 3, tau = 1, metric = "euclidean", h = 1, weighted = TRUE, verbose = FALSE)
print(pc)
#> Pattern Causality Analysis Results:
#> Total: 0.3505
#> Positive: 0.5125
#> Negative: 0.1039
#> Dark: 0.3837

The percentages of each causality status will be displayed below.

To examine the causality status at each time point, we can run the following code and find the causality strength at each time point by function pcFullDetails, the causality_predict is the predicted causality status at each point, the parameter weighted = TRUE is used to for erf function and if itâs FALSE, then it will just use the 1 or 0 to present the causality strength, however, whatever which one is used, the total causality points will be the same.

X <- climate_indices$AO
Y <- climate_indices$AAO
detail <- pcFullDetails(X, Y, E = 3, tau = 1, metric = "euclidean", h = 1, weighted = TRUE, verbose = FALSE)
predict_status <- detail$causality_pred
real_status <- detail$causality_real

Then the causality strength series will be saved in predict_status and real_status, if we want to plot the causality strength series, we can use the plot_causality function for the pc_full_details class, and it will show the continuous causality strength series in the whole time period, we can find the dynamic pattern causality strength by this way.

Conclusion

After calculating the causality, we can get the result here.

Apple â> Microsoft 0.2778 0.2342 0.2641 0.5017 DJS Microsoft â> Apple 0.2820 0.2278 0.2226 0.5496 DJS AO â> AAO 0.3505 0.5125 0.1039 0.3837 climate_indices AAO â> AO 0.3010 0.3914 0.1085 0.5000 climate_indices AO â> P 0.4091 0.1197 0.7808 0.0995 AUCO P â> AO 0.3636 0.2924 0.2171 0.4905 AUCO

Stavros is lecturer in credit risk and fin-tech at the University of Edinburgh Business School and is the main creator for the algorithm of the pattern causality.

Athanasios is professor in econometrics and business statistics of Monash Business School and is the main author of the pattern causality.

Hui is MPhil student in econometrics and business statistics of Monash Business School and is the author and maintainer of the patterncausality package.

References

Stavroglou, S. K., Pantelous, A. A., Stanley, H. E., & Zuev, K. M. (2019). Hidden interactions in financial markets. Proceedings of the National Academy of Sciences, 116(22), 10646-10651.
Stavroglou, S. K., Pantelous, A. A., Stanley, H. E., & Zuev, K. M. (2020). Unveiling causal interactions in complex systems. Proceedings of the National Academy of Sciences, 117(14), 7599-7605.
Stavroglou, S. K., Ayyub, B. M., Kallinterakis, V., Pantelous, A. A., & Stanley, H. E. (2021). A novel causal riskâbased decisionâmaking methodology: The case of coronavirus. Risk Analysis, 41(5), 814-830.

Test environments

local R installation, R 4.1.0
ubuntu 20.04 (on GitHub Actions), R 4.1.0
win-builder (devel and release)

R CMD check results

0 errors | 0 warnings | 0 notes

Downstream dependencies

There are currently no downstream dependencies for this package

# Example with relative parameter (default is TRUE)
pc <- pcLightweight(X, Y, E = 3, tau = 1, metric = "euclidean", h = 1, 
                   weighted = TRUE, relative = TRUE, verbose = FALSE)
print(pc)

# Example with optimal parameter search
dataset <- climate_indices[, -1] # remove the date column
parameter <- optimalParametersSearch(Emax = 5, tauMax = 5, metric = "euclidean", 
                                   dataset = dataset, relative = TRUE)

# Example with full details
detail <- pcFullDetails(X, Y, E = 3, tau = 1, metric = "euclidean", h = 1, 
                       weighted = TRUE, relative = TRUE, verbose = FALSE)

The relative parameter (default is TRUE) determines whether to calculate relative changes ((new-old)/old) or absolute changes (new-old) in signature space. Using relative changes is particularly useful when:

Analyzing time series with different scales
Comparing percentage changes rather than absolute differences
Studying the relative importance of changes in the system

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