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, it’s 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 = 5, tauMax = 5, metric = "euclidean", dataset = dataset)

E	tau	Total	Positive	Negative	Dark
2	1	0.5503802	0.5529091	0.44647239	0.0006185057
2	2	0.5672403	0.5722529	0.42461112	0.0031359329
2	3	0.5647436	0.5471488	0.45106762	0.0017836150
2	4	0.5538362	0.5485637	0.44961187	0.0018243903
2	5	0.5616083	0.5433907	0.45513014	0.0014791531
3	1	0.3203775	0.3460809	0.24690959	0.4070094904
3	2	0.3362460	0.4010403	0.25410446	0.3448552507
3	3	0.3388998	0.3657369	0.26857083	0.3656922393

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: 0.2336
#> Positive: 0.4471
#> Negative: 0.1380
#> Dark: 0.4150

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 it’s 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$causality_predict
real_status <- detail$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.

Pairs	total	positive	negative	dark	Dataset
AAPL –> MSFT	0.2698665	0.3881279	0.1369863	0.4748858	stock
MSFT –> AAPL	0.2759887	0.4075893	0.1388393	0.4535714	stock
AO –> AAO	0.2841121	0.326087	0.2318841	0.442029	climate
AAO –> AO	0.2803738	0.3602941	0.2647059	0.375	climate
AO –> P	0.3084112	0.1192053	0.4503311	0.4304636	AUCO
P –> AO	0.3308411	0.3374233	0.2515337	0.4110429	AUCO

About the authors

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 risk‐based decision‐making 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