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 -1.64This 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: 0.4150The 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_realThen 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.