Pattern Causality

Overview

The goal of patterncausality is to measure the causality in the complex system. The core of this algorithm is measure the strength of each causality status like positive, negative, and dark in the view of complex system, this method could be used for many different fields like financial market, ecosystem, medical diagnosis and so on.

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 time series of climate index, we could use the patterncausality in this dataset.

Then we need to determine the E and tao.

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

		Total	of which Positive	of which Negative	of which Dark
E=2	tau=1	0.5543614	0.5519477	0.4474361	0.0006162144
E=2	tau=2	0.5727414	0.5736100	0.4232828	0.0031071596
E=2	tau=3	0.5711838	0.5469069	0.4513270	0.0017660870
E=3	tau=1	0.3305296	0.3457169	0.2470929	0.4071902523
E=3	tau=2	0.3500000	0.4037138	0.2547524	0.3415338782
E=3	tau=3	0.3570093	0.3657638	0.2690536	0.3651826225

Of course, we can also change the distance style to calculate the distance matrix. 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 = 2, metric = "euclidean", h = 1, weighted = TRUE, tpb=FALSE)
print(pc)
#>       total positive  negative     dark
#> 1 0.2841121 0.326087 0.2318841 0.442029

Then the percentage of each status will be showed below.

If we wonder the status in each time point, we can run the code.

X <- climate_indices$AO
Y <- climate_indices$AAO
detail <- pcFullDetails(X, Y, E = 2, tau = 1, metric = "euclidean", h = 3, weighted = TRUE)
predict_status <- detail$spectrumOfCausalityPredicted
real_status <- detail$spectrumOfCausalityReal

Then the status series will be saved in predict_status and real_status.

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.