Introduction to patterncausality

Hui Wang

Pattern Causality gives us a method to measure the causality in the complex system, it has its own ability to catch the hidden pattern in many kinds of series, so that it is statistically sufficient.

PC in financial market

First of all, we can import the data of AAPL and MSFT, also we can import data from the yahooo api.

library(patterncausality)
data(stock)
head(stock)
#>            AAPL.Open AAPL.High AAPL.Low AAPL.Close AAPL.Volume AAPL.Adjusted
#> 1986-03-13  0.110491  0.111607 0.108817   0.110491   115964800    0.08527586
#> 1986-03-14  0.110491  0.117188 0.110491   0.116629   384854400    0.09001311
#> 1986-03-17  0.116071  0.116071 0.113281   0.116071   118720000    0.08958244
#> 1986-03-18  0.116071  0.121652 0.115513   0.119978   249356800    0.09259786
#> 1986-03-19  0.119978  0.121652 0.117746   0.118304   189884800    0.09130585
#> 1986-03-20  0.125000  0.132254 0.125000   0.126116   904131200    0.09733511
#>            MSFT.Open MSFT.High MSFT.Low MSFT.Close MSFT.Volume MSFT.Adjusted
#> 1986-03-13  0.088542  0.101563 0.088542   0.097222  1031788800    0.06005456
#> 1986-03-14  0.097222  0.102431 0.097222   0.100694   308160000    0.06219922
#> 1986-03-17  0.100694  0.103299 0.100694   0.102431   133171200    0.06327216
#> 1986-03-18  0.102431  0.103299 0.098958   0.099826    67766400    0.06166304
#> 1986-03-19  0.099826  0.100694 0.097222   0.098090    47894400    0.06059071
#> 1986-03-20  0.098090  0.098090 0.094618   0.095486    58435200    0.05898221

We can visualize this stock price.

Search the parameters

Then search the best parameters for the PC.

dataset <- stock
parameter <- optimalParametersSearch(Emax = 5, tauMax = 5, metric = "euclidean", dataset = dataset)

Calculate the causality

After that, calculate the causality of each status.

X <- stock$AAPL.Close
Y <- stock$MSFT.Close
pc <- pc_lightweight(X, Y, E = 3, tau = 2, metric = "euclidean", h = 1, weighted = TRUE, tpb=FALSE)
print(pc)
#>       total  positive  negative      dark
#> 1 0.2698665 0.3881279 0.1369863 0.4748858

Lastly we can also visualize this result.

library(ggplot2)
df <- data.frame(
  name = stringr::str_to_title(c(colnames(pc))),
  val = as.vector(unlist(pc))
)

ggplot(df, aes(x = name, y = val, fill = name)) +
  geom_bar(stat = "identity", alpha = .6, width = .4) +
  scale_fill_grey(start = 0, end = 0.8) + # start and end define the range of grays
  labs(x = "Status", y = "Strength") +
  theme_bw(base_size = 12, base_family = "Times New Roman") +
  theme(
    legend.position = "none", axis.text = element_text(size = rel(0.8)),
    strip.text = element_text(size = rel(0.8))
  )

Full details

The details could be found with following code.

X <- stock$AAPL.Close
Y <- stock$MSFT.Close
detail <- pc_fulldetails(X, Y, E = 3, tau = 2, metric = "euclidean", h = 1, weighted = TRUE)
predict_status <- detail$spectrumOfCausalityPredicted
real_status <- detail$spectrumOfCausalityReal
names(detail)

So far, the whole process of this algorithm has finished.