In PINstimation: Estimation of the Probability of Informed Trading

Overview

---

This vignette describes various scenarios of creating sample datasets that fit the preferences and needs of the users; and this for the different models. The functions in the package PINstimation use two types of datasets: (1) A sequence of daily buys and sells (2) A high-frequency trading data. This is the reason why only two sample datasets are preloaded with the package, namely dailytrades, and hfdata. The users can also generate simulation data using the function generatedata_mpin() for PIN, and MPIN models; and the function generatedata_adjpin() for the ADJPIN model. Below we provide some scenarios of creating sample datasets both for the PIN, MPIN, and ADJPIN models.

library(PINstimation)

options(crayon.enabled = TRUE)
knitr::knit_hooks$set(output = function(x, options){
  paste0(
    '<pre class="r-output"><code>',
    fansi::sgr_to_html(x = htmltools::htmlEscape(x), warn = FALSE),
    '</code></pre>'
  )
})

Sample datasets for the PIN model

---

The PIN model is an multilayer PIN model with a single information layer. We can, therefore, use the function generatedata_mpin(), in order to generate sample data for the PIN model. Generically, this is done as follows:

generatedata_mpin(..., layers=1)

If the user would like to create a sample dataset for infrequently traded stock, she can specify low values or ranges for the trade intensity rates. For instance, let's assume that the user suspects that an infrequently-traded stock has an average of uninformed trading intensity for buys and sells between 300 and 500. They generate a single sample dataset for this scenario as follows:

pindata <- generatedata_mpin(layers=1, ranges = list(eps.b=c(300, 500), eps.s=c(300,500)), verbose = FALSE)

The details of the generated sample dataset can be displayed with the following code

show(pindata)

You access the sequences of buys, and sells through the slot @data of the object pindata.

show(pindata@data[1:10, ])

You can, now use the dataset object pindata to check the accuracy of the different estimation functions. You can do that by comparing the actual parameters of the sample datasets to the estimated parameters of the estimation functions. Let us start with displaying the actual parameters of the sample datasets. These can be accessed through the slot @empiricals of the dataset object, which stores the empirical parameters computed from the sequences of buys and sells generated. Please refer to the documentation of generatedata_mpin() for more information.

actual <- unlist(pindata@empiricals)
show(actual)

Estimate the PIN model using the function pin_ea(), and display the estimated parameters

model <- pin_ea(data=pindata@data, verbose = FALSE)
estimates <- model@parameters 
show(estimates)

Now calculate the absolute errors of the estimation method.

errors <- abs(actual - estimates)
show(errors)

Sample datasets for the MPIN model

---

In contrast to the PIN model, the number of information layers is free. We can, therefore, use the function generatedata_mpin() with the desired number of information layers, in order to generate sample data for the MPIN model. We can also skip specifying the number of layers, and the default setting will be used: the number of layers will be randomly selected from the integer set from 1 to 5. Generically, this is done as follows:

generatedata_mpin(...)

If the user would like to create a sample dataset for frequently traded stock with two information layers, she can set the argument layers to 2, and specify high values or ranges for the trade intensity rates. For instance, let's assume that the user suspects that a frequently-traded stock has an average of uninformed trading intensity for buys and sells between 12000 and 15000. They generate a single sample dataset for this scenario as follows:

mpindata <- generatedata_mpin(layers=2, ranges = list(eps.b=c(12000, 15000), eps.s=c(12000,15000)), verbose = FALSE)

The details of the generated sample dataset can be displayed with the following code

show(mpindata)

You access the sequences of buys, and sells through the slot @data of the object pindata.

show(mpindata@data[1:10, ])

You can, now use the dataset object mpindata to check the accuracy of the different estimation functions, namely mpin_ml(), and mpin_ecm(). You can do that by comparing the empirical PIN value derived from the sample dataset to the estimated PIN value of the estimation functions. Let us start with displaying the empirical PIN value obtained from the sample dataset. This value can be accessed through the slot @emp.pin of the dataset object, which stores the empirical PIN value computed from the sequences of buys and sells generated. Please refer to the documentation of generatedata_mpin() for more information.

actualmpin <- unlist([e-mail])
show(actualmpin)

Estimate the MPIN model using the functions mpin_ml(), and mpin_ecm, and display the estimated MPIN values.

model_ml <- mpin_ml(data=mpindata@data, verbose = FALSE)
model_ecm <- mpin_ecm(data=mpindata@data, verbose = FALSE)
mlmpin <- model_ml@mpin
ecmpin <- model_ecm@mpin
estimates <- setNames(c(mlmpin, ecmpin), c("ML", "ECM"))
show(estimates)

Now calculate the absolute errors of both estimation methods.

errors <- abs(actualmpin - estimates)
show(errors)

The function generatedata_mpin() can generate a data.series object that contains a collection of dataset objects. For instance, the user can generate a collection of 10 datasets, whose data sequences span 60 days, and contain 3 layers, and use it to check the accuracy of the MPIN estimation.

size <- 10
collection <- generatedata_mpin(series = size, layers = 3, verbose = FALSE)
show(collection)

accuracy <- devmpin <- 0
for (i in 1:size) {
    sdata <- collection@datasets[[i]]
    model <- mpin_ml(sdata@data, xtraclusters = 3, verbose=FALSE)
    accuracy <- accuracy + (sdata@layers == model@layers)
    devmpin <- devmpin + abs([e-mail] - model@mpin)

}
cat('The accuracy of layer detection: ', paste0(accuracy*(100/size),"%.\n"), sep="")
cat('The average error in MPIN estimates: ', devmpin/size, ".\n", sep="")

Sample datasets for the ADJPIN model

---

The AdjPIN model is an extension of the PIN model that includes the possibility of liquidity shocks. To obtain a sample dataset distributed according to the assumptions of the AdjPIN model, users can use the function generatedata_adjpin(). Generically, this is done as follows:

generatedata_adjpin(...)

If the user desires to create 10 sample datasets for frequently traded stock, they can specify high values or ranges for the trade intensity rates. For instance, let's assume that the user suspects that a frequently-traded stock has an average of uninformed trading intensity for buys and sells between 10000 and 15000.

adjpindatasets <- generatedata_adjpin(series = 10, ranges = list(eps.b=c(10000, 15000), eps.s=c(10000,15000)), verbose = FALSE)

The details of the generated sample data series can be displayed with the following code:

show(adjpindatasets)

You access the first dataset from adjpindata using this code:

adjpindata <- adjpindatasets@datasets[[1]]
show(adjpindata)

You can, now use the dataset object adjpindata to check the accuracy of the different estimation functions, namely MLE, and ECM algorithms. You can do that by comparing the empirical adjpin, and psos values derived from the sample dataset to the estimated adjpin, and psos values obtained from the estimation functions. Let us start with displaying the empirical adjpin, and psos values obtained from the sample dataset. These values can be accessed through the slot @emp.pin of the dataset object, which stores the empirical adjpin/psos value computed from the sequences of buys and sells generated. Please refer to the documentation of generatedata_adjpin() for more information.

actualpins <- unlist([e-mail])
show(actualpins)

Estimate the AdjPIN model using adjpin(method="ML"), and adjpin(method="ECM", and display the estimated adjpin/psos values.

model_ml <- adjpin(data=adjpindata@data, method = "ML", verbose = FALSE)
model_ecm <- adjpin(data=adjpindata@data, method = "ECM", verbose = FALSE)
mlpins <- c(model_ml@adjpin, model_ml@psos)
ecmpins <- c(model_ecm@adjpin, model_ecm@psos)
estimates <- rbind(mlpins, ecmpins)
colnames(estimates) <- c("adjpin", "psos")
rownames(estimates) <- c("ML", "ECM")
show(estimates)

Now calculate the absolute errors of both estimation methods.

errors <- abs(estimates - rbind(actualpins, actualpins))
show(errors)

Getting help

---

If you encounter a clear bug, please file an issue with a minimal reproducible example on GitHub.

PINstimation documentation built on March 31, 2023, 6:32 p.m.