Estimation of the Probability of Informed Trading

A comprehensive bundle of utilities for the estimation of probability of informed trading models: original PIN in Easley and O'Hara (1992) and Easley et al. (1996); Multilayer PIN (MPIN) in Ersan (2016); Adjusted PIN (AdjPIN) in Duarte and Young (2009); and volume-synchronized PIN (VPIN) in Easley et al. (2011, 2012). Implementations of various estimation methods suggested in the literature are included. Additional compelling features comprise posterior probabilities, an implementation of an expectation-maximization (EM) algorithm, and PIN decomposition into layers, and into bad/good components. Versatile data simulation tools, and trade classification algorithms are among the supplementary utilities. The package provides fast, compact, and precise utilities to tackle the sophisticated, error-prone, and time-consuming estimation procedure of informed trading, and this solely using the raw trade-level data.

PINstimation: Estimating Models of Probability of Informed Trading

PINstimation provides utilities for the estimation of probability of informed trading models: original PIN (PIN) in Easley and O'Hara (1992) and Easley et al. (1996); multilayer PIN (MPIN) in Ersan (2016); Adjusted PIN (AdjPIN) in Duarte and Young (2009); and volume- synchronized PIN (VPIN) in Easley et al. (2011, 2012); and an improved VPIN implemented (iVPIN), which follows Lin and Ke (2017). Various computation methods suggested in the literature are included. Data simulation tools and trade classification algorithms are among the supplementary utilities. The package enables fast and precise solutions for the sophisticated, error-prone and time-consuming estimation procedure of the probability of informed trading measures, and it is compact in the sense detailed estimation results can be achieved by solely the use of raw trade level data.

Recent changes (0.2.0)

• initials_adjpin(): Updated the generation of initial parameter sets for the adjusted PIN model to align with the procedure described in Ersan and Ghachem (2024).
• adjpin(): The reported runtime now includes the time spent generating initial parameter sets, giving a more complete view of total computation time.
• ivpin(): Added an improved VPIN estimator based on Ke and Lin (2017). Using maximum-likelihood estimation, ivpin() provides more stable VPIN estimates—especially with small volume buckets or infrequent informed trades—by capturing information embedded in volume time, yielding more consistent measures of flow toxicity.

See NEWS.md for the full version history.

Table of contents

• Main functionalities
• Installation
• Examples
  • PIN model estimation
  • MPIN model estimation
  • AdjPIN model estimation
  • VPIN model estimation
  • Data classification
• Resources
• Note to frequent users
• Contributions
• Alternative packages
• Getting help

Main functionalities

The functionalities that the package offers are summarized below:

• PIN model

  • estimate the PIN model using the functions pin(), pin_yz(), pin_gwj(), and pin_ea().
  • compute initial parameter sets using the functions initials_pin_yz(), initials_pin_gwj(), and initials_pin_ea().
  • generate simulation data following the PIN model using generatedata_mpin(layers=1).
  • evaluate factorizations of the PIN likelihood functions using fact_pin_eho(), fact_pin_lk(), fact_pin_e().
  • estimate the PIN model by the Bayesian approach (Gibbs Sampler) using pin_bayes() (*) .

• MPIN model

  • estimate the MPIN model using the functions mpin_ml() and mpin_ecm().
  • compute initial parameter sets using initials_mpin().
  • detect the number of layers in data using detectlayers_e(), detectlayers_eg(), and detectlayers_ecm().
  • generate simulation data following the MPIN model using generatedata_mpin().
  • evaluate the factorization of the MPIN likelihood function through fact_mpin().

• AdjPIN model

  • estimate the AdjPIN model using the function adjpin().
  • compute initial parameter sets using functions initials_adjpin(), initials_adjpin_cl(), and initials_adjpin_rnd().
  • generate simulation data following the AdjPIN model using generatedata_adjpin().
  • evaluate the factorization of the AdjPIN likelihood function through fact_adjpin().

• VPIN

  • estimate the VPIN model using the function vpin()
  • estimate the iVPIN model using the function ivpin()

• Data classification

  • Classify high-frequency data through tick, quote, LR and EMO algorithms using the function aggregate_trades()

Installation

The easiest way to get PINstimation is the following:

install.packages("PINstimation")

To get a bugfix or to use a feature from the development version, you can install the development version of PINstimation from GitHub.

# install.packages("devtools")
# library(devtools)
devtools::install_github("monty-se/PINstimation", build_vignettes = TRUE)

Loading the package

library(PINstimation)

Examples

Example 1: Estimate the PIN model

We estimate the PIN model on preloaded dataset dailytrades using the initial parameter sets of Ersan & Alici (2016).

estimate <- pin_ea(dailytrades)

## [+] PIN Estimation started 
##   |[1] Likelihood function factorization: Ersan (2016)
##   |[2] Loading initial parameter sets   : 5 EA initial set(s) loaded
##   |[3] Estimating PIN model (1996)      : Using Maximum Likelihood Estimation
##   |+++++++++++++++++++++++++++++++++++++| 100% of PIN estimation completed
## [+] PIN Estimation completed

Example 2: Estimate the Multilayer PIN model

We run the estimation of the MPIN model on preloaded dataset dailytrades using:

• the maximum-likelihood method.

ml_estimate <- mpin_ml(dailytrades)

## [+] MPIN estimation started
##   |[1] Detecting layers from data       : using Ersan and Ghachem (2022a)
##   |[=] Number of layers in the data     : 3 information layer(s) detected
##   |[2] Computing initial parameter sets : using algorithm of Ersan (2016)
##   |[3] Estimating the MPIN model        : Maximum-likelihood standard estimation
##   |+++++++++++++++++++++++++++++++++++++| 100% of mpin estimation completed
## [+] MPIN estimation completed

• the ECM algorithm.

ecm_estimate <- mpin_ecm(dailytrades)

## [+] MPIN estimation started
##   |[1] Computing the range of layers    : information layers from 1 to 8
##   |[2] Computing initial parameter sets : using algorithm of Ersan (2016)
##   |[=] Selecting initial parameter sets : max 100 initial sets per estimation
##   |[3] Estimating the MPIN model        : Expectation-Conditional Maximization algorithm
##   |+++++++++++++++++++++++++++++++++++++| 100% of estimation completed [8 layer(s)]
##   |[3] Selecting the optimal model      : using lowest Information Criterion (BIC)
## [+] MPIN estimation completed

Compare the aggregate parameters obtained from the ML, and ECM estimations.

mpin_comparison <- rbind(ml_estimate@aggregates, ecm_estimate@aggregates)
rownames(mpin_comparison) <- c("ML", "ECM")
cat("Probabilities of ML, and ECM estimations of the MPIN model\n")
print(mpin_comparison)

Display the summary of the model estimates for all number of layers.

summary <- getSummary(ecm_estimate)
show(summary)

##          layers em.layers  MPIN Likelihood    AIC    BIC    AWE
## Model[1]      1         1 0.566  -3226.469 6462.9 6473.4 6508.9
## Model[2]      2         2 0.577   -800.379 1616.8 1633.5 1690.3
## Model[3]      3         3 0.574   -643.458 1308.9 1332.0 1410.0
## Model[4]      4         3 0.574   -643.458 1308.9 1332.0 1410.0
## Model[5]      5         3 0.574   -643.458 1308.9 1332.0 1410.0
## Model[6]      6         3 0.574   -643.458 1308.9 1332.0 1410.0
## Model[7]      7         4 0.575   -642.631 1313.3 1342.6 1441.9
## Model[8]      8         4 0.575   -642.631 1313.3 1342.6 1441.9

Example 3: Estimate the Adjusted PIN model

We estimate the adjusted PIN model on preloaded dataset dailytrades using 20 initial parameter sets computed by the algorithm of Ersan and Ghachem (2022b).

estimate_adjpin <- adjpin(dailytrades, initialsets = "GE")
show(estimate_adjpin)

## [+] AdjPIN estimation started
##   |[1] Computing initial parameter sets : 20 GE initial sets generated
##   |[2] Estimating the AdjPIN model      : Maximum-likelihood Standard Estimation
##   |+++++++++++++++++++++++++++++++++++++| 100% of AdjPIN estimation completed
## [+] AdjPIN estimation completed

Example 4: Estimate the Volume-adjusted PIN model

We run a VPIN estimation on preloaded dataset hfdata with timebarsize of 5 minutes (300 seconds).

estimate.vpin <- vpin(hfdata, timebarsize = 300)
show(estimate.vpin)

## ----------------------------------
## VPIN estimation completed successfully.
## ----------------------------------
## Type object@vpin to access the VPIN vector.
## Type object@bucketdata to access data used to construct the VPIN vector.
## Type object@dailyvpin to access the daily VPIN vectors.
## 
## [+] VPIN descriptive statistics
## 
##    Min.     1st Qu.    Median    Mean     3rd Qu.    Max.     NA's 
##  -------  ---------  --------  -------  ---------  -------  ------
##   0.129     0.208     0.252     0.269     0.319     0.643     49  
## 
## 
## [+] VPIN parameters
## 
##   tbSize    buckets    samplength      VBS       ndays 
##  --------  ---------  ------------  ----------  -------
##    300        50           50        4058.956     69   
## 
## -------
## Running time: 2.46 seconds

Example 5: Estimate the AdjPIN model using aggregated high-frequency data

We use the preloaded high-frequency dataset hfdata, prepare it for aggregation.

data <- hfdata
data$volume <- NULL

We classify data using the LR algorithm with a time lag of 500000 microseconds (0.5 s), using the function aggregate_data().

daytrades <- aggregate_trades(data, algorithm = "LR", timelag = 500000)

## [+] Trade classification started
##   |[=] Classification algorithm         : LR algorithm
##   |[=] Number of trades in dataset      : 100 000 trades
##   |[=] Time lag of lagged variables 	   : 5e+05 microseconds
##   |[1] Computing lagged variables       : using parallel processing
##   |+++++++++++++++++++++++++++++++++++++| 100% of variables computed
##   |[=] Intraday trades classified 	     : in 9.308 seconds
##   |[2] Computing aggregated trades      : using lagged variables
## [+] Trade classification completed                

We use the obtained dataset to estimate the (adjusted) probability of informed trading via the standard Maximum-likelihood method.

adjpin_ml <- adjpin(daytrades, method = "ML", initialsets = "GE")

## [+] AdjPIN estimation started
##   |[1] Computing initial parameter sets : 20 GE initial sets generated
##   |[2] Estimating the AdjPIN model      : Maximum-likelihood Standard Estimation
##   |+++++++++++++++++++++++++++++++++++++| 100% of AdjPIN estimation completed
## [+] AdjPIN estimation completed

Note to frequent users

If you are a frequent user of PINstimation, you might want to avoid repetitively loading the package PINstimation whenever you open a new R session. You can do that by adding PINstimation to .R profile either manually, or using the function load_pinstimation_for_good().

To automatically load PINstimation, run load_pinstimation_for_good(), and the following code will be added to your .R profile.

if (interactive()) suppressMessages(require(PINstimation))

After restart of the R session, PINstimation will be loaded automatically, whenever a new R session is started. To remove the automatic loading of PINstimation, just open the .R profile for editing usethis::edit_r_profile(), find the code above, and delete it.

Resources

For a smooth introduction to, and useful tips on the main functionalities of the package, please refer to:

• The sections Get Started, and Online documentation on the package site.
• The package documentation in PDF format is available for download here.
• An overview of the scientific research underlying the package is available here.

Contributions

The package makes a series of original contributions to the literature:

• An efficient, user-friendly, and comprehensive implementation of the standard models of probability of informed trading.

• A first implementation of the estimation of the multilayer probability of informed trading (MPIN) as developed by Ersan (2016).

• A comprehensive treatment of the estimation of the adjusted probability of informed trading as introduced by Duarte and Young (2009). This includes the implementation of the factorization of the AdjPIN likelihood function, various algorithms to generate initial parameter sets, and MLE method.

• The introduction of the expectation-conditional maximization (ECM) algorithm as an alternative method to estimate the models of probability of informed trading. The contribution is both theoretical and computational. The theoretical contribution is included in the paper by Ghachem and Ersan (2022b). The implementation of the ECM algorithm allows the estimation of PIN, MPIN, as well as the adjusted PIN model.

• Implementation of three layer-detection algorithms, namely of preexistent algorithm of Ersan (2016), as well as two newly developed algorithms, described in Ersan and Ghachem (2022a), and Ghachem and Ersan (2022b), respectively.

• A first implementation of the estimation of the volume-synchronized probability of informed trading (VPIN) as introduced by Easley et al. (2011, 2012).

• One do-it-all function for trade classification in buyer-initiated or seller-initiated trades that implements the standard algorithms in the field, namely Tick, Quote, LR, and EMO.

Alternative packages

To our knowledge, there are three preexisting R packages for the estimation of models of the probability of informed trading: pinbasic, InfoTrad, and FinAsym.

Getting help

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