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Estimates the Probability of Informed Trading (PIN) using the initial sets from the algorithm in Ersan and Alici (2016) .


pin_ea(data, factorization, xtraclusters = 4, verbose = TRUE)



A dataframe with 2 variables: the first corresponds to buyer-initiated trades (buys), and the second corresponds to seller-initiated trades (sells).


A character string from {"E", "EHO", "LK", "NONE"} referring to a given factorization. The default value is "E".


An integer used to divide trading days into #(2 + xtraclusters) clusters, thereby resulting in #comb(1 + xtraclusters, 1) initial parameter sets in line with Ersan and Alici (2016) . The default value is 4.


A binary variable that determines whether detailed information about the steps of the estimation of the PIN model is displayed. No output is produced when verbose is set to FALSE. The default value is TRUE.


Returns an object of class


The argument 'data' should be a numeric dataframe, and contain at least two variables. Only the first two variables will be considered: The first variable is assumed to correspond to the total number of buyer-initiated trades, while the second variable is assumed to correspond to the total number of seller-initiated trades. Each row or observation correspond to a trading day. NA values will be ignored.

The factorization variable takes one of four values:

  • "EHO" refers to the factorization in Easley et al. (2010)

  • "LK" refers to the factorization in Lin and Ke (2011)

  • "E" refers to the factorization in Ersan (2016)

  • "NONE" refers to the original likelihood function - with no factorization

The function pin_ea() implements the algorithm detailed in Ersan and Alici (2016) . The higher the number of the additional layers (xtraclusters), the better is the estimation. Ersan and Alici (2016) , however, have shown the benefit of increasing this number beyond 5 is marginal, and statistically insignificant.

The function initials_pin_ea() provides the initial parameter sets obtained through the implementation of the Ersan and Alici (2016) algorithm. For further information on the initial parameter set determination, see initials_pin_ea().


Easley D, Hvidkjaer S, Ohara M (2010). “Factoring information into returns.” Journal of Financial and Quantitative Analysis, 45(2), 293--309. ISSN 00221090.

Ersan O (2016). “Multilayer Probability of Informed Trading.” Available at SSRN 2874420.

Ersan O, Alici A (2016). “An unbiased computation methodology for estimating the probability of informed trading (PIN).” Journal of International Financial Markets, Institutions and Money, 43, 74--94. ISSN 10424431.

Lin H, Ke W (2011). “A computing bias in estimating the probability of informed trading.” Journal of Financial Markets, 14(4), 625-640. ISSN 1386-4181.


# There is a preloaded quarterly dataset called 'dailytrades' with 60
# observations. Each observation corresponds to a day and contains the
# total number of buyer-initiated trades ('B') and seller-initiated
# trades ('S') on that day. To know more, type ?dailytrades

xdata <- dailytrades

# Estimate the PIN model using the factorization of Ersan (2016), and initial
# parameter sets generated using the algorithm of Ersan and Alici (2016).
# The argument xtraclusters is omitted so will take its default value 4.

estimate <- pin_ea(xdata, verbose = FALSE)

# Display the estimated PIN value

#> [1] 0.5661721

# Display the estimated parameters

#>        alpha        delta           mu        eps.b        eps.s 
#>    0.7499975    0.1333342 1193.5179655  357.2659099  328.6291793 

# Store the initial parameter sets used for MLE in a dataframe variable,
# and display its first five rows

initialsets <- estimate@initialsets
show(head(initialsets, 5))
#>       alpha      delta        mu     eps.b    eps.s
#> 1 0.7500000 0.13333333 1213.3422  336.1429 336.1852
#> 2 0.6333333 0.10526316 1262.0469  446.8846 356.4107
#> 3 0.5333333 0.09375000 1329.2577  531.6774 367.4561
#> 4 0.4833333 0.03448276 1364.5773  556.6875 399.6780
#> 5 0.1000000 0.00000000  928.7648 1076.1852 423.2833