MPIN initial parameter sets of Ersan (2016) — initials

Based on the algorithm in Ersan (2016) , generates initial parameter sets for the maximum likelihood estimation of the MPIN model.

Usage

initials_mpin(data, layers = NULL, detectlayers = "EG",
 xtraclusters = 4, verbose = TRUE)

Arguments

data: A dataframe with 2 variables: the first corresponds to buyer-initiated trades (buys), and the second corresponds to seller-initiated trades (sells).
layers: An integer referring to the assumed number of information layers in the data. If the value of layers is NULL, then the number of layers is automatically determined by one of the following functions: detectlayers_e(), detectlayers_eg(), and detectlayers_ecm(). The default value is NULL.
detectlayers: A character string referring to the layer detection algorithm used to determine the number of layers in the data. It takes one of three values: "E", "EG", and "ECM". "E" refers to the algorithm in Ersan (2016) , "EG" refers to the algorithm in Ersan and Ghachem (2024) ; while "ECM" refers to the algorithm in Ghachem and Ersan (2025) . The default value is "EG". Comparative results between the layer detection algorithms can be found in Ersan and Ghachem (2024) .
xtraclusters: An integer used to divide trading days into #(1 + layers + xtraclusters) clusters, thereby resulting in #comb(layers + xtraclusters, layers) initial parameter sets in line with Ersan and Alici (2016) , and Ersan (2016) . The default value is 4 as chosen in Ersan (2016) .
verbose: a binary variable that determines whether information messages about the initial parameter sets, including the number of the initial parameter sets generated. No message is shown when verbose is set to FALSE. The default value is TRUE.

Value

Returns a dataframe of initial parameter sets each consisting of 3J + 2 variables {\(\alpha\), \(\delta\), \(\mu\), \(\epsilon\)_b, \(\epsilon\)_s}. \(\alpha\), \(\delta\), and \(\mu\) are vectors of length J where J is the number of layers in the MPIN model.

Details

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.

References

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.

Ersan O, Ghachem M (2024). “Identifying information types in the estimation of informed trading: an improved algorithm.” Journal of Risk and Financial Management, 17(9), 409.

Ghachem M, Ersan O (2025). “Estimation of the probability of informed trading models via an expectation-conditional maximization algorithm.” Financial Innovation, 11(1), 67.

Examples

# 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

# Obtain a dataframe of initial parameter sets for estimation of the MPIN
# model using the algorithm of Ersan (2016) with 3 extra clusters.
# By default, the number of layers in the data is detected using the
# algorithm of Ersan and Ghachem (2022a).

initparams <- initials_mpin(xdata, xtraclusters = 3, verbose = FALSE)

# Show the six first initial parameter sets

print(round(t(head(initparams)), 3))
#>                1        2        3        4        5        6
#> alpha.1    0.117    0.117    0.117    0.117    0.217    0.217
#> alpha.2    0.100    0.150    0.217    0.533    0.050    0.117
#> alpha.3    0.533    0.483    0.417    0.100    0.483    0.417
#> delta.1    0.286    0.286    0.286    0.286    0.231    0.231
#> delta.2    0.167    0.333    0.231    0.125    0.667    0.286
#> delta.3    0.094    0.034    0.040    0.000    0.034    0.040
#> mu.1     561.018  561.018  561.018  561.018  599.484  599.484
#> mu.2     644.362  762.236  973.023 1286.969  997.986 1254.732
#> mu.3    1462.722 1510.798 1520.959 1581.709 1510.798 1520.959
#> eps.b    336.143  336.143  336.143  336.143  336.143  336.143
#> eps.s    336.185  336.185  336.185  336.185  336.185  336.185

# Use 10 randomly selected initial parameter sets from initparams to
# estimate the probability of informed trading via mpin_ecm. The number
# of information layers will be detected from the initial parameter sets.

numberofsets <- nrow(initparams)
selectedsets <- initparams[sample(numberofsets, 10),]
# \donttest{
estimate <- mpin_ecm(xdata, initialsets = selectedsets, verbose = FALSE)

# Display the estimated MPIN value

show(estimate@mpin)
#> [1] 0.5744481

# Display the estimated parameters as a numeric vector.

show(unlist(estimate@parameters))
#> alpha.layer.1 alpha.layer.2 alpha.layer.3 delta.layer.1 delta.layer.2 
#>  2.166667e-01  5.000000e-02  4.833333e-01  2.307692e-01  6.666667e-01 
#> delta.layer.3    mu.layer.1    mu.layer.2    mu.layer.3         eps.b 
#>  3.448276e-02  6.028381e+02  9.864245e+02  1.506785e+03  3.369193e+02 
#>         eps.s 
#>  3.358877e+02 

# Store the posterior probabilities in a variable, and show the first 6 rows.

modelposteriors <- get_posteriors(estimate)
show(round(head(modelposteriors), 3))
#>   post.N post.G[1] post.G[2] post.G[3] Post.B[1] Post.B[2] Post.B[3]
#> 1      1         0         0         0         0         0         0
#> 2      0         1         0         0         0         0         0
#> 3      0         0         1         0         0         0         0
#> 4      0         1         0         0         0         0         0
#> 5      0         1         0         0         0         0         0
#> 6      0         1         0         0         0         0         0
# }