Estimates the Probability of Informed Trading (`PIN`

)
using custom initial parameter sets

## Arguments

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

- initialsets
A dataframe with the following variables in this order (\(\alpha\), \(\delta\), \(\mu\), \(\epsilon\)

_{b}, \(\epsilon\)_{s}).- factorization
A character string from

`{"EHO", "LK", "E", "NONE"}`

referring to a given factorization. The default value is set to`"E"`

.- verbose
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`

.

## 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.

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

## References

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*.

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.

## 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
#--------------------------------------------------------------
# Using generic function pin()
#--------------------------------------------------------------
# Define initial parameters:
# initialset = (alpha, delta, mu, eps.b, eps.s)
initialset <- c(0.3, 0.1, 800, 300, 200)
# Estimate the PIN model using the factorization of the PIN likelihood
# function by Ersan (2016)
estimate <- pin(xdata, initialsets = initialset, verbose = FALSE)
# Display the estimated PIN value
show(estimate@pin)
#> [1] 0.5661728
# Display the estimated parameters
show(estimate@parameters)
#> alpha delta mu eps.b eps.s
#> 0.7499996 0.1333280 1193.5176276 357.2656584 328.6292445
# 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 0.3 0.1 800 300 200
```