# AdjPIN initial parameter sets of Ersan & Ghachem (2022b)

Source:`R/model_adjpin.R`

`initials_adjpin.Rd`

Based on the algorithm in Ersan and Ghachem (2022b)
,
generates sets of initial parameters to be used in the maximum likelihood
estimation of `AdjPIN`

model.

## Usage

```
initials_adjpin(data, xtraclusters = 4, restricted = list(),
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).

- xtraclusters
An integer used to divide trading days into #

`(4 + xtraclusters)`

clusters, thereby resulting in #`comb(4 + xtraclusters - 1, 4 - 1)`

initial parameter sets in line with Ersan and Alici (2016) , and Ersan and Ghachem (2022b) .The default value is`4`

as chosen in Ersan (2016) .- restricted
A binary list that allows estimating restricted AdjPIN models by specifying which model parameters are assumed to be equal. It contains one or multiple of the following four elements

`{theta, mu, eps, d}`

. For instance, If`theta`

is set to`TRUE`

, then the probability of liquidity shock in no-information days, and in information days is assumed to be the same (\(\theta\)`=`

\(\theta'\)). If any of the remaining rate elements`{mu, eps, d}`

is set to`TRUE`

, (say`mu=TRUE`

), then the rate is assumed to be the same on the buy side, and on the sell side (\(\mu\)_{b}`=`

\(\mu\)_{s}). If more than one element is set to`TRUE`

, then the restrictions are combined. For instance, if the argument`restricted`

is set to`list(theta=TRUE, eps=TRUE, d=TRUE)`

, then the restricted AdjPIN model is estimated, where \(\theta\)`=`

\(\theta'\), \(\epsilon\)_{b}`=`

\(\epsilon\)_{s}, and \(\Delta\)_{b}`=`

\(\Delta\)_{s}. If the value of the argument`restricted`

is the empty list, then all parameters of the model are assumed to be independent, and the unrestricted model is estimated. The default value is the empty list`list()`

.- 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 numerical vectors of ten elements
{\(\alpha\), \(\delta\), \(\theta\), \(\theta'\),
\(\epsilon\)_{b}, \(\epsilon\)_{s}, \(\mu\)_{b}, \(\mu\)_{s}, \(\Delta\)_{b}, \(\Delta\)_{s}}.

## 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 function `initials_adjpin()`

implements the algorithm suggested in
Ersan and Ghachem (2022b)
, and uses a hierarchical
agglomerative clustering (HAC) to find initial parameter sets for
the maximum likelihood estimation.

## 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 (2022b).
“A methodological approach to the computational problems in the estimation of adjusted PIN model.”
*Available at SSRN 4117954*.

## 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 transactions ('B') and seller-initiated
# transactions ('S') on that day. To know more, type ?dailytrades
xdata <- dailytrades
# Obtain a dataframe of initial parameter sets for the maximum likelihood
# estimation using the algorithm of Ersan and Ghachem (2022b).
init.sets <- initials_adjpin(xdata)
#> The function initials_adjpin(...) has generated 49 initial parameter sets.
#>
To display the initial sets, store them in a variable or call (initials_adjpin(...)).
#>
To hide these messages, set the argument 'silent' to TRUE (silent = TRUE).
#>
# Use the list to estimate adjpin using the adjpin() method
# Show the value of adjusted PIN
estimate <- adjpin(xdata, initialsets = init.sets, verbose = FALSE)
show(estimate@adjpin)
#> [1] 0.2950832
```