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

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

# Obtain a dataframe of initial parameter sets for the maximum likelihood
# estimation using the algorithm of Ersan and Ghachem (2022b).

#> The function initials_adjpin(...) has generated 49 initial parameter sets.
#>
To display them, either store them in a variable or call (initials_adjpin(...)).
#>
To hide these messages, set the argument 'verbose' to FALSE.
#>

# Show the value of adjusted PIN

estimate <- adjpin(xdata, initialsets = init.sets, verbose = FALSE)