Based on the grid search algorithm of Yan and Zhang (2012) , generates initial parameter sets for the maximum likelihood estimation of the PIN model.

## Usage

initials_pin_yz(data, grid_size = 5, ea_correction = FALSE,
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).

grid_size

An integer between 1, and 20; representing the size of the grid. The default value is 5. See more in details.

ea_correction

A binary variable determining whether the modifications of the algorithm of Yan and Zhang (2012) suggested by Ersan and Alici (2016) are implemented. The default value is FALSE.

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 sets each consisting of five variables {$$\alpha$$, $$\delta$$, $$\mu$$, $$\epsilon$$b, $$\epsilon$$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 argument grid_size determines the size of the grid of the variables: alpha, delta, and eps.b. If grid_size is set to a given value m, the algorithm creates a sequence starting from 1/2m, and ending in 1 - 1/2m, with a step of 1/m. The default value of 5 corresponds to the size of the grid in Yan and Zhang (2012) . In that case, the sequence starts at 0.1 = 1/(2 x 5), and ends in 0.9 = 1 - 1/(2 x 5) with a step of 0.2 = 1/m.

The function initials_pin_yz() implements, by default, the original Yan and Zhang (2012) algorithm as the default value of ea_correction takes the value FALSE. When the value of ea_correction is set to TRUE; then, sets with irrelevant mu values are excluded, and sets with boundary values are reintegrated in the initial parameter sets.

## References

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.

Yan Y, Zhang S (2012). “An improved estimation method and empirical properties of the probability of informed trading.” Journal of Banking and Finance, 36(2), 454--467. ISSN 03784266.

## 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

# The function pin_yz() allows the user to directly estimate the PIN model
# using the full set of initial parameter sets generated using the algorithm
# of Yan and # Zhang (2012).
# \donttest{
estimate.1 <- pin_yz(xdata, verbose = FALSE)
# }
# Obtaining the set of initial parameter sets using initials_pin_yz allows
# us to estimate the PIN model using a subset of these initial sets.

initparams <- initials_pin_yz(xdata, verbose = FALSE)

# Use 10 randonly chosen initial sets from the dataframe 'initparams' in
# order to estimate the PIN model using the function pin() with custom
# initial parameter sets

numberofsets <- nrow(initparams)
selectedsets <- initparams[sample(numberofsets, 10),]

estimate.2 <- pin(xdata, initialsets = selectedsets, verbose = FALSE)

# Compare the parameters and the pin values of both specifications
# \donttest{
comparison <- rbind(c(estimate.1@parameters, pin = estimate.1@pin),
c(estimate.2@parameters, estimate.2@pin))

rownames(comparison) <- c("all", "10")

show(comparison)
#>         alpha     delta       mu    eps.b    eps.s       pin
#> all 0.7500027 0.1333335 1193.518 357.2654 328.6293 0.5661740
#> 10  0.7499982 0.1333331 1193.518 357.2658 328.6293 0.5661723
# }