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

model.

## 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
xdata <- 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
# }
```