Generates a dataset
object or a data.series
object (a list
of dataset
objects) storing simulation parameters as well as aggregate
daily buys and sells simulated following the assumption of the AdjPIN
model
of Duarte and Young (2009)
.
Arguments
- series
The number of datasets to generate.
- days
The number of trading days, for which aggregated buys and sells are generated. The default value is
60
.- parameters
A vector of model parameters of size
10
and it has the following form {\(\alpha\), \(\delta\), \(\theta\), \(\theta'\), \(\epsilon\)b, \(\epsilon\)s, \(\mu\)b, \(\mu\)s, \(\Delta\)b, \(\Delta\)s}.- ranges
A list of ranges for the different simulation parameters having named elements
alpha
\((\alpha)\),delta
\((\delta)\),theta
\((\theta)\),thetap
\((\theta')\),eps.b
(\(\epsilon\)b),eps.s
(\(\epsilon\)s),mu.b
(\(\mu\)b),mu.s
(\(\mu\)s),d.b
(\(\Delta\)b),d.s
(\(\Delta\)s). The value of each element is a vector of two numbers: the first one is the minimal valuemin_v
and the second one is the maximal valuemax_v
. If the element corresponding to a given parameter is missing, the default range for that parameter is used, otherwise, the simulation parameters are uniformly drawn from the interval (min_v
,max_v
). The default value islist()
.- 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, Iftheta
is set toTRUE
, 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 toTRUE
, (saymu=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 toTRUE
, then the restrictions are combined. For instance, if the argumentrestricted
is set tolist(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 argumentrestricted
is the empty list (list()
), then all parameters of the model are assumed to be independent, and the unrestricted model is estimated. The default value is the empty listlist()
.- verbose
A binary variable that determines whether detailed information about the progress of the data generation is displayed. No output is produced when
verbose
is set toFALSE
. The default value isTRUE
.
Value
Returns an object of class dataset
if series=1
, and an
object of class data.series
if series>1
.
Details
If the argument parameters
is missing, then the parameters are
generated using the ranges specified in the argument ranges
.
If the argument ranges
is set to list()
, default ranges are used. Using
the default ranges, the simulation parameters are obtained using the
following procedure:
\(\alpha\), \(\delta\):
(alpha, delta)
uniformly distributed on(0, 1)
.\(\theta\), \(\theta'\):
(theta,thetap)
uniformly distributed on(0, 1)
.\(\epsilon\)b:
(eps.b)
an integer uniformly drawn from the interval(100, 10000)
with step50
.\(\epsilon\)s:
(eps.s)
an integer uniformly drawn from ((4/5)
\(\epsilon\)b,(6/5)
\(\epsilon\)b) with step50
.\(\Delta\)b:
(d.b)
an integer uniformly drawn from ((1/2)
\(\epsilon\)b,2
\(\epsilon\)b).\(\Delta\)s:
(d.s)
an integer uniformly drawn from ((4/5)
\(\Delta\)b,(6/5)
\(\Delta\)b).\(\mu\)b:
(mu.b)
uniformly distributed on the interval((1/2) max
(\(\epsilon\)b, \(\epsilon\)s), 5 max
(\(\epsilon\)b, \(\epsilon\)s))
.\(\mu\)s:
(mu.s)
uniformly distributed on the interval ((4/5)
\(\mu\)b,(6/5)
\(\mu\)b)..
Based on the simulation parameters parameters
, daily buys and sells are
generated by the assumption that buys and sells follow Poisson
distributions with mean parameters:
(\(\epsilon\)b, \(\epsilon\)s) in a day with no information and no liquidity shock;
(\(\epsilon\)b+\(\Delta\)b, \(\epsilon\)s+\(\Delta\)s) in a day with no information and with liquidity shock;
(\(\epsilon\)b+\(\mu\)b, \(\epsilon\)s) in a day with good information and no liquidity shock;
(\(\epsilon\)b+\(\mu\)b+\(\Delta\)b, \(\epsilon\)s+\(\Delta\)s) in a day with good information and liquidity shock;
(\(\epsilon\)b, \(\epsilon\)s+\(\mu\)s) in a day with bad information and no liquidity shock;
(\(\epsilon\)b+\(\Delta\)s, \(\epsilon\)s+\(\mu\)s+\(\Delta\)s) in a day with bad information and liquidity shock;
References
Duarte J, Young L (2009). “Why is PIN priced?” Journal of Financial Economics, 91(2), 119--138. ISSN 0304405X.
Examples
# ------------------------------------------------------------------------ #
# Generate data following the AdjPIN model using generatedata_adjpin() #
# ------------------------------------------------------------------------ #
# With no arguments, the function generates one dataset object spanning
# 60 days, and where the parameters are chosen as described in the section
# 'Details'.
sdata <- generatedata_adjpin()
# Alternatively, simulation parameters can be provided. Recall the order of
# parameters (alpha, delta, theta, theta', eps.b, eps.s, mub, mus, db, ds).
givenpoint <- c(0.4, 0.1, 0.5, 0.6, 800, 1000, 2300, 4000, 500, 500)
sdata <- generatedata_adjpin(parameters = givenpoint)
# Data can be generated following restricted AdjPIN models, for example, with
# restrictions 'eps.b = eps.s', and 'mu.b = mu.s'.
sdata <- generatedata_adjpin(restricted = list(eps = TRUE, mu = TRUE))
# Data can be generated using provided ranges of simulation parameters as fed
# to the function using the argument 'ranges', where thetap corresponds to
# theta'.
sdata <- generatedata_adjpin(ranges = list(
alpha = c(0.1, 0.15), delta = c(0.2, 0.2),
theta = c(0.2, 0.6), thetap = c(0.2, 0.4)
))
# The value of a given simulation parameter can be set to a specific value by
# setting the range of the desired parameter takes a unique value, instead of
# a pair of values.
sdata <- generatedata_adjpin(ranges = list(
alpha = 0.4, delta = c(0.2, 0.7),
eps.b = c(100, 7000), mu.b = 8000
))
# Display the details of the generated simulation data
show(sdata)
#> ----------------------------------
#> Data series successfully generated
#> ----------------------------------
#> Simulation model : AdjPIN model
#> Model Restrictions : Unrestricted model
#> Number of trading days : 60 days
#> ----------------------------------
#> Type object@data to get the simulated data
#>
#> Data simulation
#>
#> =========== ============== ============
#> Variables Theoretical. Empirical.
#> =========== ============== ============
#> alpha 0.4 0.416667
#> delta 0.34835 0.32
#> theta 0.971039 1
#> theta' 0.387802 0.4
#> ----
#> eps.b 4256 4263.4
#> eps.s 3767 3764.4
#> mu.b 8000 8012.85
#> mu.s 8007 8014.07
#> d.b 7833 7815.47
#> d.s 8820 8803.86
#> ----
#> Likelihood (800.903)
#> adjPIN 0.136 0.14
#> PSOS 0.523 0.523
#> =========== ============== ============
#>
#> -------
#> Running time: 0.031 seconds
# ------------------------------------------------------------------------ #
# Use generatedata_adjpin() to check the accuracy of adjpin() #
# ------------------------------------------------------------------------ #
model <- adjpin(sdata@data, verbose = FALSE)
summary <- cbind(
c(sdata@emp.pin['adjpin'], model@adjpin, abs(model@adjpin -
sdata@emp.pin['adjpin'])),
c(sdata@emp.pin['psos'], model@psos, abs(model@psos -
sdata@emp.pin['psos']))
)
colnames(summary) <- c('adjpin', 'psos')
rownames(summary) <- c('Data', 'Model', 'Difference')
show(knitr::kable(summary, 'simple'))
#>
#>
#> adjpin psos
#> ----------- ---------- ----------
#> Data 0.1401044 0.5230339
#> Model 0.1398891 0.5234626
#> Difference 0.0002153 0.0004287