This vignette describes various scenarios of creating sample datasets
that fit the preferences and needs of the users; and this for the
different models. The functions in the package PINstimation use two
types of datasets: (1) A sequence of daily buys and sells (2) A
high-frequency trading data. This is the reason why only two sample
datasets are preloaded with the package, namely
dailytrades, and hfdata. The users can also
generate simulated data using the function
generatedata_mpin() for PIN, and MPIN models; and the
function generatedata_adjpin() for the ADJPIN model. Below
we provide some scenarios of creating sample datasets both for the PIN,
MPIN, and ADJPIN models.
The PIN model is a multilayer PIN model with a single information
layer. We can, therefore, use the function
generatedata_mpin(), in order to generate sample data for
the PIN model. Generically, this is done as follows:
If the user would like to create a sample dataset for infrequently
traded stock, she can specify low values or ranges for the trade
intensity rates. For instance, let’s assume that the user suspects that
an infrequently-traded stock has an average of uninformed trading
intensity for buys and sells between 300 and
500. They generate a single sample dataset for this
scenario as follows:
pindata <- generatedata_mpin(layers=1, ranges = list(eps.b=c(300, 500), eps.s=c(300,500)), verbose = FALSE)The details of the generated sample dataset can be displayed with the following code
## ----------------------------------
## Data series successfully generated
## ----------------------------------
## Simulation model : MPIN model
## Number of layers : 1 layer(s)
## Number of trading days : 60 days
## ----------------------------------
## Type object@data to get the simulated data
##
## Data simulation
##
## =========== ============== ============ =============
## Variables Theoretical. Empirical. Aggregates.
## =========== ============== ============ =============
## alpha 0.094838 0.133333 0.133333
## delta 0.796153 0.75 0.75
## mu 173 169.37 169.37
## eps.b 423 424.03 424.03
## eps.s 409 406.33 406.33
## ----
## Likelihood - (559.851) (559.851)
## mpin - 0.026475 0.026475
## =========== ============== ============ =============
##
## -------
## Running time: 0.003 seconds
You access the sequences of buys, and sells through the slot
@data of the object pindata.
## b s
## 1 435 403
## 2 447 416
## 3 402 405
## 4 439 423
## 5 425 411
## 6 422 379
## 7 400 436
## 8 428 407
## 9 606 396
## 10 414 403
You can, now use the dataset object pindata to check the
accuracy of the different estimation functions. You can do that by
comparing the actual parameters of the sample datasets to the estimated
parameters of the estimation functions. Let us start with displaying the
actual parameters of the sample datasets. These can be accessed through
the slot @empiricals of the dataset object, which stores
the empirical parameters computed from the sequences of buys and sells
generated. Please refer to the documentation of
generatedata_mpin() for more information.
## alpha delta mu eps.b eps.s
## 0.1333333 0.7500000 169.3663793 424.0344828 406.3333333
Estimate the PIN model using the function pin_ea(), and
display the estimated parameters
## alpha delta mu eps.b eps.s
## 0.1333324 0.7499957 169.3533320 423.9771743 406.3924509
Now calculate the absolute errors of the estimation method.
## alpha delta mu eps.b eps.s
## 8.956509e-07 4.282267e-06 1.304729e-02 5.730844e-02 5.911761e-02
In contrast to the PIN model, the number of information layers is
free. We can, therefore, use the function
generatedata_mpin() with the desired number of information
layers, in order to generate sample data for the MPIN model. We can also
skip specifying the number of layers, and the default setting will be
used: the number of layers will be randomly selected from the integer
set from 1 to 5. Generically, this is done as
follows:
If the user would like to create a sample dataset for frequently
traded stock with two information layers, she can set the argument
layers to 2, and specify high values or ranges for the trade intensity
rates. For instance, let’s assume that the user suspects that a
frequently-traded stock has an average of uninformed trading intensity
for buys and sells between 12000 and 15000.
They generate a single sample dataset for this scenario as follows:
mpindata <- generatedata_mpin(layers=2, ranges = list(eps.b=c(12000, 15000), eps.s=c(12000,15000)), verbose = FALSE)The details of the generated sample dataset can be displayed with the following code
## ----------------------------------
## Data series successfully generated
## ----------------------------------
## Simulation model : MPIN model
## Number of layers : 2 layer(s)
## Number of trading days : 60 days
## ----------------------------------
## Type object@data to get the simulated data
##
## Data simulation
##
## =========== ================== ================== =============
## Variables Theoretical. Empirical. Aggregates.
## =========== ================== ================== =============
## alpha 0.437577, 0.169096 0.666667, 0.050000 0.716667
## delta 0.502144, 0.517968 0.525, 0.000 0.488372
## mu 1020, 2531 1035.62, 2498.03 1137.64
## eps.b 13482 13487.97 13487.97
## eps.s 14051 14041.56 14041.56
## ----
## Likelihood - (806.82) (806.82)
## mpin - 0.028764 0.028764
## =========== ================== ================== =============
##
## -------
## Running time: 0.003 seconds
You access the sequences of buys, and sells through the slot
@data of the object mpindata.
## b s
## 1 13626 13870
## 2 13434 14983
## 3 13470 14081
## 4 13403 13943
## 5 14457 14075
## 6 14557 14266
## 7 13554 15131
## 8 16096 13938
## 9 14351 13984
## 10 13507 15229
You can, now use the dataset object mpindata to check
the accuracy of the different estimation functions, namely
mpin_ml(), and mpin_ecm(). You can do that by
comparing the empirical PIN value derived from the sample dataset to the
estimated PIN value of the estimation functions. Let us start with
displaying the empirical PIN value obtained from the sample dataset.
This value can be accessed through the slot @emp.pin of the
dataset object, which stores the empirical PIN value computed from the
sequences of buys and sells generated. Please refer to the documentation
of generatedata_mpin() for more information.
## MPIN
## 0.02876403
Estimate the MPIN model using the functions mpin_ml(),
and mpin_ecm(), and display the estimated MPIN values.
model_ml <- mpin_ml(data=mpindata@data, verbose = FALSE)
model_ecm <- mpin_ecm(data=mpindata@data, verbose = FALSE)
mlmpin <- model_ml@mpin
ecmpin <- model_ecm@mpin
estimates <- setNames(c(mlmpin, ecmpin), c("ML", "ECM"))
show(estimates)## ML ECM
## 0.02876317 0.02876227
Now calculate the absolute errors of both estimation methods.
## ML ECM
## 8.639907e-07 1.759255e-06
The function generatedata_mpin() can generate a
data.series object that contains a collection of
dataset objects. For instance, the user can generate
layers, and use it to check the accuracy of the MPIN estimation.
size <- 3
collection <- generatedata_mpin(series = size, layers = 3, verbose = FALSE)
show(collection)## ----------------------------------
## Simulated data successfully generated
## ----------------------------------
## Simulation model : MPIN model
## Number of layers : 3 layer(s)
## Number of datasets : 3 datasets
## Number of trading days : 60 days
## ----------------------------------
## Type object@datasets to access the list of dataset objects
##
## Data simulation
##
## -------
## Running time: 0.011 seconds
accuracy <- devmpin <- 0
for (i in 1:size) {
sdata <- collection@datasets[[i]]
model <- mpin_ml(sdata@data, xtraclusters = 3, verbose=FALSE)
accuracy <- accuracy + (sdata@layers == model@layers)
devmpin <- devmpin + abs(sdata@emp.pin - model@mpin)
}
cat('The accuracy of layer detection: ', paste0(accuracy*(100/size),"%.\n"), sep="")## The accuracy of layer detection: 100%.
## The average error in MPIN estimates: 0.001772188.
The AdjPIN model is an extension of the PIN model that includes the
possibility of liquidity shocks. To obtain a sample dataset distributed
according to the assumptions of the AdjPIN model, users can use the
function generatedata_adjpin(). Generically, this is done
as follows:
If the user desires to create 2 sample datasets for frequently traded
stock, they can specify high values or ranges for the trade intensity
rates. For instance, let’s assume that the user suspects that a
frequently-traded stock has an average of uninformed trading intensity
for buys and sells between 10000 and
15000.
adjpindatasets <- generatedata_adjpin(series = 2, ranges = list(eps.b=c(10000, 15000), eps.s=c(10000,15000)), verbose = FALSE)The details of the generated sample data series can be displayed with the following code:
## ----------------------------------
## Simulated data successfully generated
## ----------------------------------
## Simulation model : AdjPIN model
## Model Restrictions : Unrestricted model
## Number of datasets : 2 datasets
## Number of trading days : 60 days
## ----------------------------------
## Type object@datasets to access the list of dataset objects
##
## Data simulation
##
## -------
## Running time: 0.017 seconds
You access the first dataset from adjpindatasets using
this code:
## ----------------------------------
## 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 0.238214 0.35
## delta 0.229543 0.333333
## theta 0.96825 0.948718
## theta' 0.98392 1
## ----
## eps.b 14669 14709.5
## eps.s 10627 10459.5
## mu.b 19385 19300.6
## mu.s 22930 22921.87
## d.b 57111 57139.62
## d.s 52799 52913.77
## ----
## Likelihood (889.205)
## adjPIN 0.035 0.052
## PSOS 0.78 0.767
## =========== ============== ============
##
## -------
## Running time: 0.007 seconds
You can, now use the dataset object adjpindata to check
the accuracy of the different estimation functions, namely MLE, and ECM
algorithms. You can do that by comparing the empirical adjpin, and psos
values derived from the sample dataset to the estimated adjpin, and psos
values obtained from the estimation functions. Let us start with
displaying the empirical adjpin, and psos values obtained from the
sample dataset. These values can be accessed through the slot
@emp.pin of the dataset object, which stores the empirical
adjpin/psos value computed from the sequences of buys and sells
generated. Please refer to the documentation of
generatedata_adjpin() for more information.
## adjpin psos
## 0.05173796 0.76683983
Estimate the AdjPIN model using adjpin(method="ML"), and
adjpin(method="ECM"), and display the estimated adjpin/psos
values.
model_ml <- adjpin(data=adjpindata@data, method = "ML", verbose = FALSE)
model_ecm <- adjpin(data=adjpindata@data, method = "ECM", verbose = FALSE)
mlpins <- c(model_ml@adjpin, model_ml@psos)
ecmpins <- c(model_ecm@adjpin, model_ecm@psos)
estimates <- rbind(mlpins, ecmpins)
colnames(estimates) <- c("adjpin", "psos")
rownames(estimates) <- c("ML", "ECM")
show(estimates)## adjpin psos
## ML 0.05170524 0.7668897
## ECM 0.05173184 0.7668605
Now calculate the absolute errors of both estimation methods.
## adjpin psos
## ML 3.271189e-05 4.988198e-05
## ECM 6.114091e-06 2.070096e-05
If you encounter a clear bug, please file an issue with a minimal reproducible example on GitHub.