estimate_compml: Estimated the probability of informed trading of the...
In simonsays1980/bayespin: An R package for Bayesian estimation of the probability of informed trading

Description Usage Arguments Details Value References See Also Examples

Calling estimate_compml() estimates the probability of informed trading (PIN) from the model of Jackson (2007) using maximum likelihood (ML). As described in the paper by Jackson (2007) and similar to the Bayesian estimation used in Grammig et al. (2015) this model needs only the number of trades per day provided in the parameter data.

estimate_compml(
  data,
  startpar,
  T = 390,
  methodLik = c("precise", "approx"),
  fnscale = -1,
  trace = 0,
  grad_free = TRUE,
  return_opt = FALSE,
  opt_out = TRUE
)

`data`	A `vector` containing the number of trades per day.
`startpar`	A vector containing start parameters for maximum likelihood estimation. These must be starting values for the logit of alpha, epsilon, and mu. If no starting values are provided the function chooses the values `(0, mean(trades)x.75/2, mean(trades)x.25/2)`.
`T`	A double specifying the minutes of a trading day.
`methodLik`	A character specifying, if undefined function values in optimization should be approximated by large defined values (`1e+6`). This can help to make maximum likelihood estimation more stable.
`fnscale`	A negatve double specifying a scaling factor for the likelihood function. This can in some cases help when the algorithm does not reach convergence or suffer from number overflow.
`trace`	An integer specifying which level of tracing should be used. see `?optim` for more details.
`grad_free`	A logical indicating if gradient-free optimization should be used when gradient descent did not converge. If `TRUE` the optimization procedure `nmkb` is used.
`return_opt`	A logical indicating, if in addition to the PIN estimates also the results from the optimization procedure should be returned. If `TRUE` a list is returned with an element `pin_estimates` holding the PIN estimates and an element `opt_results` holding the output of the optimization procedure.
`opt_out`	(Deprecated) A logical indicating if only the output of the optimization procedure should be returned. Some older applications still rely on this output. In the next version this feature will be removed. Note that the default value is `TRUE`.

Optimization algorithms

Optimization is performed gradient-based by using the optim function. The algorithm used is the L-BFGS-B that allows for parameter restrictions. This is necessary because we use for the probability alpha the logistic transformation exp()/(1+exp()) to produce valid probabilities in optimization.

In case that the gradient-based algorithm does not converge in between 100 steps, a gradient-free optimization is applied. For gradient-free optimization nmkb, a bounded Nelder-Mead algorithm is used. Derivative-free optimization is only performed after gradient-based optimization did not converge and the argument grad_free is TRUE.

The argument fnscale can be used to scale the likelihood function in case of very large values (e.g. very large volumes) that might lead to number overflow during computation. Note, fnscale must always be negative as the likelihood function should be maximized.

A list with all components as returned by optim or nmkb.

Jackson, D., 2007. Infering trader behavior from transaction data: A trade count model. Journal of Computational and Graphical Statistics 12, 55-79.
Grammig, J., Theissen, E., Zehnder, L.S., 2015. Bayesian Estimation of the Probability of Informed Trading. Conference on Financial Econometrics & Empirical Asset Pricing 2016, Lancaster University

estimate_pin() for estimating the PIN with a Bayesian approach that needs only the total number of trades
estimate_mlekop() for estimating the PIN with the original EKOP model that needs the numbers of buyer- and seller-initiated trades per day
compute_comp_lik() for the implementation of the likelihood function of the paper of Jackson (2007).

# Simulate data from the EKOP model. 
trades_data <- simulate_ekop()
# Estimate the EKOP model by maximum likelihood.
pin_estml <- estimate_compml(trades_data$Trades, methodLik="approx", 
                             opt_out=FALSE)