estimate_pin: Estimates the Bayesian probability of informed trading

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

Description

Calling estimate_pin() on trades data estimates the probability of informed trading from the compressed EKOP model presented in Grammig, Theissen and Zehnder (2015).

Usage

estimate_pin(pin_data, return_mcmc = FALSE, with_stephens = FALSE)

Arguments

pin_data	A vector of trades data (number of trades per day).
return_mcmc	A logical indicating, if MCMC parameter samples should be returned in addition to the final PIN estimates.
with_stephens	A logical indicating, if in addition to kmeans re- labeling also re-labeling via the algorithms from Stephens (1997a) and Stephens (1997b) should be applied.

Details

Internally this function uses the finmix package for estimation of the finite mixture parameters. The finmix package performs MCMC sampling for the parameters of the compressed EKOP model and computes three parameter estimates namely

• Maximum a posterior (MAP) the mode of the joint posterior of parameters and indicators,

• Bayesian maximum likelihood (BML) the mode of the joint posterior of parameters and indicators in case of a flat prior distribution,

• Identified ergodic average (IEAVG) is the ergodic average over the MCMC parameter traces after relabeling the parameters.

Relabeling

The MCMC sampling uses a socalled random permutation algorithm to force the labels of the two distributions in the mixture to switch randomly between iterations. Label switching occurs naturally in estimation of finite mixture distributions and is documented in the literature. Random permutation tries not to eliminate label switching, but to bring it into a more controlled setting. As a result each MCMC parameter trace contains parameter values of the other trace. For this reason re-labeling is performed after sampling.

The finmix package offers three different re-labeling algorithms:

• kmeans re-labels parameters by applying K-means clustering to the merged component parameters,

• Stephens1997a applies the algorithm suggested by Stephens (1997a) that tries to make the posterior marginal distributions of parameters uni-modal,

• Stephens1997b uses the algorithm presented in Stephens (1997b) that tries to re-label parameter values by minimizing the Kullback-Leibler distance between a parameter clustering via assignment probabilities and the classification probabilities defined by Poisson distributions.

To offer the user more flexibility the function can also return the MCMC samples for further inspection. Setting return_mcmc to TRUE (default) returns also the MCMC traces.

Value

A data.frame() with PIN estimates, if return_mcmc is FALSE. Otherwise, a list containing the data.frame of PIN estimates together with a finmix::mcmcoutput (see mcmcoutput-class) object containing the MCMC traces of the component paramaters.

References

• Easley, D., Kiefer, N., O’Hara, M., Paperman, J., 1996. Liquidity, information, and infrequently traded stocks. Journal of Finance 51, 1405–1436.

• 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

• Stephens, M., 1997a. Discussion 'On Bayesian analysis of mixtures with an unknown number of components' (by S. Richardson and P.J. Green), J. R. Statist. Soc., B, 59, 768-769.

• Stephens, M., 1997b. Bayesian methods for mixtures of normal distributions. DPhil. Thesis. University of Oxford, Oxford.

See Also

• mixturemcmc for performing MCMC sampling

• mcmcestimate for estimating parameters from MCMC samples

• compute_bayespin() for computing the Bayesian PIN from Bayesian estimates of the component parameters of the compressed EKOP model

Examples

# Simulate trades data
trades_data <- simulate_ekop()
# Estimate the Bayesian PIN.
estimate_pin(trades_data$Trades)

simonsays1980/bayespin documentation built on Dec. 23, 2021, 2:25 a.m.