Statistical model for price discovery

Abstract

Statistical models for price discovery have traditionally been time series models with fixed intervals. Analysis of ultra high frequency data requires modeling the time along with the characteristics of the transactional data . Auto-regressive conditional duration (ACD) models account for irregular time intervals and estimate the distribution of arrival times for the irregular time intervals and estimate the distribution of arrival times for the next event conditional on all past information. A family of ACD models can be defined using different specification for the the conditional density and conditional mean of the duration. The motivation for developing the various extension of ACD modles has been dwelt upon and the properties of these extensions have been briefly covered . In this report , The general ACD model with weibull as the conditional distribution is considered . Attempt has been made to parameterize the model using the maximum likelihood estimation mehod. however , Finally an estimation of the undertaken and the final parameters are the output of MLE on GARH (1,1) model with the square root of the duration as the dependent variable. The applicability of the model in the Indian context has been explored by analyzing the stock data of Infosys traded at NSE with the IBM stock data From NYSE originally studied by Engle and Russell in their paper on ACD Models. The infosys stock data shows comparably significant levels of auto correlation in duration to that of the IBM data. It is noted that the frequency of transactions is much higher as compared to correlations . The parameters obtained from the EACD ( 1,1) estimates are of the same order as the expected values based on the previous estimates of the ACD model for the dataset and re strongly persistent.