Time transformations, intraday data and volatility models

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Abstract
In this paper, we focus on the trade and quote data for the IBM stock traded at the NYSE.We present two different frameworks for analyzing this dataset. First, using regularly sampled observations, we characterize the intraday volatility of the mid-point of the bid-ask quotes by estimating GARCH and EGARCH models, with intraday seasonalitybeing accounted for. We also highlight the impact of characteristics of the trade process (traded volume, number of trades and average volume per trade) on the volatility specifications. Secondly, we deal directly with the irregularly spaced data. We review two time transformations that allowa thinning of the original dataset such that new durations are defined. The newly defined price and volume durations are characterized and the performance of the Log-ACD model for modelling these durations is assessed. Moreover, price durations allowan easy computation of intraday volatility and this method compares favorablyto ARCH estimations.

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