# Empirical Results and Extensions

## Abstract

In this chapter we consider two extensions of the models presented in Chapter 3. Firstly, we use the intraday duration models to test some market microstructure effects. The models presented in Chapter 3 introduce a new way of modelling the times between market events and are directly related to quantitative tools developed in labour econometrics. While the models can be used to characterize the point processes defined by trade, quote, price or volume durations, they can also be used to test market microstructure effects such as presented in Chapter 1. This has been one of the main motivations for the use of such intraday duration models, and most recent papers focusing on the econometric modelling of the durations usually include a market microstructure section (Engle and Russell, 1997, 1998; Engle and Lunde, 1998; Bauwens and Giot, 1998, 2000; Grammig and Wellner, 1999). In Section 2 of this chapter, we review some possible applications of the Log-ACD model to the testing of market microstructure issues which deal with the (bid-ask quotes) updating behavior of a market maker with respect to the information flow.

## Keywords

Trading Intensity Trading Strategy Price Process Market Maker Market Microstructure## Preview

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## Notes

- 1.The main property of QMLE is its consistency even if the assumed error distribution is not the exponential (under usual regularity conditions). This robustness comes at the expense of efficiency, but in very large samples this drawback is not a big worry.Google Scholar
- 2.The unexpected volume is defined as the volume in excess of the normal volume or liquidity volume. The source of the unexpected volume is the arrival of informed traders in the market.Google Scholar
- 3.Published as Engle (2000).Google Scholar
- 4.In principle, a third end state is possible: the state where there is no price change in the mid-price over duration xi. This state does not occur given that we use price durations. The model could easily be extended to a multi-state transition model. Another reason for considering more than two states arises if one wants to account for several levels of price increase or decrease. Notice, however, that a continuous price change is excluded because of the discreteness of price changes.Google Scholar
- 5.For example, in Lindeboom and Van den Berg (1994) and in Carling (1996), dependence between durations arises because the hazard rates depend on stochastically related unobserved components.Google Scholar
- 6.However, when γ+ and γ- are not equal, we cannot obtain the conditional (on the past) transition probabilities analytically.Google Scholar
- 7.Strictly speaking, there should be 12 estimation outcomes, but the Disney stock with c
_{p}= $ 1/2 gives too few price durations to be meaningfully estimated.Google Scholar - 8.Student tests for the hypothesis that γ+ = 1 give p-values of 0.04, 0.94, 0.23 and 0 for the Disney, IBM, Boeing and Exxon stocks, respectively; corresponding tests for the hypothesis that γ- =1 give p-values of 0.60, 0.94, 0 and 0.Google Scholar
- 9.Student tests for the hypothesis that γ+ = γ- give p-values of 0.07, very close to 1, 0, and 0.93 for the Disney, IBM, Boeing and Exxon stocks, respectively.Google Scholar
- 10.Student tests for the hypothesis that α1 < α2 give p-values of 0.40, 0, 0 and 0.04 for the Disney, IBM, Boeing and Exxon stocks, respectively.Google Scholar
- 11.Student tests for the hypothesis that α3 > α4 give p-values of 0.01, 0.09, 0.09 and 0.01 for the Disney, IBM, Boeing and Exxon stocks, respectively.Google Scholar
- 12.We have estimated the model for each set of price durations corresponding to a different threshold of the price change used to thin the quote process. Estimates are not reported since they are qualitatively similar to those reported in the previous subsection.Google Scholar
- 13.This strategy is only meant to be illustrative. In a ‘real life’ situation, other parameters have to be taken into account: risk analysis of the position, overnight positions, limited amount of short-selling, limit positions in tradingchrw(133)Google Scholar
- 14.Under the given trading strategy, the model is required to trade at the end of every price durations, which explains the very high transaction costs.Google Scholar