Modelling the relationships between duration and variation in asset prices

Abstract

This paper proposes a Generalized Logarithmic Autoregressive Conditional Duration (GLACD) model to examine the interaction between duration and variation in asset prices, and thus provides a convenient framework to test statistically the existence of such relationship. The model is flexible and contains various well known models as special cases, including, the Exponential Generalised Autoregressive Heteroskedasticity (EGARCH) model of Nelson (1991) and the Logarithmic Conditional Duration (Log-ACD) model of Bauwens and Giot (2000). The paper also obtains theoretical results for the Quasi-Maximum Likelihood Estimator (QMLE) for the proposed model. Specifically, sufficient conditions for consistency and asymptotic normality are derived under mild assumptions. Monte Carlo experiments also provide further support of the theoretical results and demonstrate that the QMLE has reasonably good finite sample performance. The paper then applies the model to nine different assets from three different asset classes, namely two exchange rate, two commodities and five stocks. The two currencies are Australia/US and British Pound/US exchange rates; the two commodities are Gold and Silver and the five stocks are BHP, Rio Tinto, CBA, ANZ and Apple. The sample spans from 1 March 2010 to 31 May 2010 with the number of observations ranges from 44178 to 1109897. The results show that there are strong relationship between duration and variation in price changes. The forecast performance of GLACD is also compared with the Log-ACD model and the results show that the proposed model performed better than the Log-ACD model.