A Pure-Jump Transaction-Level Price Model Yielding Cointegration

Hurvich, Clifford M.; Wang, Yi

doi:10.1198/jbes.2009.07116

Cited by 4 publications

(1 citation statement)

References 72 publications

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“…Recent interest in the point process approach to modeling transactionlevel data was spurred by the seminal paper of Engle and Russell (1998), who proposed a model for inter-trade durations. Other work on modeling transactionlevel data as point processes and/or constructing duration models includes that of Prigent (2001), Bowsher (2007), Billingsley (1968), Hautsch (2012), Bacry et al (2011), Deo et al (2009), Deo et al (2010), Hurvich and Wang (2010), Aue et al (2014), Shenai (2012), Chen et al (2012).…”

Section: Introductionmentioning

confidence: 99%

Drift in Transaction‐Level Asset Price Models

Cao

Hurvich

Soulier

2017

Journal Time Series Analysis

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We study the effect of drift in pure-jump transaction-level models for asset prices in continuous time, driven by point processes. The drift is assumed to arise from a non-zero mean in the efficient shock series. It follows that the drift is proportional to the driving point process itself, that is, the cumulative number of transactions. This link reveals a mechanism by which properties of intertrade durations (such as heavy tails and long memory) can have a strong impact on properties of average returns, thereby potentially making it extremely difficult to determine long-term growth rates or to reliably detect an equity premium. We focus on a basic univariate model for log price, coupled with general assumptions on the point process that are satisfied by several existing flexible models, allowing for both long memory and heavy tails in durations. Under our pure-jump model, we obtain the limiting distribution for the suitably normalized log price. This limiting distribution need not be Gaussian and may have either finite variance or infinite variance. We show that the drift can affect not only the limiting distribution for the normalized log price but also the rate in the corresponding normalization. Therefore, the drift (or equivalently, the properties of durations) affects the rate of convergence of estimators of the growth rate and can invalidate standard hypothesis tests for that growth rate. As a remedy to these problems, we propose a new ratio statistic that behaves more robustly and employ subsampling methods to carry out inference for the growth rate. Our analysis also sheds some new light on two long-standing debates as to whether stock returns have long memory or infinite variance. .Nevertheless, it must be recognized that time series of asset returns in discrete (say, equally spaced) time are still in widespread use and indeed may be the only recorded form of the data that encompass many decades. Such long historical series are of importance for understanding long-term trends (a prime focus of this article) and, arguably, for a realistic assessment of risk. So given the ubiquitous nature of the time series data and also keeping in mind the underlying price-generating process that occurred at the level of individual transactions, it is important to make sure that transaction-level models obey the stylized facts, not only for the intertrade durations but also for the lower-frequency time series.It has been observed empirically that time series of financial returns are weakly autocorrelated (although perhaps not completely uncorrelated), while squared returns or other proxies for volatility show strong autocorrelations that decay very slowly with increasing lag, possibly suggesting long memory (see Andersen et al. (2001)). It is also generally accepted that such time series show asymmetries, such as a correlation between the current return and the next period's squared return, and this effect (often referred to traditionally as the 'leverage effect') is addressed, for example, by the exponential generaliz...

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Section: Introductionmentioning

confidence: 99%

Drift in Transaction‐Level Asset Price Models

Cao

Hurvich

Soulier

2017

Journal Time Series Analysis

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Estimation ofα,βand portfolio weights in a pure-jump model with long memory in volatility

Zhang

Hurvich

2022

Stochastic Processes and their Applications

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Limit Laws in Transaction-Level Asset Price Models

et al. 2013

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We consider pure-jump transaction-level models for asset prices in continuous time, driven by point processes. In a bivariate model that admits cointegration, we allow for time deformations to account for such effects as intraday seasonal patterns in volatility, and non-trading periods that may be different for the two assets. We also allow for asymmetries (leverage effects). We obtain the asymptotic distribution of the log-price process. We also obtain the asymptotic distribution of the ordinary least-squares estimator of the cointegrating parameter based on data sampled from an equally-spaced discretization of calendar time, in the case of weak fractional cointegration. For this same case, we obtain the asymptotic distribution for a tapered estimator under more general assumptions. In the strong fractional cointegration case, we obtain the limiting distribution of a continuously-averaged tapered estimator as well as other estimators of the cointegrating parameter, and find that the rate of convergence can be affected by properties of intertrade durations. In particular, the persistence of durations (hence of volatility) can affect the degree of cointegration. We also obtain the rate of convergence of several estimators of the cointegrating parameter in the standard cointegration case. Finally, we consider the properties of the ordinary least squares estimator of the regression parameter in a spurious regression, i.e., in the absence of cointegration.

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A Pure-Jump Transaction-Level Price Model Yielding Cointegration

Cited by 4 publications

References 72 publications

Drift in Transaction‐Level Asset Price Models

Drift in Transaction‐Level Asset Price Models

Estimation ofα,βand portfolio weights in a pure-jump model with long memory in volatility

Limit Laws in Transaction-Level Asset Price Models

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