Asymptotics for duration-driven long range dependent processes

Hsieh, Meng-Chen; Hurvich, Clifford M.; Soulier, Philippe

doi:10.1016/j.jeconom.2006.12.001

Cited by 10 publications

(7 citation statements)

References 35 publications

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“…The econometric implication of our result is that temporal aggregation of models with heavy tailed regime durations can lead to nonpersistent, although highly leptokurtic, behavior. A similar lack of persistency of long memory seems characteristic also to some other econometric models, in particular, to Parke's (1999) error duration model (see Davidson and Sibbertsen, 2002;Hsieh et al, 2003). See also Davydov (1973) for early probabilistic example of such behavior.…”

Section: Introductionsupporting

confidence: 57%

Renewal regime switching and stable limit laws

Leipus

Paulauskas

Сургайлис

2005

Journal of Econometrics

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Section: Introductionsupporting

confidence: 57%

Renewal regime switching and stable limit laws

Leipus

Paulauskas

Сургайлис

2005

Journal of Econometrics

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“…stable random variables with infinite variance. Such an example may come from durations that obey a positive version of the renewal-reward process discussed in Taqqu and Levy (1986) (see also Hsieh et al (2007)). In such a model, durations would have finite variance but their sums would converge to a process with infinite variance.…”

Section: Discussionmentioning

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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“…They showed that large and small bandwidths correspond to different asymptotic distributions of the kernel estimates. See also Surgailis (2004), Sly and Heyde (2008), Mikosch et al (2002), and Hsieh et al (2007) for similar observations under different settings. In Theorem 5, the lag parameter k n plays a similar role.…”

mentioning

confidence: 86%

Covariances Estimation for Long-Memory Processes

Huang²,

Zheng³

2010

Advances in Applied Probability

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For a time series, a plot of sample covariances is a popular way to assess its dependence properties. In this paper we give a systematic characterization of the asymptotic behavior of sample covariances of long-memory linear processes. Central and noncentral limit theorems are obtained for sample covariances with bounded as well as unbounded lags. It is shown that the limiting distribution depends in a very interesting way on the strength of dependence, the heavy-tailedness of the innovations, and the magnitude of the lags.

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Asymptotics for duration-driven long range dependent processes

Cited by 10 publications

References 35 publications

Renewal regime switching and stable limit laws

Renewal regime switching and stable limit laws

Drift in Transaction‐Level Asset Price Models

Covariances Estimation for Long-Memory Processes

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