Estimating the Marginal Law of a Time Series With Applications to Heavy-Tailed Distributions

Francq, Christian; Zakoïan, Jean‐Michel

doi:10.1080/07350015.2013.801776

Cited by 18 publications

(11 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Similar models have been successfully adopted in different application fields, and seem to be particularly attractive in economics and finance (Menn and Rachev, 2005;Rachev et al, 2011;Francq and Zakoian, 2013;Babaei et al, 2015). The main applied contribution of our work is to show that the model that we propose is able to capture most of the basic features observed in international trade data.…”

Section: Introductionmentioning

confidence: 89%

Modeling international trade data with the Tweedie distribution for anti-fraud and policy support

Barabesi

Cerasa

Perrotta

et al. 2016

European Journal of Operational Research

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 89%

Modeling international trade data with the Tweedie distribution for anti-fraud and policy support

Barabesi

Cerasa

Perrotta

et al. 2016

European Journal of Operational Research

View full text Add to dashboard Cite

“…The data in this study demonstrates dependence, but this does not remove the necessity for one to consider the heavy tailed features present in the data, nor diminish the importance of a study on heavy tailed marginal distributions and ways in which these features are a crucial contribution to dynamical models of LOB volume profiles. The study of heavy tails in a marginal context is critical, as this has important effects on the accuracy of the estimators (Francq and Zakoian 2013). Studies that consider heavy tailed features in financial market data include and are not limited to: Cont (2001); Francq and Zakoian (2013).…”

Section: 34mentioning

confidence: 99%

Heavy-tailed features and dependence in limit order book volume profiles in futures markets

2015

View full text Add to dashboard Cite

Extensive literature on the properties of the Limit Order Book (LOB) has emerged with the access to ultra-high frequency data from electronic exchanges. The study of fundamental statistical attributes in such data plays an increasingly important role in aspects of financial modeling. This research is of particular relevance to trading strategies and best execution practices to satisfy the increasing proliferation of regulation.Only a limited number of studies have focused primarily on stochastic features of the volume process in the LOB, with the majority of studies centred on the price process. This paper investigates fundamental stochastic attributes of the random structures of the volume profiles in each level of the LOB. In particular, we investigate the ability to capture core features of the volume processes at different levels of depth under three families of models: α-stable, generalized Pareto distribution and generalized extreme value and find that there is statistical evidence that heavy-tailed sub-exponential volume profiles occur on the LOB bid and ask and on both intra-day and inter-day time scales. In futures exchanges, the heavy tail features are not asset class dependent and they occur on ultra or mid-range high frequency data. Of the distributions and estimation methods considered, the generalized Pareto distribution MLE provided the best fit for all assets. We demonstrate the impact of the appropriate modeling of the heavy tailed volume profiles on a commonly used liquidity measure, XLM. In addition, utilizing the generalized Pareto distribution to model LOB volume profiles allows one to avoid over-estimating the round trip cost of trading and also avoids erroneous estimations of volume leading to significant LOB imbalances in less liquid assets. We conclude that building blocks for any volume forecasting model should account for heavy tails, time varying parameters and long memory present in the data. Quantitative Finance FullManuscript˙HeavyTailsLOB˙QUF˙20150317 underlying the forecasting models on available liquidity in the Limit Order Book (LOB), can very quickly cannibalize any profits made for that trade. Moving the price by under-estimating the liquidity, or alternatively, failing to execute enough volume when there is a larger liquidity event will degrade the quality of the trading strategy. Thus, key to the performance of any high frequency trading strategy is the underlying distributional assumptions made about the volumes on the LOB. The study of volume processes in the LOB also provides direct information regarding liquidity structures intra-daily in the LOB on a given exchange.In addition, understanding fundamental features of the volume process at different depths of the LOB intra-daily are crucial in ensuring the standards of electronic exchange regulations are met with best practice. There are a range of new regulations being implemented throughout Europe and the US to further regulate the processing, placement and clearing of trades in electronic exchanges. These regulations,...

show abstract

“…Koedijk and Kool (1992) studied the exchange rate returns for three East European currencies and found that their tail indices are smaller than 2. Francq and Zakoïan (2013) investigated nine major financial markets in the world and argued that the time series modelling driven by a heavy-tailed noise may be more appropriate to financial data analysis; see Rachev (2003) and She and Ling (2020), among many others. All previous evidences show that there is a practical and urgent need to study the heavy-tailed time series.…”

Section: Introductionmentioning

confidence: 99%

Tests of Unit Root Hypothesis With Heavy-Tailed Heteroscedastic Noises

She¹

2023

STAT SINICA

View full text Add to dashboard Cite

This paper studies the unit-root testing with unspecified and heavy-tailed heteroscedastic noises. A new weighted least squares estimation (WLSE) is designed to be used in the Dickey-Fuller (DF) test, of which the asymptotic normality is verified. However, the performance of the DF test strongly relies on the estimation accuracy of the asymptotic variance, which is not stable for dependent time series. To overcome this issue, we develop two novel unit-root tests by applying the empirical likelihood technique to the WLSE score equation. It is shown that both of the empirical likelihood-based tests converge weakly to a chi-squared distribution with one degree of freedom. Furthermore, the limiting theory is extended to the weighted M -estimation score equation. In contrast to existing unit-root tests for heavy-tailed time series, the empirical likelihood tests do not involve any estimators of the unknown parameters or any restrictions on the tail index of noise, which is of more practical appealing, and thus can be widely used in finance and econometrics. Extensive simulation studies are conducted to examine the effectiveness of the proposed methods.

show abstract

Estimating the Marginal Law of a Time Series With Applications to Heavy-Tailed Distributions

Cited by 18 publications

References 44 publications

Modeling international trade data with the Tweedie distribution for anti-fraud and policy support

Modeling international trade data with the Tweedie distribution for anti-fraud and policy support

Heavy-tailed features and dependence in limit order book volume profiles in futures markets

Tests of Unit Root Hypothesis With Heavy-Tailed Heteroscedastic Noises

Contact Info

Product

Resources

About