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Keywords = functional central limit theorems (FCLT)

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16 pages, 302 KB  
Article
Asymptotic Confidence Intervals for the Mean with Increased Finite-Sample Coverage Probabilities
by Shivani Bhardwaj, Jervis Gallanosa and Yuliya V. Martsynyuk
Mathematics 2025, 13(24), 3931; https://doi.org/10.3390/math13243931 - 9 Dec 2025
Viewed by 847
Abstract
We consider a Student process based on independent copies of a random variable X. If X is in the domain of attraction of the normal law (DAN), a weighted version of the Student process is known to follow a functional Central Limit [...] Read more.
We consider a Student process based on independent copies of a random variable X. If X is in the domain of attraction of the normal law (DAN), a weighted version of the Student process is known to follow a functional Central Limit Theorem (FCLT). Accordingly, appropriate functionals of such a process converge in distribution to the same functionals of the similarly weighted standard Wiener process. We use such a convergence for an integral functional and derive asymptotic confidence intervals (CIs) for the mean of X. For right-skewed distributions of X in DAN, we show that the obtained CIs have higher finite-sample coverage probabilities than, and may be preferred over, a CI I1 of the same asymptotic confidence level 1−α that is based on the CLT for the Student t-statistic, since the finite-sample coverage probabilities of the latter CI may be lower than 1−α. Moreover, for such distributions, the finite-sample coverage probabilities of our best two CIs are also higher than those of their respective equal-expected-length I1 counterparts. Full article
(This article belongs to the Section D1: Probability and Statistics)
20 pages, 693 KB  
Article
Multivariate General Compound Point Processes in Limit Order Books
by Qi Guo, Bruno Remillard and Anatoliy Swishchuk
Risks 2020, 8(3), 98; https://doi.org/10.3390/risks8030098 - 11 Sep 2020
Cited by 6 | Viewed by 4808
Abstract
In this paper, we focus on a new generalization of multivariate general compound Hawkes process (MGCHP), which we referred to as the multivariate general compound point process (MGCPP). Namely, we applied a multivariate point process to model the order flow instead of the [...] Read more.
In this paper, we focus on a new generalization of multivariate general compound Hawkes process (MGCHP), which we referred to as the multivariate general compound point process (MGCPP). Namely, we applied a multivariate point process to model the order flow instead of the Hawkes process. The law of large numbers (LLN) and two functional central limit theorems (FCLTs) for the MGCPP were proved in this work. Applications of the MGCPP in the limit order market were also considered. We provided numerical simulations and comparisons for the MGCPP and MGCHP by applying Google, Apple, Microsoft, Amazon, and Intel trading data. Full article
(This article belongs to the Special Issue Stochastic Modelling in Financial Mathematics)
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25 pages, 1782 KB  
Article
General Compound Hawkes Processes in Limit Order Books
by Anatoliy Swishchuk and Aiden Huffman
Risks 2020, 8(1), 28; https://doi.org/10.3390/risks8010028 - 14 Mar 2020
Cited by 14 | Viewed by 10538
Abstract
In this paper, we study various new Hawkes processes. Specifically, we construct general compound Hawkes processes and investigate their properties in limit order books. With regard to these general compound Hawkes processes, we prove a Law of Large Numbers (LLN) and a Functional [...] Read more.
In this paper, we study various new Hawkes processes. Specifically, we construct general compound Hawkes processes and investigate their properties in limit order books. With regard to these general compound Hawkes processes, we prove a Law of Large Numbers (LLN) and a Functional Central Limit Theorems (FCLT) for several specific variations. We apply several of these FCLTs to limit order books to study the link between price volatility and order flow, where the volatility in mid-price changes is expressed in terms of parameters describing the arrival rates and mid-price process. Full article
(This article belongs to the Special Issue Stochastic Modelling in Financial Mathematics)
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