Related papers: Discretization of Self-Exciting Peaks Over Thresho…
In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process.…
Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
We consider regular variation for marked point processes with independent heavy-tailed marks and prove a single large point heuristic: the limit measure is concentrated on the cone of point measures with one single point. We then…
High-frequency market making is a liquidity-providing trading strategy that simultaneously generates many bids and asks for a security at ultra-low latency while maintaining a relatively neutral position. The strategy makes a profit from…
We consider a continuous-time financial market with an asset whose price is modeled by a linear stochastic differential equation with drift and volatility switching driven by a uniformly ergodic jump Markov process with a countable state…
We consider a sequence of systems of Hawkes processes having mean field interactions in a diffusive regime. The stochastic intensity of each process is a solution of a stochastic differential equation driven by N independent Poisson random…
Hawkes process models are used in settings where past events increase the likelihood of future events occurring. Many applications record events as counts on a regular grid, yet discrete-time Hawkes models remain comparatively underused and…
The Hawkes process is a popular point process model for event sequences that exhibit temporal clustering. The intensity process of a Hawkes process consists of two components, the baseline intensity and the accumulated excitation effect due…
Hawkes processes are a class of simple point processes that are self-exciting and have clustering effect, with wide applications in finance, social networks and many other fields. This paper considers a self-exciting Hawkes process where…
Predicting irregularly spaced event sequences with discrete marks poses significant challenges due to the complex, asynchronous dependencies embedded within continuous-time data streams.Existing sequential approaches capture dependencies…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
Hawkes processes have been shown to be efficient in modeling bursty sequences in a variety of applications, such as finance and social network activity analysis. Traditionally, these models parameterize each process independently and assume…
This paper investigates the cumulative Integer-Valued Autoregressive model of infinite order, denoted as INAR($\infty$), a class of processes crucial for modeling count time series and equivalent to discrete-time Hawkes processes. We…
For each $n\geq 1$, let $ {X_{in}, \quad i \geq 1} $ be independent copies of a nonnegative continuous stochastic process $X_{n}=(X_n(t))_{t\in T}$ indexed by a compact metric space $T$. We are interested in the process of partial maxima…
We propose a novel class of network models for temporal dyadic interaction data. Our goal is to capture a number of important features often observed in social interactions: sparsity, degree heterogeneity, community structure and…
Statistical modelling of spatial extreme events has gained increasing attention over the last few decades with max-stable processes, and more recently $r$-Pareto processes, becoming the reference tools for the statistical analysis of…
We have established a sparse estimation method for the generalized exponential marked Hawkes process by the penalized method to the ordinary method (P-O) estimator. Furthermore, we evaluated the probability of correct variable selection. In…
We study optimal liquidation strategies under partial information for a single asset within a finite time horizon. We propose a model tailored for high-frequency trading, capturing price formation driven solely by order flow through…
Consider a first-order autoregressive process $X_i=\beta X_{i-1}+\varepsilon_i,$ where $\varepsilon_i=G(\eta_i,\eta_{i-1},\ldots)$ and $\eta_i,i\in\mathbb{Z}$ are i.i.d. random variables. Motivated by two important issues for the inference…
For integers $n\geq r$, we treat the $r$th largest of a sample of size $n$ as an $\mathbb{R}^\infty$-valued stochastic process in $r$ which we denote $\mathbf{M}^{(r)}$. We show that the sequence regarded in this way satisfies the Markov…