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Cassandra Milbradt

Publications and source records attributed to Cassandra Milbradt.

4 recordsLinked to original sources
arXiv2022

Parametric change point detection with random occurrence of the change point

We are concerned with the problem of detecting a single change point in the model parameters of time series data generated from an exponential family. In contrast to the existing literature, we allow that the true location of the change point is itself random, possibly depending on the data. Under the alternative, we study the case when the size of the change point converges to zero while the sample size goes to infinity. Moreover, we concentrate on change points in the "middle of the data", i.e., we assume that the change point fraction (the location of the change point relative to the sample size) converges weakly to a random variable $λ^*$ which takes its values almost surely in a closed subset of $(0,1).$ We show that the known statistical results from the literature also transfer to this setting. We substantiate our theoretical results with a simulation study.

math.ST↗
arXiv2022

A cross-border market model with limited transmission capacities

We develop a cross-border market model for two countries based on a continuous trading mechanism, in which the transmission capacities that enable transactions between market participants from different countries are limited. Our market model can be described by a regime-switching process alternating between active and inactive regimes, in which cross-border trading is possible respectively prohibited. Starting from a reduced-form representation of the two national limit order books, we derive a high-frequency approximation of the microscopic model, assuming that the size of an individual order converges to zero while the order arrival rate tends to infinity. If transmission capacities are available, the limiting dynamics are as follows: the queue size processes at the top of the two limit order books follow a four-dimensional linear Brownian motion in the positive orthant with oblique reflection at the axes. Each time the two best ask queues or the two best bid queues simultaneously hit zero, the queue size process is reinitialized. The capacity process can be described as a linear combination of local times and is hence of finite variation. The analytic tractability of the limiting dynamics allows us to compute key quantities of interest.

math.PR↗
arXiv2022

Jump diffusion approximation for the price dynamics of a fully state dependent limit order book model

We study a microscopic limit order book model, in which the order dynamics depend on the current best bid and ask price and the current volume density functions, simultaneously, and derive its macroscopic high-frequency dynamics. As opposed to the existing literature on scaling limits for limit order book models, we include price changes which do not scale with the tick size in our model to account for large price movement, being for example triggered by highly unforeseen events. Our main result states that, when the size of an individual limit order and the tick size tend to zero while the order arrival rate tends to infinity, the microscopic limit order book model dynamics converge to two one-dimensional jump diffusion processes describing the prices coupled with two infinite dimensional fluid processes describing the standing volumes at the buy and sell side.

math.PR↗