Jump detection in high-frequency order prices

Paper: arXiv 2403.00819

Abstract

We propose methods to infer jumps of a semi-martingale, which describes long-term price dynamics, based on discrete, noisy, high-frequency observations. Different to the classical model of additive, centered market microstructure noise, we consider one-sided microstructure noise for order prices in a limit order book. We develop methods to estimate, locate and test for jumps using local minima of best ask quotes. We provide a local jump test and show that we can consistently estimate jump sizes and jump times. One main contribution is a global test for jumps. We establish the asymptotic properties and optimality of this test. We derive the asymptotic distribution of a maximum statistic under the null hypothesis of no jumps based on extreme value theory. We prove consistency under the alternative hypothesis. The rate of convergence for local alternatives is determined and shown to be much faster than optimal rates for the standard market microstructure noise model. This allows the identification of smaller jumps. In the process, we establish uniform consistency for spot volatility estimation under one-sided noise. Online jump detection based on the new approach is shown to achieve a speed advantage compared to standard methods applied to mid quotes. A simulation study sheds light on the finite-sample implementation and properties of the new approach and draws a comparison to a popular method for market microstructure noise. We showcase how our new approach helps to improve jump detection in an empirical analysis of intra-daily limit order book data.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced stochastic calculus and extreme value theory, with dense theoretical derivations, placing it in the high math quadrant. It includes simulation studies and empirical analysis of limit order book data, demonstrating implementation readiness, but the focus remains heavily on theoretical optimality and proofs rather than a fully packaged backtesting framework.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Jump Detection in Limit Order Books"] --> B["Data Input<br>High-Frequency Order Prices"]
  B --> C["Methodology<br>Local Minima of Best Ask Quotes"]
  C --> D{"Key Computation<br>Estimate & Locate Jumps"}
  D --> E["Local Jump Test<br>Consistent estimation of jump sizes/times"]
  D --> F["Global Jump Test<br>Asymptotically optimal via EVT"]
  E & F --> G["Outcomes<br>Faster detection of small jumps"]
  G --> H["Validation<br>Simulation & Empirical Analysis"]

Cited References (57)

1. Statistical inference for rough volatility: Minimax theory (2024) — link
2. Optimal Nonparametric Range-Based Volatility Estimation (2024) — link
3. A note on the Gumbel convergence for the Lee and Mykland jump tests (2023) — link
4. High frequency market making: The role of speed (2023) — link
5. Inference on the intraday spot volatility from high-frequency order prices with irregular microstructure noise (2023) — link
6. Reading the Candlesticks: An OK Estimator for Volatility (2022) — link
7. Gumbel convergence of the maximum of convoluted half-normally distributed random variables (2021) — link
8. Volatility measurement with pockets of extreme return persistence (2021) — link

0 of 57 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.