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Exact Phase-Type Point Processes for Certified Measurement and Prediction of Event Streams

Sayak Dutta · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.14948 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

易于实现的PPE间隔是用来测量数据市场机制,例如,价格在开始时如何快速吸收新闻,以及市场对自身反应的反应有多大,以及预测接下来的事件。我们展示了一个算法对象,阶段类型(Erlang-chain)状态间隔空间,用来衡量两个目的,准确的差异性。对于测量,我们构建了一个多尺寸的阶段类型认证霍克斯过程,其参数都进入线性水平。其分支序列的测量概率是圆形的,我们计算了全球最大值与Fenchel双重差距证书(Fenchel-chain)一起。Markov嵌入给出了对外冲击的响应,包括响应,在封闭的形式中发布,这种响应是稳定的,只有如果分支矩阵的谱

Machine translation (Meta M2M100); the English original follows.

Abstract

Temporal point processes are used both to measure market mechanisms, for example how fast prices absorb news and how much of the reaction is the market responding to itself, and to predict the next event. We show that one algebraic object, the phase-type (Erlang-chain) state space, serves both purposes with exact likelihoods. For measurement, we build a multiscale phase-type Hawkes process whose parameters all enter linearly. Its log-likelihood is concave, and we compute the global maximum together with a Fenchel duality-gap certificate. A Markov embedding gives the response to an exogenous shock, echoes included, in closed form, and this response is stable if and only if the spectral radius of the branching matrix is below one. Applied to six markets around 670 scheduled macroeconomic releases (2022-2026) with a built-in placebo test, the model shows that the direct reaction to CPI, payrolls, PPI and the FOMC statement is absorbed in about a second, while the market's own echoes stretch half of the response to 16-137 s. For prediction, we introduce EPT-X, a neural point process that adds a history-dependent mixture-of-Erlang renewal channel to a linear Hawkes backbone. Its intensity and compensator remain in closed form, its states follow an affine recursion that trains with a parallel scan, and it can start from the certified fit of the measurement model. EPT-X has the best test likelihood on all five LOBSTER order-book streams and on Retweet and Taobao, and is level with the best published model on StackOverflow. We also find that the EasyTPP implementation of IntensityFree clamps short inter-event times before scoring, and that the gaps of the EasyTPP Amazon data are uniform on two fixed intervals.

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Topics: Point process, Heteroscedasticity, Computer science, Algorithm, Process (computing), Markov process

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