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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

Indonesian

Easy Staapshood adalah proses penutupan titik waktu yang digunakan untuk mengukur mekanisme pasar, misalnya, seberapa cepat harga menyerap berita dan seberapa banyak reaksi pasar merespon pada dirinya sendiri, dan untuk memprediksi peristiwa berikutnya. Kami menunjukkan bahwa satu objek aljabar, fase-tipe (Erlang-chain) ruang interwalking, melayani kedua tujuan dengan probabilitas yang tepat. Untuk pengukuran, kami membangun multi-skala fase-tipe sertifikat Hawkes proses yang semua parameter yang masuk secara linear. Log-probabilitas skornya adalah concave, dan kami menghitung maksimum global di sekitar pasar dengan sertifikat duality-gap Fenchel. A Markov embedding memberikan tanggapan untuk shock eksogenic, echoes termasuk, dalam bentuk tertutup, dan tanggapan ini dapat diperbarui setengah dan hanya jika radius spektral matriks

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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