Paper: arXiv 2610.14948

Authors: Sayak Dutta

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical and novel approach to modeling event streams using phase-type point processes, demonstrating strong empirical validation across multiple datasets. The methodology is well-defined, and the results are significant for both measurement and prediction in quantitative finance and machine learning.

Research Flowchart

  flowchart TD
    A[Research Goal: Certified Measurement & Prediction of Event Streams] --> B{Key Methodology: Exact Phase-Type Point Processes};
    B -- Measurement --> C[Multiscale Phase-Type Hawkes Process: Linear Parameters, Concave Likelihood, Fenchel Duality];
    B -- Prediction --> D[EPT-X: Neural Point Process, Erlang Renewal Channel, Closed-Form Intensity/Compensator];
    C -- Data/Inputs --> E[6 Markets, 670 Macroeconomic Releases (2022-2026), Placebo Test];
    D -- Data/Inputs --> F[5 LOBSTER Order-Book Streams, Retweet, Taobao, StackOverflow];
    E -- Computational Process --> G[Global Maximum Likelihood, Markov Embedding for Response];
    F -- Computational Process --> H[Affine Recursion, Parallel Scan Training, Certified Fit from Measurement Model];
    G --> I[Key Findings (Measurement): Direct Reaction ~1s, Market Echoes 16-137s];
    H --> J[Key Findings (Prediction): Best Test Likelihood on LOBSTER, Retweet, Taobao; Level with Best on StackOverflow; EasyTPP Issues Identified];