Story: Stochastic tick arrival times for synthetic feeds

Today the synthetic FX spot feed emits a tick on a FIXED clock — a constant interval derived from ticks_per_hour (fx_spot_feed::start, projects/ores.synthetic/service/src/fx_spot_feed.cpp:64-106), sleeping the full period before every publish including the first. Real market data does not arrive on a fixed cadence: trades/quotes cluster and gap, with bursty, irregular inter-arrival times. Make the feed tick at RANDOM times drawn from a distribution that approaches reality, while keeping the price process (GMM geometric/arithmetic) decoupled from the arrival process — two independent configurable models.

Raised while tuning synthetic_fx_spot_configs_realistic_populate.sql's tick cadence (see Task: Seed Basic and Realistic dataset bundles) — settled on a fixed 2-second cadence there as good enough for a first pass, but a genuinely "realistic" feed should vary its arrival timing, not just its price distribution.

Candidate models for the arrival (timing) process, to be confirmed by a literature review:

• Homogeneous Poisson process — exponential inter-arrival times; the simplest step up from a fixed clock (constant intensity λ).
• Inhomogeneous Poisson — time-varying intensity λ(t) for intraday seasonality (open/close bursts, lunch lull).
• Self-exciting Hawkes processes — capture the clustering / burstiness of real order flow (an arrival raises the short-term intensity of further arrivals).
• Two-state quiet/burst regime, formally a Markov-Modulated Poisson Process (MMPP): a Poisson process whose intensity λ switches between discrete states (quiet/burst, or more) via a hidden Markov chain. This is the standard, well-established model for exactly the clustering/regime behaviour this story wants, at much lower calibration cost than a full Hawkes process. Note: this is not a Gaussian Mixture Model (GMM) — ores.synthetic's existing price process uses a weighted mixture of continuous Gaussian components (gmm_process=/=gmm_component), which doesn't transfer directly to a discrete counting/arrival-time process; MMPP is the analogous-in- spirit but technically distinct construct for this domain (a regime-mixture, not a magnitude-mixture). Worth confirming during the literature review below whether MMPP or a simpler two-state regime-switch (without the full Markov-chain machinery) is the better starting point.

Scope: a configurable arrival process on the feed (alongside the existing price engine), exposed in the config (e.g. an "arrival model" with its parameters, analogous to the price-process engine choice). Find and summarise the relevant papers first (market microstructure / point processes / Hawkes in finance), then design the model and config surface.

• Arrival-process parameters are NOT configured per market-data feed. Instead, a small set of named, top-level arrival-profile configs (e.g. liquid_spot_rates, illiquid_spot_rates) each bundle a distribution choice (Poisson / inhomogeneous Poisson / Hawkes / two-state quiet-burst) with its parameters; individual feed configs reference one profile by name/FK rather than duplicating parameters. This keeps calibration in one place and lets many feeds share a tuned profile (all liquid G10 pairs use liquid_spot_rates, say) without re-tuning per pair.
• The arrival process is decoupled from the price process: swapping arrival profile never changes the GMM price-process configuration and vice versa.
• At least one non-trivial arrival model (homogeneous Poisson at minimum) is implemented and wired into fx_spot_feed (or its successor abstraction) as a real alternative to the fixed clock, selectable via the arrival-profile config.
• The Basic/Realistic collection distinction (see Synthetic data collections: Basic and Realistic) can express itself through arrival profile as well as price-process parameters — e.g. Basic keeps the fixed clock (simple, easy to eyeball), Realistic uses a genuine arrival profile.

Planned tasks (not yet scaffolded as task docs):

1. Literature review: summarise Poisson/Hawkes point-process literature (see References) into a short recommendation of which model(s) to implement first.
2. Design and implement the named arrival-profile config (e.g. arrival_profile_config, codegen-driven like fx_spot_generation_config): distribution choice + parameters, referenced by FK from feed configs rather than duplicated per feed.
3. Implement at least a homogeneous Poisson arrival process, wired into fx_spot_feed (or its successor) as an alternative to the fixed clock, decoupled from the GMM price process.
4. Wire Basic=/=Realistic collections to reference an arrival profile (Basic keeps the fixed clock; Realistic uses a real profile), per Synthetic data collections: Basic and Realistic.

• Arrival-profile configs are top-level, named, and shared across feeds (liquid_spot_rates, illiquid_spot_rates, …) rather than parameters on each individual market-data feed/pair config. This avoids re-tuning the same distribution N times and lets feeds that should behave similarly (e.g. all liquid G10 pairs) share one calibrated profile.
• The arrival (timing) process stays decoupled from the price (GMM) process — two independent, independently-configurable models, per the original capture's framing.

• Curve/vol-surface generation timing (separate stories: IR Rates synthetic data generation).
• Redesigning the GMM price process itself — this story only touches arrival/tick timing.

Code:

• projects/ores.synthetic/service/src/fx_spot_feed.cpp:64-106
• projects/ores.sql/populate/synthetic/synthetic_fx_spot_configs_realistic_populate.sql
• projects/ores.synthetic/service/src/processes/gmm_process.hpp — the existing weighted-mixture pattern for the price process, referenced above for the MMPP-vs-GMM distinction.

Literature (point processes / Hawkes for trade & order arrivals):

• Bacry & Muzy, "Hawkes model for price and trades high-frequency dynamics" (2014, Quantitative Finance 14(7)); preprint arXiv:1301.1135 — https://arxiv.org/abs/1301.1135 . Foundational: multivariate Hawkes for trade arrivals + price dynamics (self-/mutually-exciting kernels).
• Bacry, Mastromatteo & Muzy, "Hawkes Processes in Finance" — survey of Hawkes applications to high-frequency data: https://www.stt.msu.edu/~viens/publications/11_hawkes.pdf
• "Hawkes processes for credit indices time series analysis: How random are trades arrival times?" arXiv:1902.03714 — directly on the irregularity of inter-arrival times.
• Hewlett / others, "Modelling order arrivals … using Hawkes processes" (ScienceDirect, Finance Research Letters): https://www.sciencedirect.com/science/article/abs/pii/S1544612316301490
• "Limit Order Book Simulations: A Review" arXiv:2402.17359 — https://arxiv.org/html/2402.17359v1 . Broader survey incl. arrival-process modelling for LOB simulators (useful comparison of fixed-clock vs point processes).

Notes from the survey reading:

• Simplest upgrade = a homogeneous Poisson process (exponential inter-arrival, constant intensity λ) — drop-in replacement for the fixed clock.
• Add intraday seasonality via an inhomogeneous Poisson intensity λ(t) (volumes/arrivals follow a stable intraday U-shape: open/close bursts).
• Hawkes (self-exciting) captures the empirical CLUSTERING/burstiness of real arrivals; main cost is calibration (kernel choice, likelihood complexity). An MMPP is a cheaper way to get similar clustering behaviour without full Hawkes calibration — worth comparing during the literature review task.

• Story: Config-driven synthetic feed generation
• Story: Synthetic generation configuration and config-driven feeds
• Task: Seed Basic and Realistic dataset bundles — the task this was deferred out of.
• Synthetic data collections: Basic and Realistic — sibling story this connects to via the Basic/Realistic arrival-profile split.