Previous-Tick Interpolation

Install and import

bash

npm install fintech-algorithms

import { previousTick } from "fintech-algorithms/market-data-engineering/time-synchronization/previous-tick-interpolation";

Signature

previousTick(observations, requests, maxStalenessMs)

Samples a series onto a grid by carrying the last value known *at that moment* forward. The only interpolation that is safe on live data: it never uses a value that had not yet arrived.

Parameters

Name	Type	Notes
`observations`	`Observation[]`	Observations carrying both `event_time` and `available_time`, which is what allows the as-of rule to be applied honestly.
`requests`	`{ grid_time: string; query_time: string }[]`	The grid points to sample, each with the knowledge time the answer must respect.
`maxStalenessMs`	`number`	How old a carried-forward value may be before the sample is reported unusable rather than silently stale. min: 0

Returns

Sample[] · length same-as-input

One sample per request with the value used, its age, and whether the staleness budget was met.

Errors

When maxStalenessMs is negative — throws

Complexity: time O(n + m), space O(m).

Worked example

executed Captured by running this function on the input its own test provides. Real output of real code — but not asserted against a published figure.

Input

observations

[
  {
    "instrument": "A",
    "event_time": "2026-01-02T14:30:00.100Z",
    "available_time": "2026-01-02T14:30:00.180Z",
    "revision": 0,
    "value": 100
  },
  {
    "instrument": "A",
    "event_time": "2026-01-02T14:30:00.100Z",
    "available_time": "2026-01-02T14:30:01.400Z",
    "revision": 1,
    "value": 99.8
  },
  {
    "instrument": "A",
    "event_time": "2026-01-02T14:30:02.200Z",
    "available_time": "2026-01-02T14:30:02.260Z",
    "revision": 0,
    "value": 100.4
  }
]

Showing 3 of 5 elements.

requests

[
  {
    "grid_time": "2026-01-02T14:30:00.000Z",
    "query_time": "2026-01-02T14:30:00.000Z"
  },
  {
    "grid_time": "2026-01-02T14:30:01.000Z",
    "query_time": "2026-01-02T14:30:01.000Z"
  },
  {
    "grid_time": "2026-01-02T14:30:01.000Z",
    "query_time": "2026-01-02T14:30:02.000Z"
  }
]

Showing 3 of 5 elements.

maxStalenessMs

Call

previousTick(observations, requests, maxStalenessMs)

Returns

array of 10 objects

[
  {
    "instrument": "A",
    "grid_time": "2026-01-02T14:30:00.000Z",
    "query_time": "2026-01-02T14:30:00.000Z",
    "value": null,
    "source_event_time": null,
    "source_available_time": null,
    "source_revision": null,
    "staleness_ms": null,
    "status": "no_history"
  },
  {
    "instrument": "A",
    "grid_time": "2026-01-02T14:30:01.000Z",
    "query_time": "2026-01-02T14:30:01.000Z",
    "value": 100,
    "source_event_time": "2026-01-02T14:30:00.100Z",
    "source_available_time": "2026-01-02T14:30:00.180Z",
    "source_revision": 0,
    "staleness_ms": 900,
    "status": "carried"
  },
  {
    "instrument": "A",
    "grid_time": "2026-01-02T14:30:01.000Z",
    "query_time": "2026-01-02T14:30:02.000Z",
    "value": 99.8,
    "source_event_time": "2026-01-02T14:30:00.100Z",
    "source_available_time": "2026-01-02T14:30:01.400Z",
    "source_revision": 1,
    "staleness_ms": 900,
    "status": "carried"
  }
]

Showing 3 of 10 elements.

Diagrams

Previous-Tick Interpolation — article hero

Previous-Tick Interpolation — causality and staleness

Calculation flow

Point-in-time previous-tick decision

flowchart LR
    A["Stored source revisions"] --> B{"Event time <= grid time?"}
    B -->|No| C["No history"]
    B -->|Yes| D{"Availability time <= query time?"}
    D -->|No| E["Not yet available"]
    D -->|Yes| F["Latest event, latest available revision"]
    F --> G{"Source age <= expiry?"}
    G -->|Yes| H["Exact or carried value"]
    G -->|No| I["Stale missing value with lineage"]

How it works

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References

R01 - RFC 3339: Date and Time on the Internet: Timestamps — Internet Engineering Task Force; G. Klyne and C. Newman
R02 - On covariance estimation of non-synchronously observed diffusion processes — Takaki Hayashi and Nakahiro Yoshida
R03 - NYSE Holidays and Trading Hours — New York Stock Exchange
Implementation choices in this package
Dataset and historical-evidence classification