PIN

Install and import

bash

npm install fintech-algorithms

import { pin } from "fintech-algorithms/market-microstructure/order-flow-and-impact/pin";

Signature

pin(inputRows, starts, balancedNoise, iterations)

Probability of informed trading, estimated by maximum likelihood on daily buy and sell counts. Notoriously hard to optimise — the likelihood has flat regions and local optima, which is why the starting points are a parameter.

Parameters

Name	Type	Notes
`inputRows`	`Row[]`	Daily buy and sell trade counts.
`starts`	`number[][]`	Starting parameter vectors. Multiple starts are the standard defence against local optima; a single start frequently converges somewhere wrong.
`balancedNoise`	`number`	Initial guess for the balanced uninformed arrival rate. min: 0
`iterations`	`number`	Maximum optimiser iterations. min: 1 · integer: true

Returns

{ pin, alpha, mu, epsilon_buy, epsilon_sell, converged, … }

The PIN estimate with every structural parameter and a convergence flag — an unconverged PIN is not an estimate.

Errors

When no starting vector is supplied — throws

Complexity: time O(days × iterations × starts), space O(days).

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

inputRows

[
  {
    "id": "D001",
    "day": 1,
    "buys": 12,
    "sells": 29
  },
  {
    "id": "D002",
    "day": 2,
    "buys": 14,
    "sells": 12
  },
  {
    "id": "D003",
    "day": 3,
    "buys": 16,
    "sells": 13
  }
]

Showing 3 of 60 elements.

starts

balancedNoise

false

iterations

Call

pin(inputRows, starts, balancedNoise, iterations)

Returns

object with 13 fields: model, state, observation_count, starts, balanced_noise, alpha, delta, mu, …

{
  "model": "ekop-pin",
  "state": "estimated",
  "observation_count": 60,
  "starts": 3,
  "balanced_noise": false,
  "alpha": 0.3335769653,
  "delta": 0.3998646736,
  "mu": 19.2332579136,
  "epsilon_buy": 14.0464750051,
  "epsilon_sell": 13.0377527714,
  "log_likelihood": -335.6690937078,
  "pin": 0.1915155787,
  "trace": [
    {
      "id": "D001",
      "index": 0,
      "buys": 12,
      "sells": 29,
      "imbalance": -17,
      "side": "sell-heavy",
      "reason": "daily-count-input"
    },
    {
      "id": "D002",
      "index": 1,
      "buys": 14,
      "sells": 12,
      "imbalance": 2,
      "side": "buy-heavy",
      "reason": "daily-count-input"
    },
    {
      "id": "D003",
      "index": 2,
      "buys": 16,
      "sells": 13,
      "imbalance": 3,
      "side": "buy-heavy",
      "reason": "daily-count-input"
    }
  ]
}

Other exports

This module also exports orderFlowImbalance, queueImbalance, kyleLambda, hasbrouckPriceImpact, vpin, runTopic. Every module additionally exports run as an alias of its primary function, and a meta object carrying its catalog id, domain, family, shape and article URL.