# Stationarity and Differencing Intuition

`D00-F10-A08` · Financial Mathematics, Statistics, and Data Foundations → Financial Time-Series Foundations · archetype `record-transform` · difficulty 1/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/foundations/financial-time-series-foundations/stationarity-and-differencing-intuition/
Agent skill: `npx skills add IslamBaraka90/Fintech-Algorithms-Library` — https://docs.thefintechbuilder.com/guides/agent-skill/

## Install and import

```bash
npm install fintech-algorithms
```

```ts
import { stationarityAndDifferencingIntuition } from "fintech-algorithms/foundations/financial-time-series-foundations/stationarity-and-differencing-intuition";
```

## Signature

```ts
stationarityAndDifferencingIntuition(input)
```

Compares the average level of the second half of a series with the first half, and reports the first differences, as a rough read on whether the level drifts.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `D00Input` | yes | Reads `values`, a non-empty list of finite numbers, `timestamps` of the same length, and `stationarityTolerance`, the size of mean shift still treated as flat. |

## Returns

`D00Output`

`meanShift` is the second-half mean minus the first-half mean, `firstDifferences` the consecutive changes, `differenceMean` their average, and `levelLikelyStationary` is true when the absolute mean shift is within `stationarityTolerance`.

## Errors

- When `values` is absent, empty, or holds a non-finite number — throws RangeError
- When `timestamps` and `values` have different lengths — throws RangeError
- When the series holds fewer than two observations — throws RangeError

## Complexity

Time `O(n^2)`, space `O(n)`.

## Worked example

This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

### Input

`input`:

```json
{
  "timestamps": [
    "2025-01-01T00:00:00Z",
    "2025-01-02T00:00:00Z",
    "2025-01-03T00:00:00Z",
    "2025-01-04T00:00:00Z",
    "2025-01-05T00:00:00Z",
    "2025-01-06T00:00:00Z"
  ],
  "values": [100, 102, 101, 104, 106, 105],
  "lag": 1,
  "window": 3,
  "resampleSize": 2,
  "period": 3,
  "stationarityTolerance": 3,
  "alpha": 0.4,
  "splitIndex": 4
}
```

### Call

```ts
stationarityAndDifferencingIntuition(input)
```

### Returns

object with 2 fields: meanShift, firstDifferences

```json
{
  "meanShift": 4,
  "firstDifferences": [2, -1, 3, 2, -1]
}
```

## Verification and provenance

Tier: **verified** (via input-expected).

The worked example below is the figure published in this algorithm's article, replayed and asserted by the test suite on every build. The arithmetic cannot drift without the build failing.

Both tiers guarantee the signature. Full explanation: https://docs.thefintechbuilder.com/guides/verification/

Generated from the docs.json payload shipped inside fintech-algorithms@0.13.0.
The signature and parameter list are checked against the compiled implementation at build time,
so a description that contradicts the code fails the build rather than reaching this file.

## Links

- Article (how it works, step by step): https://thefintechbuilder.com/foundations/financial-time-series-foundations/stationarity-and-differencing-intuition/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/foundations/financial-time-series-foundations/stationarity-and-differencing-intuition/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/foundations/llms.txt