# STL Decomposition

`D09-F05-A01` · Statistical Time Series → Decomposition and Cycles · archetype `record-transform` · difficulty 3/5 · verification **contract**

Full page: https://docs.thefintechbuilder.com/statistical-time-series/decomposition-and-cycles/stl-decomposition/
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 { stlDecompose } from "fintech-algorithms/statistical-time-series/decomposition-and-cycles/stl-decomposition";
```

## Signature

```ts
stlDecompose(values, period, seasonalWindow, trendWindow, robustIterations)
```

Seasonal-trend decomposition by loess: splits a series into seasonal, trend and remainder. Unlike a fixed seasonal index it lets the seasonal shape evolve, which is why it survives series where the pattern drifts.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `values` | `number[]` | yes | Observation series, chronological. |
| `period` | `number` | yes | Seasonal period — 12 for monthly, 5 for a trading week. · min: 1, integer: true |
| `seasonalWindow` | `number` | yes | Loess span for the seasonal component. Larger holds the seasonal shape more constant across cycles. · min: 1, integer: true |
| `trendWindow` | `number` | yes | Loess span for the trend. · min: 1, integer: true |
| `robustIterations` | `number` | yes | Robustness passes that downweight outliers. Zero gives the non-robust fit. · min: 0, integer: true |

## Returns

`{ seasonal, trend, remainder, … }`

The three components, which sum back to the original series.

## Errors

- When the series is shorter than two full periods — throws

## Complexity

Time `O(n × window × iterations)`, space `O(n)`.

## Worked example

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

`values`:

```json
[
  100.0901805654,
  101.3367333472,
  102.4083163971,
  102.9128416721,
  103.198587938,
  102.4311805579
]
```

Showing 6 of 192 elements.

`period`:

```json
12
```

`seasonalWindow`:

```json
7
```

`trendWindow`:

```json
19
```

`robustIterations`:

```json
2
```

### Call

```ts
stlDecompose(values, period, seasonalWindow, trendWindow, robustIterations)
```

### Returns

object with 10 fields: observed, trend, seasonal, residual, robust_weights, period, seasonal_window, trend_window, …

```json
{
  "observed": [
    100.0901805654,
    101.3367333472,
    102.4083163971,
    102.9128416721,
    103.198587938,
    102.4311805579
  ],
  "trend": [
    101.80653184631831,
    101.74335719017421,
    101.68290299767973,
    101.62622211934938,
    101.5743610938178,
    101.52818917545937
  ],
  "seasonal": [
    -1.675059270552302,
    -0.37793707310334934,
    0.5876119710645483,
    1.128755113942449,
    1.414763613255315,
    0.6984276428857473
  ],
  "residual": [
    -0.041292010366001275,
    -0.028686769870863493,
    0.13780142835571352,
    0.15786443880817314,
    0.20946323092688846,
    0.20456373955488483
  ],
  "robust_weights": [
    0.9997399824592482,
    0.9998384208965301,
    0.9966750447871305,
    0.9957359792237003,
    0.9926684141414982,
    0.9930448769484919
  ],
  "period": 12,
  "seasonal_window": 7,
  "trend_window": 19,
  "robust_iterations": 2,
  "reconstruction_max_error": 0
}
```

## Other exports

`hpFilter`, `bkFilter`, `cfFilter`, `fftPeriodogram`, `haarWavelet`, `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.

## Verification and provenance

Tier: **contract**.

The module loads, the entry point is callable and its declared signature matches the compiled code. The example below is real captured output, but no independently published figure asserts the numbers.

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

Generated from the docs.json payload shipped inside fintech-algorithms@0.13.1.
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/statistical-time-series/decomposition-and-cycles/stl-decomposition/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/statistical-time-series/decomposition-and-cycles/stl-decomposition/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/statistical-time-series/llms.txt