# Holt's Linear Exponential Smoothing Forecast

> Holt's Linear Exponential Smoothing Forecast is a paid API for AI agents from agent402.tools, paid per call via x402, $0.001/call, status unknown (last checked 2026-09-14).

Applies Holt's two-parameter linear trend smoothing to a time series and returns a straight-line forecast for a specified number of future periods.

## Facts

- Endpoint: POST https://agent402.tools/api/forecast-holt
- Price: $0.001/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/holt-s-linear-exponential-smoothing-forecast-5fd8966f
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_yvMJOs6EmQOQIrAXeOMUe

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability holt-s-linear-exponential-smoothing-forecast-5fd8966f -d '<json body>'
```

Example prompt: Use Holt's linear trend method to forecast the next 12 periods for this monthly sales series [120, 135, 148, 160, 175, 190, 205, 220], with alpha set to 0.4 and beta set to 0.2.

## When to prefer this

Choose this endpoint when your time series has a clear linear trend but no seasonal pattern, and you need a simple, interpretable forecast. It is ideal for demand planning, sales projection, or any monotonically growing or declining series where Holt's two-parameter model suffices. Prefer it over seasonal models (Holt-Winters) when seasonality is absent or irrelevant, and over simple exponential smoothing when a trend component must be captured.

## Known failure modes

- Series too short (fewer than 4 values) — returns validation error
- Horizon out of range (less than 1 or greater than 1000) — returns error
- Alpha or beta not between 0 and 1 (exclusive) — returns parameter validation error
- Series exceeds 10000 values — returns size limit error
- Non-numeric values in series — returns type error
- Payment not provided — returns 402 Payment Required

## How this service works

Holt's linear trend method - level + trend (no seasonality). Two smoothing parameters: alpha (level) and beta (trend). Forecast extrapolates as a straight line from the last fitted level along the last fitted trend, so it grows or shrinks linearly with horizon. Use this when your series has a persistent up/down trend but no seasonal cycle (e.g. a SaaS MRR climb, a deflating cohort retention curve).

## Output

Returns forecasted values for the requested number of future periods, extrapolated as a straight line from the last fitted level along the last fitted trend, along with the fitted level and trend at the end of the series.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "beta": {
   "type": "number",
   "description": "Trend smoothing, 0 < beta < 1 (default 0.3)"
  },
  "alpha": {
   "type": "number",
   "description": "Level smoothing, 0 < alpha < 1 (default 0.5)"
  },
  "values": {
   "type": "array",
   "description": "Numeric series in chronological order (max 10000, min 4)"
  },
  "horizon": {
   "type": "number",
   "description": "Number of future periods to forecast (1 to 1000)"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "json",
 "example": {
  "n": 10,
  "beta": 0.3,
  "alpha": 0.5,
  "method": "holt",
  "horizon": 3,
  "forecast": [
   {
    "step": 1,
    "point": 163.2012,
    "lower95": 161.6463,
    "upper95": 164.756
   },
   {
    "step": 2,
    "point": 169.7416,
    "lower95": 167.8871,
    "upper95": 171.596
   },
   {
    "step": 3,
    "point": 176.282,
    "lower95": 174.049,
    "upper95": 178.515
   }
  ]
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/holt-s-linear-exponential-smoothing-forecast-5fd8966f/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from agent402.tools](https://www.zero.xyz/host/agent402.tools/llms.txt)