Forecast (Holt linear trend)

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).

Input

Field	Type	Description
values *	array	Numeric series in chronological order (max 10000, min 4)
horizon *	number	Number of future periods to forecast (1 to 1000)
alpha	number	Level smoothing, 0 < alpha < 1 (default 0.5)
beta	number	Trend smoothing, 0 < beta < 1 (default 0.3)

Example output

{
  "method": "holt",
  "n": 10,
  "horizon": 3,
  "alpha": 0.5,
  "beta": 0.3,
  "forecast": [
    {
      "step": 1,
      "point": 163.2012,
      "lower95": 162.4237,
      "upper95": 163.9786
    },
    {
      "step": 2,
      "point": 169.7416,
      "lower95": 168.4665,
      "upper95": 171.0167
    },
    {
      "step": 3,
      "point": 176.282,
      "lower95": 174.5007,
      "upper95": 178.0633
    }
  ]
}

Try it — see the 402 challenge (free)

curl -i -X POST https://agent402.tools/api/forecast-holt \
  -H "Content-Type: application/json" \
  -d '{"values":[100,105,111,118,124,131,137,144,150,157],"horizon":3,"alpha":0.5,"beta":0.3}'

The response is HTTP 402 Payment Required with exact payment requirements. Any x402 v2 client pays automatically and retries:

Paid call (JavaScript agent)

import { wrapFetchWithPayment } from "@x402/fetch";
import { x402Client } from "@x402/core/client";
import { registerExactEvmScheme } from "@x402/evm/exact/client";
import { privateKeyToAccount } from "viem/accounts";

const client = new x402Client();
registerExactEvmScheme(client, { signer: privateKeyToAccount(KEY) });
const payFetch = wrapFetchWithPayment(fetch, client);

const res = await payFetch("https://agent402.tools/api/forecast-holt", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    "values": [
      100,
      105,
      111,
      118,
      124,
      131,
      137,
      144,
      150,
      157
    ],
    "horizon": 3,
    "alpha": 0.5,
    "beta": 0.3
  }),
});

No wallet? Pay with compute

This is a pure-CPU tool, so an agent without a wallet can pay with proof-of-work instead of USDC: fetch a challenge, solve the sha256 puzzle (16 leading zero bits — a fraction of a second of CPU, no money, no AI tokens), and resend with the X-Pow-Solution header.

import { createHash } from "node:crypto";
const lz = (b) => { let t = 0; for (const x of b) { if (!x) { t += 8; continue; } t += Math.clz32(x) - 24; break; } return t; };
const c = await (await fetch("https://agent402.tools/api/pow/challenge?slug=forecast-holt")).json();
let n = 0;
while (lz(createHash("sha256").update(c.challenge + ":" + n).digest()) < c.difficulty) n++;
await fetch("https://agent402.tools/api/forecast-holt", { method: "POST", headers: { "X-Pow-Solution": c.token + ":" + n, "Content-Type": "application/json" }, body: JSON.stringify({"values":[100,105,111,118,124,131,137,144,150,157],"horizon":3,"alpha":0.5,"beta":0.3}) });

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