Forecast (Holt-Winters seasonal)

Holt-Winters triple exponential smoothing — level + trend + seasonal component. Use for series with a repeating cycle (weekly retail traffic, monthly utility usage, quarterly revenue). Additive seasonality (constant amplitude) or multiplicative (amplitude grows with level). `period` is optional — if omitted, the kit auto-detects via autocorrelation on first differences and surfaces what it picked (with the ACF strength) so you can audit. Needs at least two full seasonal cycles to fit reliably.

Input

Field	Type	Description
values *	array	Numeric series in chronological order (max 10000)
horizon *	number	Number of future periods to forecast (1 to 1000)
period	number	Optional seasonal period (e.g. 7 for daily/weekly, 12 for monthly/yearly). Auto-detected via ACF if omitted.
seasonality	string	"additive" (default) or "multiplicative"
alpha	number	Level smoothing, 0 < alpha < 1 (default 0.5)
beta	number	Trend smoothing, 0 < beta < 1 (default 0.1)
gamma	number	Seasonal smoothing, 0 < gamma < 1 (default 0.1)

Example output

{
  "method": "holt-winters",
  "n": 12,
  "horizon": 4,
  "period": 4,
  "periodSource": "provided",
  "seasonality": "additive",
  "alpha": 0.5,
  "beta": 0.1,
  "gamma": 0.1,
  "forecast": [
    {
      "step": 1,
      "point": 12.5324,
      "lower95": 11.6958,
      "upper95": 13.369
    },
    {
      "step": 2,
      "point": 16.7253,
      "lower95": 15.5421,
      "upper95": 17.9084
    },
    {
      "step": 3,
      "point": 20.9462,
      "lower95": 19.4972,
      "upper95": 22.3952
    },
    {
      "step": 4,
      "point": 25.1831,
      "lower95": 23.5098,
      "upper95": 26.8563
    }
  ]
}

Try it — see the 402 challenge (free)

curl -i -X POST https://agent402.tools/api/forecast-holt-winters \
  -H "Content-Type: application/json" \
  -d '{"values":[10,14,18,22,11,15,19,23,12,16,20,24],"horizon":4,"period":4}'

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-winters", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    "values": [
      10,
      14,
      18,
      22,
      11,
      15,
      19,
      23,
      12,
      16,
      20,
      24
    ],
    "horizon": 4,
    "period": 4
  }),
});

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-winters")).json();
let n = 0;
while (lz(createHash("sha256").update(c.challenge + ":" + n).digest()) < c.difficulty) n++;
await fetch("https://agent402.tools/api/forecast-holt-winters", { method: "POST", headers: { "X-Pow-Solution": c.token + ":" + n, "Content-Type": "application/json" }, body: JSON.stringify({"values":[10,14,18,22,11,15,19,23,12,16,20,24],"horizon":4,"period":4}) });

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