Forecast (simple exponential smoothing)

Simple exponential smoothing (SES) — level-only forecast for series without trend or seasonality. Higher alpha (closer to 1) tracks recent values aggressively; lower alpha (closer to 0) smooths through noise. Default alpha=0.3 is a common conservative pick; pass an explicit alpha or use forecast-eval to pick the one that minimizes backtest error. Forecast is flat (= last fitted level) for all horizons.

Input

Field	Type	Description
values *	array	Numeric series in chronological order (max 10000, min 3)
horizon *	number	Number of future periods to forecast (1 to 1000)
alpha	number	Smoothing parameter, 0 < alpha < 1 (default 0.3)

Example output

{
  "method": "ses",
  "n": 10,
  "horizon": 3,
  "alpha": 0.3,
  "forecast": [
    {
      "step": 1,
      "point": 45.4431,
      "lower95": 42.7805,
      "upper95": 48.1057
    },
    {
      "step": 2,
      "point": 45.4431,
      "lower95": 42.6633,
      "upper95": 48.2229
    },
    {
      "step": 3,
      "point": 45.4431,
      "lower95": 42.5508,
      "upper95": 48.3354
    }
  ]
}

Try it — see the 402 challenge (free)

curl -i -X POST https://agent402.tools/api/forecast-ses \
  -H "Content-Type: application/json" \
  -d '{"values":[42,44,41,43,45,44,46,45,47,46],"horizon":3,"alpha":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-ses", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    "values": [
      42,
      44,
      41,
      43,
      45,
      44,
      46,
      45,
      47,
      46
    ],
    "horizon": 3,
    "alpha": 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-ses")).json();
let n = 0;
while (lz(createHash("sha256").update(c.challenge + ":" + n).digest()) < c.difficulty) n++;
await fetch("https://agent402.tools/api/forecast-ses", { method: "POST", headers: { "X-Pow-Solution": c.token + ":" + n, "Content-Type": "application/json" }, body: JSON.stringify({"values":[42,44,41,43,45,44,46,45,47,46],"horizon":3,"alpha":0.3}) });

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