Forecast backtest (MAPE + RMSE)

Backtest a forecasting method on the input series by holding out the last `testSize` observations, forecasting them, and computing MAPE (mean absolute percentage error) + RMSE (root mean squared error). Lets an agent pick which method (mean / naive / drift / ses / holt / holt-winters) actually fits its data before committing to a forward forecast. Always returns a `warnings` array — empty when the backtest is well-posed, populated when `testSize` exceeds n/2 (treat error as indicative not predictive).

Input

Field	Type	Description
values *	array	Numeric series (max 10000)
testSize *	number	Trailing observations to hold out (1 to values.length - 2). Values above n/2 trigger a warning, not an error.
method *	string	"mean", "naive", "drift", "ses", "holt", "holt-winters"
alpha	number	Smoothing for ses/holt/holt-winters
beta	number	Trend smoothing for holt/holt-winters
gamma	number	Seasonal smoothing for holt-winters
period	number	Seasonal period for holt-winters (auto-detected if omitted)
seasonality	string	"additive" or "multiplicative" for holt-winters

Example output

{
  "method": "drift",
  "n": 10,
  "testSize": 3,
  "trainSize": 7,
  "mape": 1.1139,
  "rmse": 0.2722,
  "forecast": [
    {
      "step": 1,
      "actual": 19,
      "predicted": 19.3333
    },
    {
      "step": 2,
      "actual": 21,
      "predicted": 20.6667
    },
    {
      "step": 3,
      "actual": 22,
      "predicted": 22
    }
  ],
  "warnings": []
}

Try it — see the 402 challenge (free)

curl -i -X POST https://agent402.tools/api/forecast-eval \
  -H "Content-Type: application/json" \
  -d '{"values":[10,12,13,12,15,16,18,19,21,22],"testSize":3,"method":"drift"}'

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-eval", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    "values": [
      10,
      12,
      13,
      12,
      15,
      16,
      18,
      19,
      21,
      22
    ],
    "testSize": 3,
    "method": "drift"
  }),
});

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-eval")).json();
let n = 0;
while (lz(createHash("sha256").update(c.challenge + ":" + n).digest()) < c.difficulty) n++;
await fetch("https://agent402.tools/api/forecast-eval", { method: "POST", headers: { "X-Pow-Solution": c.token + ":" + n, "Content-Type": "application/json" }, body: JSON.stringify({"values":[10,12,13,12,15,16,18,19,21,22],"testSize":3,"method":"drift"}) });

Part of these workflows

This tool is one step in a curated multi-tool workflow — agents can fetch the whole sequence as an MCP prompt or call https://agent402.tools/api/skill-packs/{slug}/prompt.

• Trend analysis — Take any numeric time series — a stock's daily close, a FRED macro indicator, a treasury yield history — and run it through the full quantitative workup: descriptives, moving averages, trend line, outliers, optional correlation against a benchmark, and a deterministic forecast forward with a 95% prediction interval. Everything an analyst writes a notebook for, in one chain of cheap calls.

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