Moving average (SMA + EMA)

Compute simple (SMA) and exponential (EMA) moving averages over a numeric series. Returns one value per input position — the first (window-1) SMA values are null since there isn't enough history. EMA uses the standard alpha = 2/(window+1) smoothing factor used in technical analysis.

Input

Field	Type	Description
values *	array	Numeric series (max 10000)
window *	number	Window size, 2 to values.length
which	string	"sma", "ema", or "both" (default "both")

Example output

{
  "window": 3,
  "count": 10,
  "sma": [
    null,
    null,
    11,
    12,
    13,
    14,
    15,
    16,
    17,
    18
  ],
  "ema": [
    10,
    10.5,
    11.25,
    12.125,
    13.0625,
    14.0312,
    15.0156,
    16.0078,
    17.0039,
    18.002
  ]
}

Try it — see the 402 challenge (free)

curl -i -X POST https://agent402.tools/api/moving-average \
  -H "Content-Type: application/json" \
  -d '{"values":[10,11,12,13,14,15,16,17,18,19],"window":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/moving-average", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    "values": [
      10,
      11,
      12,
      13,
      14,
      15,
      16,
      17,
      18,
      19
    ],
    "window": 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=moving-average")).json();
let n = 0;
while (lz(createHash("sha256").update(c.challenge + ":" + n).digest()) < c.difficulty) n++;
await fetch("https://agent402.tools/api/moving-average", { method: "POST", headers: { "X-Pow-Solution": c.token + ":" + n, "Content-Type": "application/json" }, body: JSON.stringify({"values":[10,11,12,13,14,15,16,17,18,19],"window":3}) });

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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