Full variance ratio test at horizons 2/4/8/16 with z-stats and p-values

Code snippets

curl "https://api.oanor.com/varianceratio-api/v1/asset" \
  -H "x-oanor-key: oanor_test_..."

await fetch("https://api.oanor.com/varianceratio-api/v1/asset", {
  headers: { "x-oanor-key": "oanor_test_..." }
});

$ch = curl_init("https://api.oanor.com/varianceratio-api/v1/asset");
curl_setopt($ch, CURLOPT_HTTPHEADER, ["x-oanor-key: oanor_test_..."]);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
$out = curl_exec($ch);

import requests
requests.get(
    "https://api.oanor.com/varianceratio-api/v1/asset",
    headers={"x-oanor-key": "oanor_test_..."}
)

Example response

A real response from this endpoint, captured by the latest health check.

{
    "data": {
        "name": "S&P 500 ETF",
        "note": "Lo-MacKinlay variance ratio test at horizons 2/4/8/16 days. variance_ratio = 1 under a random walk; > 1 = momentum (positive autocorrelation), < 1 = mean-reversion. z_stat is heteroskedasticity-robust; |z| >= 1.96 rejects the random walk at 95% (p < 0.05). Read fresh per call, nothing cached.",
        "class": "index",
        "source": "Yahoo Finance",
        "symbol": "SPY",
        "horizons": [
            {
                "q": 2,
                "z_stat": -0.72,
                "p_value": 0.47,
                "verdict": "random walk (cannot reject at 95%)",
                "variance_ratio": 0.936
            },
            {
                "q": 4,
                "z_stat": -0.51,
                "p_value": 0.6085,
                "verdict": "random walk (cannot reject at 95%)",
                "variance_ratio": 0.924
            },
            {
                "q": 8,
                "z_stat": -0.7,
                "p_value": 0.4818,
                "verdict": "random walk (cannot reject at 95%)",
                "variance_ratio": 0.837
            },
            {
                "q": 16,
                "z_stat": -0.63,
                "p_value": 0.5318,
                "verdict": "random walk (cannot reject at 95%)",
                "variance_ratio": 0.804
            }
        ],
        "window_days": 756,
        "overall_verdict": "random walk — no horizon rejects the random-walk hypothesis at 95%"
    },
    "meta": {
        "timestamp": "2026-06-12T10:34:37.479Z",
        "request_id": "ab8261a3-b5c1-4e42-bc3d-35b4f9cac0bd"
    },
    "status": "ok",
    "message": "Variance ratio test retrieved successfully",
    "success": true
}