Cross-Sectional Herding Detection

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/** D17 reference algorithms. JSON boundary validation is deliberate and shared.
 * Arrays are copied before sorting; callers' inputs are never mutated.
 * QR solves least squares without forming normal equations.
 */
type Data = Record<string, any>;
type Result = Record<string, any>;
class ContractError extends Error {
}
const fail = (code: string): never => { throw new ContractError(code); };
const num = (x: unknown): number => typeof x === 'number' && Number.isFinite(x) ? x : fail('INVALID_NUMBER');
function integer(x: unknown, lo: number, hi: number): number { const v = num(x); return Number.isInteger(v) && v >= lo && v <= hi ? v : fail('INVALID_PARAMETER'); }
function vec(x: unknown, min = 1): number[] { if (!Array.isArray(x))
    fail('INVALID_SHAPE'); const a = x as unknown[]; if (a.length < min)
    fail('INSUFFICIENT_DATA'); return a.map(num); }
function mat(x: unknown, min = 1): number[][] { if (!Array.isArray(x) || x.length < min)
    fail('INSUFFICIENT_DATA'); const a = (x as unknown[]).map(v => vec(v)); if (new Set(a.map(r => r.length)).size !== 1)
    fail('LENGTH_MISMATCH'); return a; }
function same(...x: {
    length: number;
}[]): void { if (new Set(x.map(a => a.length)).size !== 1)
    fail('LENGTH_MISMATCH'); }
function ids(d: Data, n: number): string[] { required(d, ['ids']); if (!Array.isArray(d.ids) || d.ids.length !== n)
    fail('LENGTH_MISMATCH'); if (d.ids.some((v: unknown) => typeof v !== 'string' || !/^[A-Za-z0-9_.-]+$/.test(v)))
    fail('INVALID_ID'); if (new Set(d.ids).size !== n)
    fail('DUPLICATE_ID'); return [...d.ids]; }
function required(d: Data, keys: string[]): void { for (const key of keys)
    if (!Object.hasOwn(d, key))
        fail('MISSING_FIELD'); }
function validDate(v: unknown): boolean { if (typeof v !== 'string' || !/^\d{4}-\d{2}-\d{2}$/.test(v) || v.startsWith('0000'))
    return false; const date = new Date(v + 'T00:00:00Z'); return Number.isFinite(date.valueOf()) && date.toISOString().slice(0, 10) === v; }
function context(d: Data, op: string): void {
    const keys = ['as_of', 'formation_at', 'inputs_available_at'];
    const evaluation = ['ic', 'rank_ic', 'spread', 'decay'].includes(op);
    if (evaluation)
        keys.push('outcomes_start_at', 'outcomes_end_at', 'outcomes_available_at');
    required(d, keys);
    if (keys.some(k => !validDate(d[k])))
        fail('INVALID_DATE');
    if (d.formation_at > d.as_of || d.inputs_available_at > d.formation_at)
        fail('FUTURE_INPUT');
    if (evaluation) {
        if (d.outcomes_start_at < d.formation_at || d.outcomes_end_at < d.outcomes_start_at)
            fail('INVALID_OUTCOME_WINDOW');
        if (d.outcomes_available_at < d.outcomes_end_at)
            fail('INVALID_DATE_ORDER');
        if (d.outcomes_available_at > d.as_of)
            fail('IMMATURE_OUTCOME');
    }
}
const sum = (a: number[]): number => a.reduce((s, v) => s + v, 0);
const mean = (a: number[]): number => sum(a) / a.length;
const dot = (a: number[], b: number[]): number => sum(a.map((v, i) => v * b[i]));
const tr = (a: number[][]): number[][] => a[0].map((_, j) => a.map(r => r[j]));
const mm = (a: number[][], b: number[][]): number[][] => { const cols = tr(b); return a.map(row => cols.map(col => dot(row, col))); };
function sd(x: number[], ddof = 0): number { const m = mean(x); return Math.sqrt(sum(x.map(v => (v - m) ** 2)) / (x.length - ddof)); }
function standard(x: number[]): number[] { const m = mean(x), s = sd(x); if (s <= 1e-14 * Math.max(1, ...x.map(Math.abs)))
    fail('CONSTANT_CROSS_SECTION'); return x.map(v => (v - m) / s); }
function corr(x: number[], y: number[]): number | null { same(x, y); if (Math.max(...x) === Math.min(...x) || Math.max(...y) === Math.min(...y))
    return null; const xm = mean(x), ym = mean(y), a = x.map(v => v - xm), b = y.map(v => v - ym), den = Math.sqrt(dot(a, a) * dot(b, b)); return den <= 0 ? null : Math.max(-1, Math.min(1, dot(a, b) / den)); }
function ranks(x: number[]): number[] { const order = x.map((_, i) => i).sort((a, b) => x[a] - x[b]); const out = x.map(() => 0); let start = 0; while (start < x.length) {
    let end = start + 1;
    while (end < x.length && x[order[end]] === x[order[start]])
        end++;
    for (let j = start; j < end; j++)
        out[order[j]] = (start + 1 + end) / 2;
    start = end;
} return out; }
function quantile(x: number[], p: number): number { const y = [...x].sort((a, b) => a - b), h = (y.length - 1) * p, j = Math.floor(h), f = h - j; return y[j] * (1 - f) + y[Math.min(j + 1, y.length - 1)] * f; }
function compound(x: number[]): number { if (x.some(v => v <= -1))
    fail('INVALID_RETURN'); return Math.expm1(sum(x.map(Math.log1p))); }
/** erfc(|z|/sqrt(2)) via regularized Gamma(1/2,x); converged series/CF. */
function normalP(z: number): number {
    const x = z * z / 2, a = 0.5, lg = 0.5723649429247001;
    if (x === 0)
        return 1;
    const factor = Math.exp(-x + a * Math.log(x) - lg);
    if (x < a + 1) {
        let term = 1 / a, total = term, ap = a;
        for (let i = 1; i < 500; i++) {
            ap++;
            term *= x / ap;
            total += term;
            if (Math.abs(term) < Math.abs(total) * 1e-15)
                break;
        }
        return Math.max(0, 1 - total * factor);
    }
    let b = x + 1 - a, c = 1e300, d = 1 / b, h = d;
    for (let i = 1; i < 500; i++) {
        const an = -i * (i - a);
        b += 2;
        d = an * d + b;
        if (Math.abs(d) < 1e-300)
            d = 1e-300;
        c = b + an / c;
        if (Math.abs(c) < 1e-300)
            c = 1e-300;
        d = 1 / d;
        const delta = d * c;
        h *= delta;
        if (Math.abs(delta - 1) < 1e-15)
            break;
    }
    return Math.max(0, Math.min(1, factor * h));
}
export function ols(y: number[], x: number[][], lags = 0): Result {
    const n = y.length, p = x[0].length;
    same(y, x);
    if (n <= p)
        fail('INSUFFICIENT_DATA');
    integer(lags, 0, n - 1);
    const cols = tr(x), scales = cols.map(c => Math.sqrt(dot(c, c)));
    if (scales.some(s => s === 0))
        fail('SINGULAR_DESIGN');
    const q: number[][] = [], r = Array.from({ length: p }, () => Array(p).fill(0) as number[]);
    for (let j = 0; j < p; j++) {
        let v = cols[j].map(z => z / scales[j]);
        for (let pass = 0; pass < 2; pass++)
            for (let i = 0; i < j; i++) {
                const proj = dot(q[i], v);
                r[i][j] += proj;
                v = v.map((z, t) => z - proj * q[i][t]);
            }
        r[j][j] = Math.sqrt(dot(v, v));
        if (r[j][j] < 1e-10)
            fail('SINGULAR_DESIGN');
        q.push(v.map(z => z / r[j][j]));
    }
    const solve = (v: number[]): number[] => { const b = Array(p).fill(0) as number[]; for (let i = p - 1; i >= 0; i--) {
        let s = 0;
        for (let j = i + 1; j < p; j++)
            s += r[i][j] * b[j];
        b[i] = (v[i] - s) / r[i][i];
    } return b; };
    const beta = solve(q.map(c => dot(c, y))).map((b, i) => b / scales[i]), fitted = x.map(row => dot(row, beta)), residuals = y.map((v, i) => v - fitted[i]);
    const invr = tr(Array.from({ length: p }, (_, j) => solve(Array.from({ length: p }, (_, i) => Number(i === j)))));
    const bread = mm(invr, tr(invr)).map((row, i) => row.map((v, j) => v / scales[i] / scales[j]));
    const scores = x.map((row, t) => row.map(v => v * residuals[t])), meat = mm(tr(scores), scores);
    for (let lag = 1; lag <= lags; lag++) {
        const w = 1 - lag / (lags + 1);
        for (let t = lag; t < n; t++)
            for (let i = 0; i < p; i++)
                for (let j = 0; j < p; j++)
                    meat[i][j] += w * (scores[t][i] * scores[t - lag][j] + scores[t - lag][i] * scores[t][j]);
    }
    const cov = mm(mm(bread, meat), bread), se = cov.map((row, i) => Math.sqrt(Math.max(0, row[i]))), sse = dot(residuals, residuals), ym = mean(y), sst = sum(y.map(v => (v - ym) ** 2));
    return { coefficients: beta, standard_errors: se, fitted, residuals, r_squared: sst === 0 ? null : 1 - sse / sst, n, df_residual: n - p, hac_lags: lags, residual_sum_squares: sse, qr_min_diagonal: Math.min(...r.map((row, i) => row[i])) };
}
function hacVariance(g: number[], lags: number): number { const n = g.length, m = mean(g), a = g.map(v => v - m); let v = dot(a, a) / n; for (let lag = 1; lag <= lags; lag++)
    v += 2 * (1 - lag / (lags + 1)) * dot(a.slice(lag), a.slice(0, -lag)) / n; return v; }
function choose(n: number, k: number): number { if (k < 0 || k > n)
    return 0; k = Math.min(k, n - k); let out = 1; for (let j = 1; j <= k; j++)
    out *= (n - k + j) / j; return out; }
function behavior(d: Data, op: string): Result {
    if (op === 'herding') {
        required(d, ['returns']);
        const panel = mat(d.returns, 12);
        if (panel.some(row => row.some(v => v < -1)))
            fail('INVALID_RETURN');
        if (panel[0].length < 3)
            fail('INSUFFICIENT_DATA');
        const market = panel.map(mean), csad = panel.map((row, t) => mean(row.map(v => Math.abs(v - market[t])))), fit = ols(csad, market.map(m => [1, Math.abs(m), m * m]), d.hac_lags ?? 2), se = fit.standard_errors[2], z = se <= 1e-14 ? null : fit.coefficients[2] / se;
        return { ...fit, market, csad, curvature: fit.coefficients[2], z, p_value: z === null ? null : normalP(z), primary: fit.coefficients[2] };
    }
    if (op === 'event') {
        required(d, ['estimation_asset', 'estimation_market', 'event_asset', 'event_market', 'event_times', 'estimation_end', 'event_start']);
        const a = vec(d.estimation_asset, 8), m = vec(d.estimation_market, 8), ea = vec(d.event_asset), em = vec(d.event_market), times = vec(d.event_times);
        same(a, m);
        same(ea, em, times);
        if (Math.min(...a, ...m, ...ea, ...em) < -1)
            fail('INVALID_RETURN');
        if (!validDate(d.estimation_end) || !validDate(d.event_start))
            fail('INVALID_DATE');
        if (d.estimation_end >= d.event_start)
            fail('OVERLAPPING_WINDOWS');
        if (d.event_start > d.inputs_available_at)
            fail('FUTURE_INPUT');
        if (times.some((t, i) => !Number.isInteger(t) || (i > 0 && t <= times[i - 1])))
            fail('INVALID_ORDER');
        const fit = ols(a, m.map(v => [1, v]), 0), expected = em.map(v => fit.coefficients[0] + fit.coefficients[1] * v), ar = ea.map((v, i) => v - expected[i]);
        let total = 0;
        const car = ar.map(v => (total += v));
        return { coefficients: fit.coefficients, expected_returns: expected, abnormal_returns: ar, car, event_times: times, primary: car[car.length - 1] };
    }
    required(d, ['returns']);
    const r = vec(d.returns, 2), n = r.length;
    if (['expectations', 'adaptive'].includes(op) && Math.min(...r) < -1)
        fail('INVALID_RETURN');
    if (op === 'variance_ratio') {
        const q = integer(d.q ?? 2, 2, n - 1), mu = mean(r), e = r.map(v => v - mu), ss = dot(e, e);
        if (Math.max(...r) === Math.min(...r) || ss <= 0)
            fail('CONSTANT_SERIES');
        const blocks = Array.from({ length: n - q + 1 }, (_, j) => sum(r.slice(j, j + q)) - q * mu), short = ss / (n - 1), long = dot(blocks, blocks) / (q * (n - q + 1) * (1 - q / n)), vr = long / short, deltas = Array.from({ length: q - 1 }, (_, k) => { const j = k + 1; let v = 0; for (let t = j; t < n; t++)
            v += e[t] ** 2 * e[t - j] ** 2; return v / ss ** 2; }), theta = sum(deltas.map((v, k) => 4 * (1 - (k + 1) / q) ** 2 * v));
        if (theta <= 0)
            fail('ZERO_MOMENT_VARIANCE');
        const z = (vr - 1) / Math.sqrt(theta);
        return { ratio: vr, z, p_value: normalP(z), q, one_step_variance: short, q_step_variance: long, robust_variance: theta, deltas, block_sums: blocks, primary: vr };
    }
    if (op === 'runs') {
        const threshold = num(d.threshold ?? 0), signs = r.filter(v => v !== threshold).map(v => v > threshold ? 1 : -1), a = signs.filter(v => v === 1).length, b = signs.length - a, total = a + b;
        if (!a || !b)
            fail('ONE_SIGN');
        if (total > 200)
            fail('EXACT_SAMPLE_LIMIT');
        const runs = 1 + sum(signs.slice(1).map((v, i) => Number(v !== signs[i]))), expected = 1 + 2 * a * b / total, variance = 2 * a * b * (2 * a * b - total) / (total ** 2 * (total - 1)), den = choose(total, a), probs: Array<{
            runs: number;
            probability: number;
        }> = [];
        for (let k = 2; k <= total; k++) {
            let ways: number;
            if (k % 2 === 0) {
                const j = k / 2;
                ways = 2 * choose(a - 1, j - 1) * choose(b - 1, j - 1);
            }
            else {
                const j = (k - 1) / 2;
                ways = choose(a - 1, j) * choose(b - 1, j - 1) + choose(a - 1, j - 1) * choose(b - 1, j);
            }
            probs.push({ runs: k, probability: ways / den });
        }
        const observed = probs.find(p => p.runs === runs)!.probability, p = Math.min(1, sum(probs.filter(row => row.probability <= observed * (1 + 1e-12)).map(row => row.probability)));
        return { runs, expected, variance, z: variance === 0 ? null : (runs - expected) / Math.sqrt(variance), p_value: p, signs, zeros_dropped: n - total, distribution: probs, primary: p };
    }
    if (op === 'martingale') {
        if (n < 12)
            fail('INSUFFICIENT_DATA');
        const lags = integer(d.hac_lags ?? 2, 0, n - 2), moments = [1, 2].map(power => r.slice(1).map((v, t) => v * r[t] ** power)), omega = moments.map(g => hacVariance(g, lags));
        if (Math.min(...omega) <= 0)
            fail('ZERO_MOMENT_VARIANCE');
        const z = moments.map((g, i) => Math.sqrt(n - 1) * mean(g) / Math.sqrt(omega[i])), p = z.map(normalP), family = Math.min(1, 2 * Math.min(...p));
        return { moments, means: moments.map(mean), long_run_variances: omega, z, p_values: p, family_p_value: family, hac_lags: lags, primary: family };
    }
    if (op === 'horizons') {
        const a = integer(d.recent ?? 1, 1, n), b = integer(d.middle ?? 12, a + 1, n), c = integer(d.distant ?? 36, b + 1, n);
        if (Math.min(...r) <= -1)
            fail('INVALID_RETURN');
        const blocks = [r.slice(n - a), r.slice(n - b, n - a), r.slice(n - c, n - b)], logs = blocks.map(row => sum(row.map(Math.log1p))), total = Math.expm1(sum(logs));
        return { log_contributions: logs, simple_returns: logs.map(Math.expm1), candidate_signals: [-logs[0], logs[1], -logs[2]], total_return: total, endpoints: [a, b, c], primary: total };
    }
    if (op === 'expectations') {
        const lookback = integer(d.lookback ?? 12, 1, n), rho = num(d.rho ?? 0.8);
        if (rho < 0 || rho > 1)
            fail('INVALID_PARAMETER');
        const observed = r.slice(-lookback).reverse(), raw = Array.from({ length: lookback }, (_, j) => rho ** j), weights = raw.map(v => v / sum(raw)), contributions = weights.map((v, i) => v * observed[i]);
        return { weights, returns_recent_first: observed, contributions, proxy: sum(contributions), primary: sum(contributions), rho };
    }
    if (op === 'adaptive') {
        if (n < 24)
            fail('INSUFFICIENT_DATA');
        const split = integer(d.split ?? Math.floor(n / 2), 9, n - 8), design = r.slice(1).map((_, j) => { const t = j + 1, D = Number(t >= split); return [1, r[t - 1], D, D * r[t - 1]]; }), fit = ols(r.slice(1), design, d.hac_lags ?? 2), se = fit.standard_errors[3], z = se <= 1e-14 ? null : fit.coefficients[3] / se;
        return { ...fit, pre_beta: fit.coefficients[1], post_beta: fit.coefficients[1] + fit.coefficients[3], change: fit.coefficients[3], z, p_value: z === null ? null : normalP(z), split, primary: fit.coefficients[3] };
    }
    return fail('UNKNOWN_METHOD');
}
/** D17-F05-A05 public boundary. No mutation, implicit imputation or silent failure. */
export function compute(input: unknown): Result {
    const op = "herding";
    try {
        if (!input || typeof input !== 'object' || Array.isArray(input))
            fail('INVALID_SHAPE');
        const d = input as Data;
        if (Object.values(d).some(v => v === null))
            fail('INVALID_NUMBER');
        context(d, op);
        const result = behavior(d, op);
        const check = (v: unknown): void => { if (typeof v === 'number' && !Number.isFinite(v))
            fail('NUMERICAL_FAILURE'); if (Array.isArray(v))
            v.forEach(check);
        else if (v && typeof v === 'object')
            Object.values(v).forEach(check); };
        check(result);
        return { status: 'ok', method: op, ...result };
    }
    catch (error) {
        if (error instanceof ContractError)
            return { status: 'error', method: op, code: error.message };
        throw error;
    }
}