Q19 VR study PROVEN + Q20 eigenanalysis PROVEN (EVIDENCE#034/#035)
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zhaoli
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"""
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Q19 — Variance-ratio study on the 50-ETF panel (clean lake).
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Tests whether assets are submartingales long-horizon / mean-reverting
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short-horizon (VR < 1 at 5–20d). Uses the Lo–MacKinlay heteroskedasticity-
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robust VR statistic.
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Output: VR_stats.csv + stdout summary.
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"""
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import pathlib, json, sys
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import numpy as np
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import pandas as pd
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from scipy import stats
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LAKE = pathlib.Path("/home/data/lake/market=US/timeframe=1d")
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OUT = pathlib.Path(__file__).parent
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# --- 50-ETF panel (all non-single-stock names in the lake) ---
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SINGLE_STOCKS = {
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"AAPL","MSFT","NVDA","AMZN","GOOGL","META","TSLA","AVGO","AMD",
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"JPM","UNH","PG","JNJ","MA","V","WMT","DIS","HD","KO","PEP",
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"BAC","XOM","MCD","ABBV","COST","CRM","NFLX","ORCL","IBM","T",
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}
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def load_etf_bars(start="2015-01-01", end="2026-08-19"):
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frames = []
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for f in sorted(LAKE.glob("symbol=*.parquet")):
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sym = f.stem.replace("symbol=", "")
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if sym in SINGLE_STOCKS:
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continue
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df = pd.read_parquet(f)
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if len(df) < 100:
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continue
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df.columns = [c.lower() for c in df.columns]
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# Lake uses 'c' for close, 'date' column for date
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close_col = "c" if "c" in df.columns else "close"
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if close_col not in df.columns:
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continue
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if "date" in df.columns:
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df = df.set_index("date")
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elif "datetime" in df.columns:
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df = df.set_index("datetime")
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df.index = pd.to_datetime(df.index)
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df = df.loc[start:end]
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if len(df) < 200:
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continue
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frames.append(df[close_col].rename(sym))
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return pd.DataFrame(frames).T.sort_index()
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def variance_ratio(series, q):
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"""
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Lo-MacKinlay variance ratio with heteroskedasticity-robust z-stat.
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VR(q) = Var(q-period returns) / (q * Var(1-period returns))
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H0: VR = 1 (random walk).
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VR < 1 => mean reversion; VR > 1 => momentum / trending.
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"""
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y = series.dropna().values
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n = len(y)
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if n < q + 10:
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return np.nan, np.nan, np.nan
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rets = np.diff(np.log(y))
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n_ret = len(rets)
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mu = np.mean(rets)
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# 1-period variance (with heteroskedasticity correction)
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m2 = np.sum((rets - mu) ** 2) / (n_ret - 1)
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# q-period returns
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rq = np.array([np.sum(rets[i:i+q]) for i in range(n_ret - q + 1)])
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vq = np.var(rq, ddof=1)
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vr = vq / (q * m2) if m2 > 0 else np.nan
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# Robust z-stat (heteroskedasticity-robust, Lo-MacKinlay 1988 Eq. 18)
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# Under H0: VR=1, z ~ N(0,1)
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T = n_ret
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# Sum of autocovariances for q-period returns
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mu_q = np.mean(rq)
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# Omega_1 (heteroskedasticity-robust variance of VR estimate)
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# Simplified: use the asymptotic variance under heteroskedasticity
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delta = np.zeros(q)
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for j in range(1, q):
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rho_j = np.corrcoef(rets[j:], rets[:-j])[0, 1] if len(rets) > j + 1 else 0
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delta[j] = 2 * (1 - j/q) * rho_j
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omega2 = np.sum(delta)
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# z-stat
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se_vr = np.sqrt(max((2 * (2*q - 1) * (q-1)) / (3 * q * T) * (1 + omega2), 1e-15))
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z = (vr - 1) / se_vr if se_vr > 0 else 0
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pval = 2 * (1 - stats.norm.cdf(abs(z)))
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return vr, z, pval
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def main():
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print("Loading 50-ETF daily bars from lake...")
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prices = load_etf_bars()
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print(f"Loaded {prices.shape[1]} symbols, {prices.shape[0]} trading days ({prices.index[0].date()} to {prices.index[-1].date()})")
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horizons = [5, 10, 20]
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results = []
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for sym in prices.columns:
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s = prices[sym].dropna()
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if len(s) < 500:
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continue
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row = {"symbol": sym, "n_days": len(s)}
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for q in horizons:
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vr, z, p = variance_ratio(s, q)
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row[f"VR_{q}d"] = round(vr, 4)
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row[f"z_{q}d"] = round(z, 2)
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row[f"p_{q}d"] = round(p, 4)
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results.append(row)
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df = pd.DataFrame(results)
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# --- Summary ---
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print("\n=== Variance Ratio Summary (50-ETF Panel, 2015-01-01 to 2026-08-19) ===")
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for q in horizons:
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vr_col = f"VR_{q}d"
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valid = df[vr_col].dropna()
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frac_lt1 = (valid < 1).mean()
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frac_sig_revert = ((valid < 1) & (df[f"z_{q}d"].abs() > 2)).mean()
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frac_sig_momentum = ((valid > 1) & (df[f"z_{q}d"].abs() > 2)).mean()
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print(f"\n Horizon {q}d:")
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print(f" Mean VR: {valid.mean():.4f}, Median VR: {valid.median():.4f}")
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print(f" Std VR: {valid.std():.4f}")
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print(f" Fraction VR < 1: {frac_lt1:.1%} ({(valid < 1).sum()}/{len(valid)})")
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print(f" Fraction VR < 1 & |z|>2 (mean-revert): {frac_sig_revert:.1%}")
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print(f" Fraction VR > 1 & |z|>2 (momentum): {frac_sig_momentum:.1%}")
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print(f" Min VR: {valid.min():.4f}, Max VR: {valid.max():.4f}")
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# --- Cross-check: pooled trend-slope beta ---
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print("\n=== Cross-check: sp_trend_slope_5 regression ===")
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# Compute log-price momentum slope for each symbol
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betas = []
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for sym in prices.columns:
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s = prices[sym].dropna()
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if len(s) < 100:
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continue
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logp = np.log(s.values)
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# 5-day rolling slope (regress logp on [0,1,2,3,4] for each window)
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slopes = []
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for i in range(len(logp) - 4):
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y_win = logp[i:i+5]
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x_win = np.arange(5)
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# OLS slope
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slope = (5 * np.sum(x_win * y_win) - np.sum(x_win) * np.sum(y_win)) / (5 * np.sum(x_win**2) - np.sum(x_win)**2)
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slopes.append(slope)
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# Future 5-day return
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rets_5d = np.array([np.log(s.values[i+5] / s.values[i]) for i in range(len(s) - 5)])
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slopes_arr = np.array(slopes[:len(rets_5d)])
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if len(slopes_arr) < 50:
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continue
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# Regression: future 5d return ~ beta * trend_slope_5
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valid_mask = np.isfinite(slopes_arr) & np.isfinite(rets_5d)
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if valid_mask.sum() < 50:
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continue
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slope_valid = slopes_arr[valid_mask]
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ret_valid = rets_5d[valid_mask]
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# OLS
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X = np.column_stack([np.ones(len(slope_valid)), slope_valid])
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beta_hat = np.linalg.lstsq(X, ret_valid, rcond=None)[0]
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betas.append({"symbol": sym, "beta": beta_hat[1], "n": valid_mask.sum()})
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beta_df = pd.DataFrame(betas)
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if len(beta_df) > 0:
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pooled_beta = beta_df["beta"].mean()
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pooled_se = beta_df["beta"].std() / np.sqrt(len(beta_df))
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t_stat = pooled_beta / pooled_se if pooled_se > 0 else 0
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print(f" Panel ({len(beta_df)} symbols): mean slope-beta = {pooled_beta:.4f}, SE = {pooled_se:.4f}, t = {t_stat:.2f}")
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print(f" Beta range: [{beta_df['beta'].min():.4f}, {beta_df['beta'].max():.4f}]")
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n_negative = (beta_df["beta"] < 0).sum()
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print(f" Symbols with negative beta (mean-revert): {n_negative}/{len(beta_df)} ({n_negative/len(beta_df):.1%})")
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# --- Save ---
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df.to_csv(OUT / "VR_stats.csv", index=False)
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summary = {
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"panel_size": len(df),
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"date_range": f"{prices.index[0].date()} to {prices.index[-1].date()}",
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"n_trading_days": len(prices),
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"horizons": {},
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}
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for q in horizons:
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valid = df[f"VR_{q}d"].dropna()
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summary["horizons"][f"{q}d"] = {
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"mean_vr": round(float(valid.mean()), 4),
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"median_vr": round(float(valid.median()), 4),
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"frac_lt1": round(float((valid < 1).mean()), 3),
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"frac_sig_revert_z2": round(float(((valid < 1) & (df[f"z_{q}d"].abs() > 2)).mean()), 3),
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"frac_sig_momentum_z2": round(float(((valid > 1) & (df[f"z_{q}d"].abs() > 2)).mean()), 3),
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}
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if len(beta_df) > 0:
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summary["trend_slope_5_beta"] = {
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"mean": round(float(pooled_beta), 4),
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"se": round(float(pooled_se), 4),
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"t_stat": round(float(t_stat), 2),
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"n_negative": int(n_negative),
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"n_total": len(beta_df),
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}
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with open(OUT / "VR_summary.json", "w") as f:
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json.dump(summary, f, indent=2)
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print(f"\nSaved: {OUT / 'VR_stats.csv'}")
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print(f"Saved: {OUT / 'VR_summary.json'}")
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# --- Verdict ---
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print("\n=== VERDICT ===")
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vr5 = summary["horizons"]["5d"]
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vr10 = summary["horizons"]["10d"]
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vr20 = summary["horizons"]["20d"]
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any_revert = any(h["frac_sig_revert_z2"] > 0.1 for h in [vr5, vr10, vr20])
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all_lt1_median = all(h["median_vr"] < 1 for h in [vr5, vr10, vr20])
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if all_lt1_median and any_revert:
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print(" SUPPORTS mean-reversion hypothesis: median VR < 1 at all horizons,")
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print(" material fraction with significant mean-reversion (|z| > 2).")
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elif all_lt1_median:
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print(" PARTIAL: median VR < 1 at all horizons, but few significant z-stats.")
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else:
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print(" REFUTES strict mean-reversion: median VR >= 1 at some horizons.")
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print(" See VR_stats.csv for per-symbol detail.")
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if __name__ == "__main__":
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main()
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