Does a high-volume day on MES tend to see continued high volume the next day

bars_et = to_et(bars)
rth = rth_session(bars_et)
rth = rth.copy()
rth['trading_date'] = trading_date(rth)

daily_vol = rth.groupby('trading_date')['volume'].sum().sort_index()

n = len(daily_vol)
if n < 3:
    result = {"sample_size": 0}
else:
    median_vol = daily_vol.median()
    high_vol_mask = daily_vol > median_vol

    # shift to get next day's volume
    next_day_vol = daily_vol.shift(-1)

    valid = high_vol_mask & next_day_vol.notna()
    high_days_next = next_day_vol[valid]

    low_vol_mask = ~high_vol_mask
    valid_low = low_vol_mask & next_day_vol.notna()
    low_days_next = next_day_vol[valid_low]

    avg_next_after_high = float(high_days_next.mean()) if len(high_days_next) > 0 else None
    avg_next_after_low = float(low_days_next.mean()) if len(low_days_next) > 0 else None

    # correlation between day's volume and next day's volume
    combined = pd.DataFrame({'vol': daily_vol, 'next_vol': next_day_vol}).dropna()
    corr = float(combined['vol'].corr(combined['next_vol'])) if len(combined) > 1 else None

    # probability that next day is also high volume, given today is high volume
    next_high_mask = next_day_vol > median_vol
    valid_pairs = high_vol_mask & next_day_vol.notna()
    prob_next_high_given_high = float(next_high_mask[valid_pairs].mean()) if valid_pairs.sum() > 0 else None

    valid_pairs_low = low_vol_mask & next_day_vol.notna()
    prob_next_high_given_low = float(next_high_mask[valid_pairs_low].mean()) if valid_pairs_low.sum() > 0 else None

    result = {
        "sample_size": int(len(combined)),
        "median_daily_volume": float(median_vol),
        "avg_next_day_volume_after_high_day": avg_next_after_high,
        "avg_next_day_volume_after_low_day": avg_next_after_low,
        "corr_today_vol_next_day_vol": corr,
        "prob_next_day_high_given_today_high": prob_next_high_given_high,
        "prob_next_day_high_given_today_low": prob_next_high_given_low,
        "num_high_vol_days": int(high_vol_mask.sum()),
        "num_low_vol_days": int(low_vol_mask.sum()),
    }