Mean reversion z-score

A 20-day rolling z-score signal generator — the textbook mean-reversion idiom. When the price drifts more than 1.25 σ away from its rolling mean, mark it as oversold (signal = +1) or overbought (signal = -1). Otherwise flat (0).

ma_20[t]   = mean of close[t-19 … t]
std_20[t]  = sample std of close[t-19 … t]   (ddof = 1)
zscore[t]  = (close[t] − ma_20[t]) / std_20[t]
signal[t]  = +1   if zscore < −1.25
             −1   if zscore > +1.25
              0   otherwise

Query

WITH
    '2024-01-01' AS start_date,
    '2024-12-31' AS end_date,
    20 AS window_size,
    1.25 AS n_std,
    candles AS (
        SELECT toDate(start) AS day, toFloat64(close) AS close
        FROM api.ohlcv(candle_duration_in_minutes = 1440)
        WHERE exchange = 'binance'
          AND market = 'BTC-USDT'
          AND start BETWEEN start_date AND end_date
    ),
    z AS (
        SELECT day, close,
               avg(close) OVER w AS ma_20,
               stddevSamp(close) OVER w AS std_20,
               (close - avg(close) OVER w) / nullIf(stddevSamp(close) OVER w, 0) AS zscore,
               count(*) OVER w AS valid_rows
        FROM candles
        WINDOW w AS (ORDER BY day ROWS BETWEEN 19 PRECEDING AND CURRENT ROW)
    )
SELECT day, close, ma_20, std_20, zscore,
       if(zscore < -n_std, 1, if(zscore > n_std, -1, 0)) AS signal
FROM z
WHERE valid_rows = window_size
ORDER BY day

Two SQL details worth flagging:

• stddevSamp, not stddevPop. Pandas .rolling(N).std() defaults to ddof = 1 (Bessel's correction). Mixing pop / sample here changes the z-score by a factor of √(N / (N − 1)) ≈ 1.026 for N = 20 — small numerically but enough to flip a signal that's hovering near ±1.25. Use stddevSamp to match pandas exactly.

• count(*) OVER w = window_size filters out the first 19 rows before the rolling window has filled. Same effect as dropna(subset=['zscore']) in pandas.

Output (2024)

347 rows × 6 columns. The first few signal-firing days:

day	close	ma_20	std_20	zscore	signal
2024-01-22	39568.02	43335.61	1974.41	−1.91	+1
2024-01-23	39897.60	43188.22	2117.76	−1.55	+1
2024-01-24	40084.88	42984.91	2213.47	−1.31	+1
2024-02-07	44349.60	42064.01	1310.55	+1.74	−1
2024-02-08	45288.65	42245.49	1490.48	+2.04	−1
2024-02-09	47132.77	42517.32	1839.83	+2.51	−1

Signal counts for the year: 53 long, 99 short, 195 flat. Short signals dominate because BTC trended upward through 2024 — the rolling mean lagged the price most of the time, pushing the z-score above the upper threshold whenever the rally re-accelerated.

Extending it

• Different window or threshold — change window_size and n_std. Tighter window (e.g. 10) reacts faster but flips more often; wider window (60) is smoother but slower.

• Backtest the strategy — feed signal into a cumulative-returns CTE: signal[t-1] · pct_change(close)[t] then a running product via exp(sum(log(1 + ...))) (see Maximum drawdown & Calmar for the cumprod trick).