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Kalman Filter Pairs Trading System — full production-grade implementation

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Core engine (pure NumPy, zero external deps beyond NumPy):
- kalman_filter.py: KalmanFilter + KalmanPairsTrader
  - Time-varying observation matrix H_t = [1, X_t]
  - RTS smoother for offline analysis
  - Properties: alpha, beta, spread = Y - (alpha + beta*X)
  - Signal: z-score crossing z_entry/z_exit/z_stop thresholds

Pair discovery (pure NumPy):
- pair_discovery.py: Engle-Granger cointegration + OU half-life
  - ADF test with MacKinnon critical values (no statsmodels)
  - Half-life estimation via OLS on AR(1) residuals
  - Pair screening: cointegrated + 1-20 period half-life
  - Rolling OLS hedge ratio for baseline comparison

Production system:
- trading_system.py: KalmanPairsTradingSystem
  - Multi-pair orchestration with risk overlay
  - Capital allocation, stop-loss, drawdown controls
  - KalmanPairsConfig dataclass (YAML-compatible)

Backtesting:
- backtest.py: Walk-forward backtest with realistic execution
  - Transaction costs, capital tracking, per-trade PnL
  - Side-by-side Kalman vs rolling OLS comparison
  - Metrics: CAGR, Sharpe, Sortino, max DD, win rate, turnover

Tuning:
- tuning.py: Grid search over transition_covariance
  - Train/validation split (chronological)
  - Objective: maximize Sharpe - penalty * max_drawdown

Regime-shift test results:
  Kalman: Sharpe 2.17, beta adapts from 2.0 -> 0.5 in ~50 bars
  OLS 60d: Sharpe 0.17 (stuck on old beta)
  OLS 120d: Sharpe 0.66 (even slower adaptation)

Integration: Added to historical_runner.py as kalman_pairs strategy
This commit is contained in:
ramseshk
2026-08-05 06:47:33 +00:00
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commit f4c8bca15a
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strategies/kalman_pairs/backtest.py
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"""
Kalman Pairs Backtesting Framework.
Full walk-forward backtest with:
- Realistic execution (transaction costs, capital allocation)
- Per-trade P&L tracking
- Side-by-side comparison vs rolling OLS (60-day, 120-day windows)
- Performance report: CAGR, Sharpe, Sortino, max DD, win rate, turnover
- Regime-shift stress tests
"""
from __future__ import annotations
import numpy as np
from typing import Optional
from .kalman_filter import KalmanPairsTrader
from .pair_discovery import compute_rolling_ols_hedge
# Import project metrics
import sys
from pathlib import Path
sys.path.insert(0, str(Path(__file__).resolve().parent.parent.parent))
from common.metrics import sharpe, sortino, max_drawdown, win_rate
def backtest_kalman_pairs(
X: np.ndarray,
Y: np.ndarray,
trader: KalmanPairsTrader,
trade_size_usd: float = 100.0,
transaction_cost_bps: float = 2.5,
initial_capital: float = 10000.0,
) -> dict:
"""
Run a walk-forward backtest for a single pair using Kalman filter.
Args:
X, Y: Price series (must be same length).
trader: Pre-configured KalmanPairsTrader (already initialized).
trade_size_usd: Notional per leg in USD.
transaction_cost_bps: Fee per leg in basis points.
initial_capital: Starting capital.
Returns:
dict with: trades list, equity_curve, metrics, final_equity.
"""
n = min(len(X), len(Y))
trader.reset()
capital = initial_capital
peak_capital = initial_capital
equity_curve: list[dict] = []
trades: list[dict] = []
open_trade: Optional[dict] = None
fee_rate = transaction_cost_bps / 10000.0 # bps → decimal
for t in range(n):
x_t = float(X[t])
y_t = float(Y[t])
result = trader.step(x_t, y_t)
signal = result["signal"]
beta = result["beta"]
if signal != 0:
if open_trade is None:
# Open position
entry_x = x_t
entry_y = y_t
size_x = trade_size_usd / entry_x if entry_x > 0 else 0
size_y = trade_size_usd / entry_y if entry_y > 0 else 0
# Hedge: use current beta
# If signal = +1: LONG Y (size_y), SHORT X (size_x * beta)
# If signal = -1: SHORT Y (size_y), LONG X (size_x * beta)
hedge_notional = size_x * entry_x * abs(beta) if beta else 0
fee = (trade_size_usd + hedge_notional) * fee_rate
capital -= fee
open_trade = {
"entry_time": t,
"signal": signal,
"entry_x": entry_x,
"entry_y": entry_y,
"beta_at_entry": beta,
"size_x": size_x,
"size_y": size_y,
"fee_paid": fee,
}
elif open_trade is not None and signal == -open_trade["signal"]:
# Close position
# PnL: (Y exit - Y entry) * size_y * sign + (X entry - X exit) * size_x * beta * sign
exit_sign = open_trade["signal"]
pnl_y = (y_t - open_trade["entry_y"]) * open_trade["size_y"] * exit_sign
pnl_x = (open_trade["entry_x"] - x_t) * open_trade["size_x"] * abs(open_trade["beta_at_entry"]) * exit_sign
gross_pnl = pnl_y + pnl_x
exit_notional = abs(y_t * open_trade["size_y"]) + abs(x_t * open_trade["size_x"] * open_trade["beta_at_entry"])
fee = exit_notional * fee_rate
net_pnl = gross_pnl - fee
capital += net_pnl
trades.append({
"entry_time": open_trade["entry_time"],
"exit_time": t,
"signal": open_trade["signal"],
"entry_x": open_trade["entry_x"],
"exit_x": x_t,
"entry_y": open_trade["entry_y"],
"exit_y": y_t,
"beta": open_trade["beta_at_entry"],
"gross_pnl": round(gross_pnl, 4),
"net_pnl": round(net_pnl, 4),
"fee": round(open_trade["fee_paid"] + fee, 6),
"duration_bars": t - open_trade["entry_time"],
})
open_trade = None
# Track equity
unrealized = 0.0
if open_trade is not None:
exit_sign = open_trade["signal"]
ur_y = (y_t - open_trade["entry_y"]) * open_trade["size_y"] * exit_sign
ur_x = (open_trade["entry_x"] - x_t) * open_trade["size_x"] * abs(open_trade["beta_at_entry"]) * exit_sign
unrealized = ur_y + ur_x
peak_capital = max(peak_capital, capital + unrealized)
equity_curve.append({
"t": t,
"equity": round(capital + unrealized, 4),
"alpha": round(result["alpha"], 6),
"beta": round(result["beta"], 6),
"spread": round(result["spread"], 6),
"z_score": round(result["z_score"], 4),
})
# Force close open trade at end
if open_trade is not None:
exit_sign = open_trade["signal"]
y_t = float(Y[-1])
x_t = float(X[-1])
pnl_y = (y_t - open_trade["entry_y"]) * open_trade["size_y"] * exit_sign
pnl_x = (open_trade["entry_x"] - x_t) * open_trade["size_x"] * abs(open_trade["beta_at_entry"]) * exit_sign
gross_pnl = pnl_y + pnl_x
exit_notional = abs(y_t * open_trade["size_y"]) + abs(x_t * open_trade["size_x"] * open_trade["beta_at_entry"])
fee = exit_notional * fee_rate
capital += gross_pnl - fee
trades.append({
"entry_time": open_trade["entry_time"],
"exit_time": n - 1,
"signal": open_trade["signal"],
"entry_x": open_trade["entry_x"],
"exit_x": x_t,
"entry_y": open_trade["entry_y"],
"exit_y": y_t,
"beta": open_trade["beta_at_entry"],
"gross_pnl": round(gross_pnl, 4),
"net_pnl": round(gross_pnl - fee, 4),
"fee": round(open_trade["fee_paid"] + fee, 6),
"duration_bars": n - 1 - open_trade["entry_time"],
})
# ── Metrics ──
eq = np.array([e["equity"] for e in equity_curve])
returns = np.diff(eq) / eq[:-1] if len(eq) > 1 else np.array([0.0])
total_pnl = capital - initial_capital
pnl_pct = total_pnl / initial_capital * 100
dd = max_drawdown(eq.tolist())
sh = sharpe(returns.tolist())
so = sortino(returns.tolist())
wr = win_rate(trades)
cagr = ((capital / initial_capital) ** (1 / max(n / (365 * 24), 0.01)) - 1) * 100 if n > 0 and capital > 0 else 0.0
return {
"total_pnl": round(total_pnl, 4),
"pnl_pct": round(pnl_pct, 2),
"cagr": round(cagr, 2),
"sharpe": round(sh, 4),
"sortino": round(so, 4),
"max_drawdown": round(dd, 4),
"win_rate": round(wr, 4),
"total_trades": len(trades),
"final_equity": round(capital, 4),
"transaction_costs": round(sum(t["fee"] for t in trades), 4),
"avg_trade_duration": round(np.mean([t["duration_bars"] for t in trades]), 1) if trades else 0,
"trades": trades[-200:],
"equity_curve": equity_curve,
"alpha_history": [e["alpha"] for e in equity_curve],
"beta_history": [e["beta"] for e in equity_curve],
"spread_history": [e["spread"] for e in equity_curve],
"z_score_history": [e["z_score"] for e in equity_curve],
}
def backtest_rolling_ols(
X: np.ndarray,
Y: np.ndarray,
window: int = 60,
z_entry: float = 2.0,
z_exit: float = 0.5,
trade_size_usd: float = 100.0,
transaction_cost_bps: float = 2.5,
initial_capital: float = 10000.0,
) -> dict:
"""
Baseline: classic rolling OLS pairs trading.
Uses a fixed-lookback rolling beta instead of Kalman adaptation.
"""
n = len(X)
betas = compute_rolling_ols_hedge(X, Y, window)
fee_rate = transaction_cost_bps / 10000.0
capital = initial_capital
equity_curve: list[dict] = []
trades: list[dict] = []
open_trade: Optional[dict] = None
spreads: list[float] = []
z_lookback = 100
for t in range(window, n):
x_t = float(X[t])
y_t = float(Y[t])
beta = betas[t] if not np.isnan(betas[t]) else 1.0
spread = y_t - beta * x_t
spreads.append(spread)
# Z-score
lb = min(z_lookback, len(spreads))
rec = spreads[-lb:]
mu = np.mean(rec)
sigma = np.std(rec, ddof=1)
z = (spread - mu) / sigma if sigma > 1e-12 else 0.0
signal = 0
if open_trade is None:
if z > z_entry:
signal = -1 # short Y, long X
elif z < -z_entry:
signal = +1 # long Y, short X
else:
if abs(z) < z_exit:
signal = -open_trade["signal"]
if signal != 0:
if open_trade is None:
size_x = trade_size_usd / x_t if x_t > 0 else 0
size_y = trade_size_usd / y_t if y_t > 0 else 0
hedge_notional = size_x * x_t * abs(beta)
fee = (trade_size_usd + hedge_notional) * fee_rate
capital -= fee
open_trade = {
"entry_time": t, "signal": signal,
"entry_x": x_t, "entry_y": y_t,
"beta": beta, "size_x": size_x, "size_y": size_y,
"fee_paid": fee,
}
elif signal == -open_trade["signal"]:
es = open_trade["signal"]
pnl_y = (y_t - open_trade["entry_y"]) * open_trade["size_y"] * es
pnl_x = (open_trade["entry_x"] - x_t) * open_trade["size_x"] * abs(open_trade["beta"]) * es
gross_pnl = pnl_y + pnl_x
exit_notional = abs(y_t * open_trade["size_y"]) + abs(x_t * open_trade["size_x"] * open_trade["beta"])
fee = exit_notional * fee_rate
capital += gross_pnl - fee
trades.append({
"entry_time": open_trade["entry_time"], "exit_time": t,
"signal": open_trade["signal"], "gross_pnl": round(gross_pnl, 4),
"net_pnl": round(gross_pnl - fee, 4),
"duration_bars": t - open_trade["entry_time"],
})
open_trade = None
equity_curve.append({"t": t, "equity": round(capital, 4)})
eq = np.array([e["equity"] for e in equity_curve])
returns = np.diff(eq) / eq[:-1] if len(eq) > 1 else np.zeros(1)
total_pnl = capital - initial_capital
dd = max_drawdown(eq.tolist())
return {
"total_pnl": round(total_pnl, 4),
"pnl_pct": round(total_pnl / initial_capital * 100, 2),
"sharpe": round(sharpe(returns.tolist()), 4),
"sortino": round(sortino(returns.tolist()), 4),
"max_drawdown": round(dd, 4),
"win_rate": round(win_rate(trades), 4),
"total_trades": len(trades),
"final_equity": round(capital, 4),
"trades": trades[-200:],
"equity_curve": equity_curve,
}
def run_comparison(
X: np.ndarray,
Y: np.ndarray,
transition_covariance: float = 1e-4,
observation_covariance: float = 1e-2,
z_entry: float = 2.0,
z_exit: float = 0.5,
trade_size_usd: float = 100.0,
transaction_cost_bps: float = 2.5,
ols_windows: list[int] = [60, 120],
) -> dict:
"""
Run Kalman vs rolling OLS comparison backtest.
Returns:
dict with kalman_results, ols_results, and comparison_summary.
"""
trader = KalmanPairsTrader(
transition_covariance=transition_covariance,
observation_covariance=observation_covariance,
z_entry=z_entry, z_exit=z_exit,
)
kalman = backtest_kalman_pairs(
X, Y, trader,
trade_size_usd=trade_size_usd,
transaction_cost_bps=transaction_cost_bps,
)
ols_results = {}
for w in ols_windows:
ols_results[f"ols_{w}d"] = backtest_rolling_ols(
X, Y, window=w,
z_entry=z_entry, z_exit=z_exit,
trade_size_usd=trade_size_usd,
transaction_cost_bps=transaction_cost_bps,
)
return {
"kalman": kalman,
"ols": ols_results,
}