Add walk-forward validation engine with purged CV and combinatorial CPCV
Browse files- walk_forward_validation.py +432 -0
walk_forward_validation.py
ADDED
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|
| 1 |
+
"""Walk-Forward Validation Engine - The #1 Most Critical Missing Piece
|
| 2 |
+
|
| 3 |
+
Walk-forward validation is the ONLY correct way to test time series strategies.
|
| 4 |
+
Random train/test split = GUARANTEED data leakage and false results.
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| 5 |
+
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| 6 |
+
Based on: Ong & Herremans 2023 (MTL-TSMOM), Lopez de Prado 2018
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| 7 |
+
"""
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| 8 |
+
import numpy as np
|
| 9 |
+
import pandas as pd
|
| 10 |
+
from typing import Dict, List, Tuple, Optional, Callable, Iterator
|
| 11 |
+
from dataclasses import dataclass
|
| 12 |
+
import warnings
|
| 13 |
+
warnings.filterwarnings('ignore')
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| 14 |
+
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| 15 |
+
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| 16 |
+
@dataclass
|
| 17 |
+
class WalkForwardConfig:
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| 18 |
+
"""Configuration for walk-forward validation"""
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| 19 |
+
min_train_size: int = 252 # Minimum training days (1 year)
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| 20 |
+
test_size: int = 63 # Test window (3 months)
|
| 21 |
+
step_size: int = 21 # Step forward (1 month)
|
| 22 |
+
embargo_gap: int = 5 # Days between train and test (prevents leakage)
|
| 23 |
+
purge_k: int = 0 # Purge k overlapping observations
|
| 24 |
+
n_splits: Optional[int] = None # Number of splits (auto-calculated if None)
|
| 25 |
+
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| 26 |
+
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| 27 |
+
class PurgedKFoldCV:
|
| 28 |
+
"""
|
| 29 |
+
Purged K-Fold Cross-Validation for Time Series.
|
| 30 |
+
|
| 31 |
+
Based on Marcos Lopez de Prado (2018) "Advances in Financial Machine Learning".
|
| 32 |
+
|
| 33 |
+
Key idea: When you train up to date T and test starting at T+1,
|
| 34 |
+
observations NEAR T may still leak information because they're autocorrelated.
|
| 35 |
+
We "purge" (remove) observations within `purge_k` of the boundary.
|
| 36 |
+
|
| 37 |
+
This prevents the #1 error in quant backtesting: data leakage.
|
| 38 |
+
"""
|
| 39 |
+
|
| 40 |
+
def __init__(self, n_splits: int = 5, purge_k: int = 10):
|
| 41 |
+
self.n_splits = n_splits
|
| 42 |
+
self.purge_k = purge_k
|
| 43 |
+
|
| 44 |
+
def split(self, X: np.ndarray, y: Optional[np.ndarray] = None,
|
| 45 |
+
groups: Optional[np.ndarray] = None) -> Iterator[Tuple[np.ndarray, np.ndarray]]:
|
| 46 |
+
"""Generate train/test indices with purging"""
|
| 47 |
+
n_samples = len(X)
|
| 48 |
+
fold_size = n_samples // self.n_splits
|
| 49 |
+
|
| 50 |
+
for i in range(self.n_splits):
|
| 51 |
+
# Test indices
|
| 52 |
+
test_start = i * fold_size
|
| 53 |
+
test_end = min((i + 1) * fold_size, n_samples)
|
| 54 |
+
test_indices = np.arange(test_start, test_end)
|
| 55 |
+
|
| 56 |
+
# Train indices: everything before test, with purge gap
|
| 57 |
+
train_end = max(0, test_start - self.purge_k)
|
| 58 |
+
train_indices = np.arange(0, train_end)
|
| 59 |
+
|
| 60 |
+
# Also exclude overlapping test observations from previous folds
|
| 61 |
+
if i > 0:
|
| 62 |
+
# Add a gap after previous test set
|
| 63 |
+
prev_test_end = i * fold_size
|
| 64 |
+
train_indices = train_indices[train_indices < (prev_test_end - self.purge_k)]
|
| 65 |
+
|
| 66 |
+
yield train_indices, test_indices
|
| 67 |
+
|
| 68 |
+
|
| 69 |
+
class ExpandingWindowWalkForward:
|
| 70 |
+
"""
|
| 71 |
+
Expanding window walk-forward with embargo gap.
|
| 72 |
+
|
| 73 |
+
This is the standard for financial backtests:
|
| 74 |
+
- Train on [0, T]
|
| 75 |
+
- Embargo gap: [T+1, T+gap] (no overlap, no leakage)
|
| 76 |
+
- Test on [T+gap+1, T+gap+test_size]
|
| 77 |
+
- Next fold: Train on [0, T+step], test on [T+step+gap+1, T+step+gap+test_size]
|
| 78 |
+
|
| 79 |
+
The training set GROWS over time (expanding window), simulating how
|
| 80 |
+
you would actually trade: you start with less data, gain more over time.
|
| 81 |
+
"""
|
| 82 |
+
|
| 83 |
+
def __init__(self, config: Optional[WalkForwardConfig] = None):
|
| 84 |
+
self.config = config or WalkForwardConfig()
|
| 85 |
+
|
| 86 |
+
def split(self, X: np.ndarray, y: Optional[np.ndarray] = None,
|
| 87 |
+
groups: Optional[np.ndarray] = None) -> Iterator[Tuple[np.ndarray, np.ndarray]]:
|
| 88 |
+
"""Generate expanding window train/test splits"""
|
| 89 |
+
n_samples = len(X)
|
| 90 |
+
cfg = self.config
|
| 91 |
+
|
| 92 |
+
# Calculate number of splits
|
| 93 |
+
if cfg.n_splits is not None:
|
| 94 |
+
n_splits = cfg.n_splits
|
| 95 |
+
else:
|
| 96 |
+
# Calculate based on data size
|
| 97 |
+
available = n_samples - cfg.min_train_size - cfg.embargo_gap - cfg.test_size
|
| 98 |
+
n_splits = max(1, available // cfg.step_size)
|
| 99 |
+
|
| 100 |
+
for i in range(n_splits):
|
| 101 |
+
# Expanding train window
|
| 102 |
+
train_end = cfg.min_train_size + i * cfg.step_size
|
| 103 |
+
|
| 104 |
+
if train_end >= n_samples - cfg.embargo_gap - cfg.test_size:
|
| 105 |
+
break
|
| 106 |
+
|
| 107 |
+
train_indices = np.arange(0, train_end)
|
| 108 |
+
|
| 109 |
+
# Embargo gap (prevents leakage)
|
| 110 |
+
test_start = train_end + cfg.embargo_gap
|
| 111 |
+
test_end = min(test_start + cfg.test_size, n_samples)
|
| 112 |
+
test_indices = np.arange(test_start, test_end)
|
| 113 |
+
|
| 114 |
+
if len(test_indices) < 10:
|
| 115 |
+
break
|
| 116 |
+
|
| 117 |
+
yield train_indices, test_indices
|
| 118 |
+
|
| 119 |
+
def get_n_splits(self, X: np.ndarray, y=None, groups=None) -> int:
|
| 120 |
+
"""Get number of splits"""
|
| 121 |
+
count = 0
|
| 122 |
+
for _ in self.split(X):
|
| 123 |
+
count += 1
|
| 124 |
+
return count
|
| 125 |
+
|
| 126 |
+
|
| 127 |
+
class SlidingWindowWalkForward:
|
| 128 |
+
"""
|
| 129 |
+
Sliding window walk-forward (fixed-size training window).
|
| 130 |
+
|
| 131 |
+
Unlike expanding window, the training set size stays constant.
|
| 132 |
+
Old data drops off as new data comes in.
|
| 133 |
+
|
| 134 |
+
Better for: Regime-changing markets where old data becomes irrelevant.
|
| 135 |
+
Worse for: Early periods with limited data.
|
| 136 |
+
"""
|
| 137 |
+
|
| 138 |
+
def __init__(self, train_size: int = 504, test_size: int = 63,
|
| 139 |
+
step_size: int = 21, embargo_gap: int = 5):
|
| 140 |
+
self.train_size = train_size
|
| 141 |
+
self.test_size = test_size
|
| 142 |
+
self.step_size = step_size
|
| 143 |
+
self.embargo_gap = embargo_gap
|
| 144 |
+
|
| 145 |
+
def split(self, X: np.ndarray, y: Optional[np.ndarray] = None,
|
| 146 |
+
groups: Optional[np.ndarray] = None) -> Iterator[Tuple[np.ndarray, np.ndarray]]:
|
| 147 |
+
"""Generate sliding window train/test splits"""
|
| 148 |
+
n_samples = len(X)
|
| 149 |
+
|
| 150 |
+
start = self.train_size
|
| 151 |
+
while start + self.embargo_gap + self.test_size <= n_samples:
|
| 152 |
+
train_start = start - self.train_size
|
| 153 |
+
train_end = start
|
| 154 |
+
train_indices = np.arange(train_start, train_end)
|
| 155 |
+
|
| 156 |
+
test_start = train_end + self.embargo_gap
|
| 157 |
+
test_end = test_start + self.test_size
|
| 158 |
+
test_indices = np.arange(test_start, test_end)
|
| 159 |
+
|
| 160 |
+
yield train_indices, test_indices
|
| 161 |
+
start += self.step_size
|
| 162 |
+
|
| 163 |
+
|
| 164 |
+
class CombinatorialPurgedCV:
|
| 165 |
+
"""
|
| 166 |
+
Combinatorial Purged Cross-Validation (CPCV).
|
| 167 |
+
|
| 168 |
+
THE GOLD STANDARD for financial ML backtesting.
|
| 169 |
+
|
| 170 |
+
Based on Lopez de Prado (2019): Instead of sequential splits, we create
|
| 171 |
+
all possible combinations of train/test splits with embargo gaps.
|
| 172 |
+
This gives N choose K test sets, providing much more robust statistics.
|
| 173 |
+
|
| 174 |
+
Why this matters:
|
| 175 |
+
- Standard walk-forward: You test on 5 periods. Maybe 4 are bull, 1 is bear.
|
| 176 |
+
Your model looks great but fails in bear markets.
|
| 177 |
+
- CPCV: You test on ALL combinations. Some train sets include bear, some don't.
|
| 178 |
+
You get a distribution of performance, not a single number.
|
| 179 |
+
|
| 180 |
+
This is the difference between "my strategy returned 20%" and
|
| 181 |
+
"my strategy has a 95% chance of returning 10-30% with max drawdown < 15%."
|
| 182 |
+
"""
|
| 183 |
+
|
| 184 |
+
def __init__(self, n_splits: int = 6, n_test_splits: int = 2,
|
| 185 |
+
embargo_pct: float = 0.04):
|
| 186 |
+
"""
|
| 187 |
+
Args:
|
| 188 |
+
n_splits: Total number of groups to divide data into
|
| 189 |
+
n_test_splits: How many groups form the test set
|
| 190 |
+
embargo_pct: Percentage of data to embargo between train and test
|
| 191 |
+
"""
|
| 192 |
+
self.n_splits = n_splits
|
| 193 |
+
self.n_test_splits = n_test_splits
|
| 194 |
+
self.embargo_pct = embargo_pct
|
| 195 |
+
|
| 196 |
+
from itertools import combinations
|
| 197 |
+
self.test_combinations = list(combinations(range(n_splits), n_test_splits))
|
| 198 |
+
|
| 199 |
+
def split(self, X: np.ndarray, y: Optional[np.ndarray] = None,
|
| 200 |
+
groups: Optional[np.ndarray] = None) -> Iterator[Tuple[np.ndarray, np.ndarray]]:
|
| 201 |
+
"""Generate combinatorial purged train/test splits"""
|
| 202 |
+
n_samples = len(X)
|
| 203 |
+
fold_size = n_samples // self.n_splits
|
| 204 |
+
embargo_size = int(fold_size * self.embargo_pct)
|
| 205 |
+
|
| 206 |
+
for test_groups in self.test_combinations:
|
| 207 |
+
# Test indices: union of selected test groups
|
| 208 |
+
test_indices = []
|
| 209 |
+
for g in test_groups:
|
| 210 |
+
start = g * fold_size
|
| 211 |
+
end = min((g + 1) * fold_size, n_samples)
|
| 212 |
+
test_indices.extend(range(start, end))
|
| 213 |
+
test_indices = np.array(test_indices)
|
| 214 |
+
|
| 215 |
+
# Train indices: everything NOT in test, with embargo gaps
|
| 216 |
+
train_indices = []
|
| 217 |
+
for g in range(self.n_splits):
|
| 218 |
+
if g in test_groups:
|
| 219 |
+
continue
|
| 220 |
+
|
| 221 |
+
start = g * fold_size
|
| 222 |
+
end = min((g + 1) * fold_size, n_samples)
|
| 223 |
+
|
| 224 |
+
# Add embargo gap if adjacent to test group
|
| 225 |
+
for tg in test_groups:
|
| 226 |
+
if abs(g - tg) == 1: # Adjacent
|
| 227 |
+
if g < tg:
|
| 228 |
+
end = max(start, end - embargo_size)
|
| 229 |
+
else:
|
| 230 |
+
start = min(start + embargo_size, end)
|
| 231 |
+
|
| 232 |
+
if start < end:
|
| 233 |
+
train_indices.extend(range(start, end))
|
| 234 |
+
|
| 235 |
+
train_indices = np.array(train_indices)
|
| 236 |
+
|
| 237 |
+
if len(train_indices) > 0 and len(test_indices) > 0:
|
| 238 |
+
yield train_indices, test_indices
|
| 239 |
+
|
| 240 |
+
def get_n_splits(self, X=None, y=None, groups=None) -> int:
|
| 241 |
+
return len(self.test_combinations)
|
| 242 |
+
|
| 243 |
+
|
| 244 |
+
class WalkForwardBacktest:
|
| 245 |
+
"""
|
| 246 |
+
Complete walk-forward backtest engine.
|
| 247 |
+
|
| 248 |
+
This runs your ENTIRE pipeline (data → features → model → portfolio → execution)
|
| 249 |
+
through walk-forward validation, giving you the ONLY honest backtest result.
|
| 250 |
+
|
| 251 |
+
Usage:
|
| 252 |
+
backtest = WalkForwardBacktest(config=WalkForwardConfig(min_train_size=504))
|
| 253 |
+
results = backtest.run(
|
| 254 |
+
data_pipeline=data_pipeline,
|
| 255 |
+
alpha_model_factory=alpha_factory,
|
| 256 |
+
portfolio_optimizer=optimizer,
|
| 257 |
+
backtest_engine=backtest_engine
|
| 258 |
+
)
|
| 259 |
+
|
| 260 |
+
Returns: Honest Sharpe, drawdown, IC distributions — not fake overfit numbers.
|
| 261 |
+
"""
|
| 262 |
+
|
| 263 |
+
def __init__(self, config: Optional[WalkForwardConfig] = None,
|
| 264 |
+
cv_type: str = 'expanding'):
|
| 265 |
+
self.config = config or WalkForwardConfig()
|
| 266 |
+
self.cv_type = cv_type
|
| 267 |
+
|
| 268 |
+
if cv_type == 'expanding':
|
| 269 |
+
self.cv = ExpandingWindowWalkForward(config)
|
| 270 |
+
elif cv_type == 'sliding':
|
| 271 |
+
self.cv = SlidingWindowWalkForward(
|
| 272 |
+
config.min_train_size, config.test_size,
|
| 273 |
+
config.step_size, config.embargo_gap
|
| 274 |
+
)
|
| 275 |
+
elif cv_type == 'purged':
|
| 276 |
+
self.cv = PurgedKFoldCV(n_splits=5, purge_k=config.embargo_gap)
|
| 277 |
+
elif cv_type == 'combinatorial':
|
| 278 |
+
self.cv = CombinatorialPurgedCV(n_splits=6, n_test_splits=2)
|
| 279 |
+
else:
|
| 280 |
+
raise ValueError(f"Unknown cv_type: {cv_type}")
|
| 281 |
+
|
| 282 |
+
def run(self, X: np.ndarray, y: np.ndarray,
|
| 283 |
+
model_factory: Callable,
|
| 284 |
+
eval_fn: Callable[[np.ndarray, np.ndarray], Dict]) -> Dict:
|
| 285 |
+
"""
|
| 286 |
+
Run walk-forward validation.
|
| 287 |
+
|
| 288 |
+
Args:
|
| 289 |
+
X: Features array
|
| 290 |
+
y: Target array
|
| 291 |
+
model_factory: Callable that returns a NEW model instance
|
| 292 |
+
eval_fn: Callable(pred, actual) -> dict of metrics
|
| 293 |
+
|
| 294 |
+
Returns:
|
| 295 |
+
Dict with fold-by-fold results and aggregate statistics
|
| 296 |
+
"""
|
| 297 |
+
fold_results = []
|
| 298 |
+
|
| 299 |
+
print(f"Running {self.cv_type} walk-forward validation...")
|
| 300 |
+
print(f"Config: train_min={self.config.min_train_size}, "
|
| 301 |
+
f"test={self.config.test_size}, step={self.config.step_size}, "
|
| 302 |
+
f"embargo={self.config.embargo_gap}")
|
| 303 |
+
|
| 304 |
+
for fold, (train_idx, test_idx) in enumerate(self.cv.split(X, y)):
|
| 305 |
+
print(f"\nFold {fold + 1}/{self.cv.get_n_splits(X)}")
|
| 306 |
+
print(f" Train: {len(train_idx)} samples ({train_idx[0]} to {train_idx[-1]})")
|
| 307 |
+
print(f" Test: {len(test_idx)} samples ({test_idx[0]} to {test_idx[-1]})")
|
| 308 |
+
|
| 309 |
+
# Split data
|
| 310 |
+
X_train, X_test = X[train_idx], X[test_idx]
|
| 311 |
+
y_train, y_test = y[train_idx], y[test_idx]
|
| 312 |
+
|
| 313 |
+
# Train fresh model (NO LOOKAHEAD!)
|
| 314 |
+
model = model_factory()
|
| 315 |
+
model.fit(X_train, y_train)
|
| 316 |
+
|
| 317 |
+
# Predict
|
| 318 |
+
y_pred = model.predict(X_test)
|
| 319 |
+
|
| 320 |
+
# Evaluate
|
| 321 |
+
metrics = eval_fn(y_pred, y_test)
|
| 322 |
+
metrics['fold'] = fold
|
| 323 |
+
metrics['train_size'] = len(train_idx)
|
| 324 |
+
metrics['test_size'] = len(test_idx)
|
| 325 |
+
metrics['train_start'] = int(train_idx[0])
|
| 326 |
+
metrics['train_end'] = int(train_idx[-1])
|
| 327 |
+
metrics['test_start'] = int(test_idx[0])
|
| 328 |
+
metrics['test_end'] = int(test_idx[-1])
|
| 329 |
+
|
| 330 |
+
print(f" Metrics: {metrics}")
|
| 331 |
+
fold_results.append(metrics)
|
| 332 |
+
|
| 333 |
+
# Aggregate statistics
|
| 334 |
+
aggregate = self._aggregate_results(fold_results)
|
| 335 |
+
|
| 336 |
+
return {
|
| 337 |
+
'fold_results': fold_results,
|
| 338 |
+
'aggregate': aggregate,
|
| 339 |
+
'cv_type': self.cv_type,
|
| 340 |
+
'config': self.config
|
| 341 |
+
}
|
| 342 |
+
|
| 343 |
+
def _aggregate_results(self, fold_results: List[Dict]) -> Dict:
|
| 344 |
+
"""Compute aggregate statistics across folds"""
|
| 345 |
+
if not fold_results:
|
| 346 |
+
return {}
|
| 347 |
+
|
| 348 |
+
# Collect numeric metrics
|
| 349 |
+
numeric_keys = []
|
| 350 |
+
for key in fold_results[0].keys():
|
| 351 |
+
if key not in ['fold', 'train_start', 'train_end', 'test_start', 'test_end',
|
| 352 |
+
'train_size', 'test_size']:
|
| 353 |
+
if isinstance(fold_results[0][key], (int, float, np.number)):
|
| 354 |
+
numeric_keys.append(key)
|
| 355 |
+
|
| 356 |
+
aggregate = {}
|
| 357 |
+
for key in numeric_keys:
|
| 358 |
+
values = [r[key] for r in fold_results if key in r and r[key] is not None]
|
| 359 |
+
if not values:
|
| 360 |
+
continue
|
| 361 |
+
|
| 362 |
+
values = np.array(values)
|
| 363 |
+
aggregate[key] = {
|
| 364 |
+
'mean': float(np.mean(values)),
|
| 365 |
+
'std': float(np.std(values)),
|
| 366 |
+
'min': float(np.min(values)),
|
| 367 |
+
'max': float(np.max(values)),
|
| 368 |
+
'median': float(np.median(values)),
|
| 369 |
+
'pct_5th': float(np.percentile(values, 5)),
|
| 370 |
+
'pct_95th': float(np.percentile(values, 95))
|
| 371 |
+
}
|
| 372 |
+
|
| 373 |
+
return aggregate
|
| 374 |
+
|
| 375 |
+
|
| 376 |
+
def honest_backtest_example():
|
| 377 |
+
"""Example of how walk-forward prevents false results"""
|
| 378 |
+
from sklearn.linear_model import Ridge
|
| 379 |
+
from scipy.stats import spearmanr
|
| 380 |
+
|
| 381 |
+
# Generate fake time series with autocorrelation (like real markets)
|
| 382 |
+
np.random.seed(42)
|
| 383 |
+
n = 2000
|
| 384 |
+
y = np.zeros(n)
|
| 385 |
+
y[0] = np.random.randn()
|
| 386 |
+
for i in range(1, n):
|
| 387 |
+
y[i] = 0.7 * y[i-1] + np.random.randn() * 0.5 # AR(1) process
|
| 388 |
+
|
| 389 |
+
# Features: lagged y + noise (realistic)
|
| 390 |
+
X = np.zeros((n, 5))
|
| 391 |
+
for lag in range(5):
|
| 392 |
+
X[lag+1:, lag] = y[:-lag-1] if lag > 0 else y[:-1]
|
| 393 |
+
X[0, :] = 0 # First row has no history
|
| 394 |
+
|
| 395 |
+
# Random train/test split (WRONG for time series!)
|
| 396 |
+
from sklearn.model_selection import train_test_split
|
| 397 |
+
X_train_bad, X_test_bad, y_train_bad, y_test_bad = train_test_split(
|
| 398 |
+
X[5:], y[5:], test_size=0.3, random_state=42
|
| 399 |
+
)
|
| 400 |
+
|
| 401 |
+
model_bad = Ridge().fit(X_train_bad, y_train_bad)
|
| 402 |
+
pred_bad = model_bad.predict(X_test_bad)
|
| 403 |
+
ic_bad, _ = spearmanr(pred_bad, y_test_bad)
|
| 404 |
+
|
| 405 |
+
# Walk-forward split (CORRECT!)
|
| 406 |
+
wf = ExpandingWindowWalkForward(
|
| 407 |
+
WalkForwardConfig(min_train_size=500, test_size=200, step_size=200, embargo_gap=10)
|
| 408 |
+
)
|
| 409 |
+
ics_wf = []
|
| 410 |
+
for train_idx, test_idx in wf.split(X[5:], y[5:]):
|
| 411 |
+
X_train_wf, X_test_wf = X[5:][train_idx], X[5:][test_idx]
|
| 412 |
+
y_train_wf, y_test_wf = y[5:][train_idx], y[5:][test_idx]
|
| 413 |
+
|
| 414 |
+
model_wf = Ridge().fit(X_train_wf, y_train_wf)
|
| 415 |
+
pred_wf = model_wf.predict(X_test_wf)
|
| 416 |
+
ic_wf, _ = spearmanr(pred_wf, y_test_wf)
|
| 417 |
+
ics_wf.append(ic_wf)
|
| 418 |
+
|
| 419 |
+
print("=" * 60)
|
| 420 |
+
print("THE WALK-FORWARD TRUTH BOMB")
|
| 421 |
+
print("=" * 60)
|
| 422 |
+
print(f"Random split IC: {ic_bad:.4f} ← This is a LIE")
|
| 423 |
+
print(f"Walk-forward IC: {np.mean(ics_wf):.4f} ± {np.std(ics_wf):.4f}")
|
| 424 |
+
print(f"Walk-forward range: [{np.min(ics_wf):.4f}, {np.max(ics_wf):.4f}]")
|
| 425 |
+
print()
|
| 426 |
+
print("Random split looks great because future data leaked into training!")
|
| 427 |
+
print("Walk-forward is honest because it only trains on PAST data.")
|
| 428 |
+
print(f"Difference: {abs(ic_bad - np.mean(ics_wf)):.4f} — this is your FALSE HOPE.")
|
| 429 |
+
|
| 430 |
+
|
| 431 |
+
if __name__ == '__main__':
|
| 432 |
+
honest_backtest_example()
|