Feature Selection & Causal Analysis Framework for Financial Time Series

Overview

This project documents my learning journey into causal inference applied to one year of high-frequency financial time series data (Ethereum dataset used as a case example). I investigate how different selection methods handle feature redundancy, mediator preservation, and the challenges of spurious relationships in financial time series, to understand their practical limitations and applications.

Learning Objectives

I empirically test the fundamental claims of causal discovery through:

• Algorithmic validation (PC Algorithm vs. manual DAG construction)
• Statistical verification (Granger causality testing)
• Cross-validation (sentiment indicators, cross-asset relationships)

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Core Research Question

• When and how much does causal discovery provide actionable advantages over correlation-based feature selection in quantitative finance?
  Validation Gap: How often do algorithmically discovered causal relationships survive statistical testing?

Deliverable: A research repository for evidence-based causal discovery deployment with clear decision criteria for method selection.

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Market Context: Asset Returns Profile

Distribution Characteristics

• Near-zero mean return (-0.01%) with negative median (-0.05%) indicates slight bearish bias in the sample period
• High volatility (3.90% daily ≈ 74% annualized) creates rich signal environment
• Negative Sharpe ratio (-0.05 annualized) reflects challenging risk-adjusted performance

1. Histogram with Quantiles: 5%, 25%, 50%, 75%, 95% thresholds
2. Q-Q Plot: Tests normality assumptions for model selection
3. Box Plot: Summarizes outliers and distribution shape
4. Rolling Volatility: Captures volatility clustering patterns

Risk Structure

• Positive skewness (0.66) shows asymmetric tail risk → more frequent large positive moves than negative ones
• High kurtosis (4.38) indicates fat tails → extreme events occur more frequently than normal distribution would predict
• Wide interquartile range (Q1: -2.12%, Q3: 1.68%) demonstrates significant daily variation

Tail Risk Profile

• VaR 95%: -5.95% → expect daily losses exceeding 6% roughly once per month (1.5 days/month)
• VaR 99%: -9.32% → extreme tail events with losses above 9% occur approximately quarterly

Implications for Analysis Design

For Correlation Analysis:

• High volatility regime detection will be critical → features capturing volatility clustering essential
• Skewed returns indicate non-linear relationships between features → correlation may miss asymmetric dependencies
• Fat tails suggest that extreme event indicators (tail risk signals, drawdown metrics) should correlate strongly with volatility

For Causal Discovery:

• Volatility persistence (high daily volatility) suggests strong causal chains: volatility_t → volatility_t+1 → return_magnitude
• Positive skew with fat tails implies asymmetric causal patterns: upside momentum vs. downside crashes may follow different causal pathways
• VaR breaches should serve as leading indicators in the causal graph - nodes representing risk regime shifts
• Kurtosis signals suggest that extreme event detectors will be important upstream nodes influencing multiple downstream features

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Feature Taxonomy (Prioritized by Distribution Insights)

Domain	Features	Relevance to Asset Profile
Volatility	volatility_7d, vol_momentum, vol_expansion	High Priority: 74% annualized volatility
Risk	drawdown, tail_risk_signal, var_breach_95	Critical: VaR 95% = -5.95%, high kurtosis
Extremes	extreme_down, extreme_streak, reversal_setup	Essential: Positive skew, asymmetric patterns
Technical	rsi, bb_width, atr_normalized	Moderate: Support volatility clustering detection
Volume	volume_change, volume_zscore, volume_spike	Moderate: Complement to volatility signals

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Correlation Analysis

Intelligent Feature Reduction:

• Pros: Simple, fast, reduces multicollinearity
• Cons: Ignores causal structure, risks discarding valuable mediators, may miss asymmetric relationships
• Method: Remove features with high pairwise correlation (e.g., >0.8)
• Heatmap construction for full feature sets
• Identification of highly correlated pairs
• Return-correlation based removal: Names the less predictive feature from each correlated pair
• Limitation: Linear correlation may miss regime-dependent relationships critical in high-volatility environments

Key Empirical Findings:

High Correlation Clusters (>0.8):

• Price level cluster: VWAP, lagged OHLC, and Bollinger Bands show extreme correlation (0.94-0.99) - classic multicollinearity
• Risk indicator cluster: var_breach_95 and var_breach_99 (corr=0.98), redundant tail risk signals
• Technical indicator overlap: RSI correlates strongly with VWAP distance (0.93) and BB position (0.89)

Return Correlation Leaders:

• Extreme movement indicators dominate: extreme_up (0.54), extreme_down (0.43)
• Risk metrics show moderate correlation: drawdown (0.31), deep_drawdown (0.18)
• Price level features exhibit low return correlation despite high inter-correlation

Critical Observation for Causal Analysis: 33 features flagged for potential removal due to high inter-correlation but low return correlation. These are prime candidates for mediator preservation in causal discovery, as correlation-based removal might eliminate important signal propagation pathways.

Causal Discovery for Signal Architecture

Pros: Uncovers directional dependencies, preserves signal hierarchies, captures asymmetric patterns

• Cons: Computationally demanding, manual dag requires strong assumptions
• Method: Uses manual discovery as well as causal discovery algorithms (PC Algorithm, FCI)

Objectives:

• Identify leading indicators vs. lagging confirmations (critical for regime changes in markets, risk systems, or network behavior)
• Understand propagation chains (e.g., extreme_events → volatility_spike → behavioral_shifts)
• Avoid data leakage by excluding the target from the DAG
• Build interpretable signal hierarchies that account for asymmetric market behavior

Enhanced Focus Areas:

• Volatility clustering patterns: How do high-volatility periods self-perpetuate?
• Regime transition signals: What triggers moves from low to high volatility states?
• Asymmetric response patterns: Different causal pathways for positive vs. negative extreme moves
• Tail risk propagation: How do VaR breaches influence other risk indicators?

Warning: Using the target in the DAG creates look-ahead bias.

Solutions:

• Option A: Remove return entirely from causal graph
• Option B: Use lagged returns (return_t-1 → return_t) with proper temporal separation

Note: Causal graphs serve as heuristics for signal architecture informed by empirical return characteristics, not definitive causal truth.

Manual DAG Validation:

1. Exclude target variable from algo DAG (prevents data leakage)
2. Apply domain knowledge supplemented by empirical distribution insights
3. Focus on asymmetric patterns given positive skew in returns

Volatility Persistence Chain: close → volatility_7d → vol_regime → vol_regime_change aligns with observed 74% annualized volatility clustering

VaR Breach Escalation: return → var_breach_95/99 → vol_regime_change → market_stress explains the monthly/quarterly tail event patterns (VaR 95% = -5.95%)

Asymmetric Momentum: return → upside_momentum → volume_spike captures the positive skew (0.66) mechanism

Risk Propagation: drawdown → deep_drawdown → tail_risk_signal → vol_expansion models the fat tail cascade (kurtosis = 4.38)

Manual DAG Preservation Evidence: The constructed causal graph includes several correlation-flagged features as critical mediators:

• var_breach_95 → vol_regime_change (monthly tail events trigger regime shifts)
• var_breach_99 → market_stress (quarterly extreme events create stress)
• bb_position → extreme_reversal_setup (technical extremes signal reversals)
• rsi → rsi_oversold_extreme → extreme_reversal_setup (oversold conditions cascade)

The Stakes: Removing these 33 features based on correlation alone would eliminate the very pathways that explain how market stress propagates through the system.

PC Algorithm Discovery:

The algorithmic approach (37 indicators, 66 relationships) reveals additional insights:

Leading Indicators: vol_momentum (6 outgoing connections), vwap_distance (4 connections) emerge as top causal drivers - validating volatility clustering importance

Risk Aggregators: drawdown (5 incoming connections), volume_zscore (4 incoming) serve as key risk consolidation nodes

Lag Feature Over-influence: OHLC lag features show 3+ connections each, confirming correlation analysis concerns about redundancy

Volume-Volatility Hub: volume_zscore (6 total connections) emerges as central mediator between volume dynamics and volatility regime shifts

Feature Validation (Manual vs. PC Algorithm Comparison)

Theory vs. Data Validation:

1. Structural convergence: Both approaches identify volatility clustering and risk propagation as central themes
2. Leading indicator validation: PC Algorithm confirms vol_momentum and volatility features as primary drivers
3. Lag feature redundancy: Algorithmic analysis validates correlation concerns (OHLC lag features over-connected)
4. Hub discovery: volume_zscore emerges as key volume-volatility mediator (6 connections)
5. Risk consolidation validation: drawdown confirmed as primary risk aggregation node (5 incoming edges)

Critical discovery reveals only 6 relationships confirmed by both manual and algorithmic approaches out of 41 manual relationships:

• extreme_down/up → extreme_streak (extreme event clustering)
• volume_zscore → volume_spike (volume anomaly detection)
• volatility_7d → vol_regime (regime classification)
• vol_expansion → vol_persistence (volatility clustering)

Strategic Implications:

• 85% of manual relationships not data-supported suggests over-theorizing
• Confirmed relationships focus on clustering patterns (extreme events, volume anomalies, volatility persistence) - aligning with fat-tail characteristics
• Data reveals 56 additional relationships particularly around lag features and technical indicator interactions missed by domain knowledge

Key Convergence: The small overlap emphasizes the value of algorithmic discovery for revealing data-driven causal structures beyond expert intuition, especially critical in high-volatility markets where traditional relationships may not hold.

Hybrid Optimization (Empirically-Informed Feature Selection)

1. Preserve algorithmic hubs like vol_momentum (6 connections) and volume_zscore (6 connections) as core features
2. Apply selective lag pruning - reduce OHLC lag redundancy from 5 to 1-2 most predictive features based on PC Algorithm over-connectivity warning
3. Maintain risk consolidation pathways - preserve drawdown → risk cascade despite correlation flagging
4. Balance computational efficiency with causal completeness using algorithmic connection counts as feature importance weights

Granger Causality Validation

To validate the causal relationships discovered by the PC Algorithm, we applied Granger causality tests to identify features with genuine predictive power for future returns.

Results:

• Only 3 features showed significant Granger causality (p < 0.05) toward returns:
  • bb_lower (p=0.041) - Bollinger Band lower bound
  • open_lag1 (p=0.048) - Lagged opening price
  • low_lag1 (p=0.049) - Lagged low price

Critical Finding: Of ~40 features identified by PC Algorithm, 3 were validated with Granger causality tests. All 3 tested features showed significant predictive power (bb_lower, open_lag1, low_lag1), but 92.5% of algorithmic discoveries remain statistically unvalidated.

Implications:

• PC Algorithm limitations: The 66 relationships discovered algorithmically lack statistical predictive power
• Lag feature validation: 2 of 3 significant features are lag prices, supporting the "price leads price" hypothesis
• Technical indicator sparsity: Only 1 technical indicator (bb_lower) shows genuine causal predictive power

External Sentiment Validation Granger

To assess whether market sentiment metrics provide genuine causal signals beyond technical indicators, we tested the Fear & Greed Index against ETH returns using Granger causality analysis.

Methodology:

• Downloaded Fear & Greed Index data via Alternative.me API
• Applied first differencing and standardization to both series
• Tested causality across lag structures (1-5 days)

Fear & Greed → Asset Returns Results:

Lag Structure	F-Statistic	P-Value	Statistical Significance
1 day	2.124	0.146	Not significant
2 days	0.956	0.386	Not significant
3 days	1.213	0.305	Not significant
4 days	0.732	0.571	Not significant
5 days	1.330	0.251	Not significant

Key Findings:

• No significant Granger causality detected across any lag structure (all p-values > 0.05)
• 1-day lag shows strongest signal (p=0.146) but remains statistically insignificant
• Longer lags weaken predictive power with 4-day lag showing lowest F-statistic (0.732)

Cross-Asset Causal Validation (Inter-Market Relationships)

To examine whether major asset pairs exhibit predictive relationships that could enhance portfolio construction and risk management, we conducted comprehensive Granger causality analysis between BTC and ETH across multiple data dimensions.

Methodology:

• Downloaded 1-year daily BTC data from Binance API (320 observations)
• Analyzed prices, returns, log-returns, and 7-day rolling volatility
• Bidirectional Granger causality testing across 1-5 day lags
• Extreme event synchronization analysis (90th percentile threshold)

Correlation Structure Analysis:

Metric	Correlation	Interpretation
Price Levels	0.310	Moderate long-term relationship
Daily Returns	0.791	Strong same-day synchronization
Log Returns	0.796	Robust relationship confirmation
7-Day Volatility	0.722	High risk regime alignment

Cross-Asset Granger Causality Results:

BTC → ETH Causality (All Directions):

• Prices: No significant causality (p-values: 0.699-0.897)
• Returns: No significant causality (p-values: 0.429-0.645)
• Volatility: No significant causality (p-values: 0.115-0.981)

ETH → BTC Causality:

• Prices: No significant causality (p-values: 0.344-0.856)
• Returns: Significant 1-day causality (p=0.0393), no longer lags
• Volatility: No significant causality (p-values: 0.764-0.955)

Extreme Event Synchronization:

• ETH extreme days: 32 (10% threshold)
• BTC extreme days: 32 (identical frequency)
• Synchronized extreme events: 21 days
• Synchronization rate: 65.6% - high crisis contagion

Critical Findings:

The Correlation-Causality Paradox: Despite 79% daily return correlation, only one significant causal relationship exists: ETH returns predict next-day BTC returns (1-day lag). This exemplifies the fundamental distinction between correlation and causality in financial markets.

Market Leadership Dynamics:

• ETH leads BTC in return prediction - a rare finding since BTC typically leads altcoins
• No reverse causality from BTC to ETH across any timeframe
• Volatility spillovers absent despite 72% volatility correlation

Risk Management Implications:

• Limited diversification during crises: 66% probability both assets experience extreme movements simultaneously
• Contemporaneous risk dominates: Most correlation occurs same-day, not sequentially
• Cross-asset prediction minimal: Even major crypto pairs show limited predictive relationships

Strategic Insights:

• ETH momentum strategies may generate next-day BTC return signals
• Portfolio risk models must account for high extreme event synchronization
• Market efficiency validated even for highly correlated crypto asset pairs
• Technical analysis remains superior to cross-asset prediction for individual asset strategies

Integration with Previous Findings: This analysis reinforces our core thesis: rigorous statistical testing reveals that genuine predictive relationships are rare, even among highly correlated assets. The ETH → BTC causality joins the exclusive list of validated predictive features (bb_lower, open_lag1, low_lag1), while the 79% correlation with minimal causality perfectly demonstrates why correlation-based feature selection can be misleading.

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Key Learnings: When Causal Discovery Adds Value

Through this learning project, I discovered that causal discovery has narrow but specific utility:

Confirmed Practical Applications:

1. Network Hub Identification

• PC Algorithm successfully identified central features (vol_momentum, volume_zscore with 6+ connections)

• Validated benefit: Prioritizes features with maximum structural influence

• Business value: Focus computational resources on highest-impact variables

2. Redundancy Detection Enhancement

• Over-connectivity analysis flagged OHLC lag feature redundancy (3+ connections each)
• Validated benefit: Confirms correlation analysis with structural reasoning
• Business value: More confident feature elimination decisions

3. Risk Consolidation Mapping

• Identified drawdown as primary risk aggregation node (5 incoming connections)
• Validated benefit: Reveals which features serve as risk concentration points
• Business value: Better risk monitoring and stress testing design

Use Causal Discovery For:

• Feature prioritization (identify hubs for computational focus)
• Redundancy validation (confirm correlation-based elimination)
• Risk architecture (map stress propagation pathways)
• Leakage Discovery in your Features

Bottom Line: Causal discovery serves as a feature engineering enhancement tool. It's not a replacement for correlation analysis but a complementary method for structural insight in complex feature spaces.

Relevance to Risk Analysis and Structural Behavior

Causal discovery can help identify risk propagation chains such as:

• Transaction clustering patterns
• Cross-system dependency effects
• Flow dynamics in complex networks

Example causal chain:

abnormal_network_activity → access_latency → system_overload → security_alert 
claim_cluster → loss_ratio_spike → reserve_adjustment → underwriting_response
sudden_token_inflow → liquidity_stress → price_dislocation → user_exit_behavior

This makes it relevant for:

• Anomaly detection (e.g., identifying unusual market structure changes)
• Risk attribution (e.g., tracing volatility spikes back to on-chain triggers)
• Protocol monitoring (e.g., structural shifts in user behavior patterns)

Usage

bashgit clone [repository]
pip install -r requirements.txt
jupyter notebook inference_and_causality.ipynb