Problem Statement

Given a dataset with:

• Multiple symbols (stocks/assets)
• Features f0 to f25 (most constant intraday, varying by date)
• Target variable y (intraday-varying, representing returns)
• Time dimensions: date_id and time_id

Objective: Predict future values of y with maximum accuracy and directional correctness.

Key Insights

1. Target Variable Nature: y exhibits near-random-walk characteristics with values concentrated in [-0.5, 0.5]
2. Price Reconstruction: Synthetic price can be constructed as P_t = P_{t-1}(1 + y_t) with base price P_0 = 100
3. Feature Correlation: Feature f25 shows strong correlation (ρ ≈ 0.8) with constructed price series
4. Direct Regression Limitations: Simple regression models overfit severely (train RMSE: 0.0022, test RMSE: 0.00917)

Approaches

Approach 1: LSTM-Based Time Series Modeling

File: lstm_train_test.py

A deep learning approach using Long Short-Term Memory networks to capture temporal dependencies.

Architecture

• Multi-layer LSTM (4 layers, 64 hidden units)
• Dropout: 0.2
• Sequence length: 45
• Output: Price predictions (returns derived post-hoc)

Key Features

• Incremental Learning: Models are trained sequentially across symbols
• Parallel Data Loading: Utilizes multiprocessing for efficient data processing
• Lagged Features: 5 time-lagged versions of time-varying features

Performance

• Validation RMSE (Price): ~1.41
• Validation RMSE (Returns): ~0.00192
• Directional Accuracy: ~57%

Usage

python lstm_train_test.py

Requirements:

• PyTorch
• NumPy, Pandas
• scikit-learn
• tqdm, joblib

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Approach 2: Kalman Filter + Gradient Boosting (Hybrid Model)

File: kalman_train_test.py

A two-stage probabilistic approach combining state-space modeling with residual learning.

Stage 1: Kalman Filter

Models the latent trend as a random walk with Gaussian noise:

z_t = A·z_{t-1} + w_t,  w_t ~ N(0, Q)
y_t = C·z_t + v_t,      v_t ~ N(0, R)

• State dimension: 3
• Transition matrix: Identity (A = I₃)
• Observation matrix: C = [1/3, 1/3, 1/3]
• Process noise: Q = 0.01·I₃
• Observation noise: R = 0.05

Stage 2: Residual Learning

LightGBM gradient boosting model predicts residuals:

ε_t = y_t - y_kalman_t
ŷ_t = y_kalman_t + ε̂_t

Key Features

• Parallel Processing: Multi-core processing for symbol-wise training
• State Persistence: Kalman states maintained across dates within symbols
• No Lookahead Bias: Predictions use only past information

Performance

• Validation RMSE: ~0.00085
• Directional Accuracy: ~63%
• Sign Accuracy: Better market-neutral predictions

Usage

python kalman_train_test.py

Requirements:

• LightGBM
• NumPy, Pandas
• statsmodels
• scikit-learn
• matplotlib, tqdm

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Feature Engineering

Both approaches utilize extensive technical indicators derived from price series:

Regime Identification

• KAMA (Kaufman Adaptive Moving Average): Efficiency Ratio for trend detection
• CHOP (Choppiness Index): Identifies sideways markets (threshold: 43.2)
• Johnny Ribbon: Multi-timeframe moving average regimes (5, 10, 15, 25, 40, 65, 105, 180 periods)

Momentum & Oscillators

• RSI (Relative Strength Index): Overbought/oversold conditions (period: 10)
• CCI (Commodity Channel Index): Cyclical turning points (period: 20)
• CMO (Chande Momentum Oscillator): Centered momentum measure (period: 14)

Volatility

• ATR (Average True Range): Volatility normalization (period: 14)

Trend

• Aroon Up/Down: Trend strength and direction (period: 20)
• EMA (Exponential Moving Average): Multiple timeframes for trend analysis

Note: All technical features are calculated from price assuming f0 as returns: P_t = P_{t-1}(1 + f0)

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Data Preprocessing

Symbol Splitting

Both scripts split train.csv and test.csv into individual symbol files:

train_csvs/symbol_0.csv
train_csvs/symbol_1.csv
...

Feature Normalization

1. Within time-slice ranking: Features ranked within each (date_id, time_id) group
2. Standard scaling: Applied after ranking transformation
3. Global scaler fitting: Trained on sample from multiple symbols

Train-Test Split

• Temporal split: 80% earliest dates for training, 20% latest for validation
• No shuffling: Maintains temporal ordering to prevent lookahead bias

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Model Outputs

LSTM Model

• submission.csv: Predicted returns for test set
• Model artifacts: Saved scalers and trained network

Kalman-GBM Model

• kalman_model.pkl: Contains:
  • Trained LightGBM model
  • Feature scaler
  • Symbol-wise Kalman states
  • Feature column definitions
  • Kalman parameters
• submission.csv: Final predictions
• prediction_distribution.png: Visualization of prediction distribution

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Directory Structure

.
├── train.csv                          # Original training data
├── test.csv                           # Original test data
├── train_csvs/                        # Split training symbols
│   ├── symbol_0.csv
│   ├── symbol_1.csv
│   └── ...
├── test_csvs/                         # Split test symbols
│   ├── symbol_0.csv
│   └── ...
├── lstm_train_test.py                 # LSTM approach
├── kalman_train_test.py               # Kalman + GBM approach
├── submission.csv                     # Final predictions
├── kalman_model.pkl                   # Saved Kalman-GBM model
├── prediction_distribution.png        # Prediction visualization
└── README.md                          # This file

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Hyperparameters

LSTM Model

Parameter	Value
Sequence Length	45
Hidden Size	64
Number of Layers	4
Dropout	0.2
Learning Rate	0.001
Epochs	40
Batch Size	512
Lag Features	5

Kalman-GBM Model

Parameter	Value
Latent Dimension	3
Process Noise (Q)	0.01
Observation Noise (R)	0.05
GBM Learning Rate	0.01
GBM Max Depth	6
GBM Num Leaves	31
Early Stopping Rounds	300

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Performance Comparison

Metric	LSTM	Kalman-GBM
Validation RMSE (Returns)	0.00192	0.00085
Directional Accuracy	57%	63%
Approach	End-to-end deep learning	Probabilistic + residual learning
Training Time	Longer (GPU recommended)	Moderate (CPU parallel)

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Key Differences Between Approaches

LSTM Approach

• Strengths:
  • Captures complex temporal patterns
  • End-to-end learning
  • Good for long sequences
• Weaknesses:
  • Requires more data
  • Longer training time
  • Less interpretable

Kalman-GBM Approach

• Strengths:
  • Probabilistically grounded
  • Better directional accuracy
  • Interpretable components
  • Handles random-walk nature explicitly
• Weaknesses:
  • Assumes linear latent dynamics
  • Two-stage training complexity

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Running the Code

Prerequisites

pip install numpy pandas scikit-learn matplotlib tqdm
pip install lightgbm statsmodels  # For Kalman approach
pip install torch joblib           # For LSTM approach

Training and Prediction

LSTM:

python lstm_train_test.py

Kalman-GBM:

python kalman_train_test.py

Both scripts will:

1. Split raw data into symbol-specific files
2. Engineer features
3. Train models
4. Generate submission.csv

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Theoretical Foundation

Random Walk Hypothesis

The target variable y exhibits near-random-walk behavior:

y_t = y_{t-1} + η_t,  η_t ~ N(0, σ²)

Kalman Filter Formulation

The Kalman approach models the latent state evolution:

p(y_t | y_{1:t-1}) = ∫ p(y_t | z_t) p(z_t | y_{1:t-1}) dz_t

This provides a smoothed estimate of returns while filtering high-frequency noise.

Residual Learning

The gradient boosting stage models systematic deviations:

ε_t = y_t - ŷ_kalman_t
E[ε_t | F] = G(F)

where F represents engineered features capturing regime shifts and market conditions.

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