Overview: Predicting Tomorrow’s Open Price with an Ensemble of XGBoost and LightGBM In this solution, we will use an ensemble of XGBoost and LightGBM models to predict whether tomorrow’s open price will be greater than today’s close price. The features will be derived using the Unscented Kalman Filter (UKF) for smoothing. 1. Problem Setup and Classification Goal Task: Predict if tomorrow’s open price > today’s close price. Condition: Only include cases where today’s close > yesterday’s close (bullish trend today). Target Variable (Y): 1: If tomorrow’s open > today’s close (bullish). 0: If tomorrow’s open <= today’s close (neutral/bearish). 2. Data Preprocessing and Feature Engineering Smoothing OHLC Prices: We will apply the Unscented Kalman Filter (UKF) to each of the OHLC prices (Open, High, Low, Close) to create smooth and noise-free input features. Feature List: Open_UKF: Smoothed Open Price. High_UKF: Smoothed High Price. Low_UKF: Smoothed Low Price. Close_UKF: Smoothed Close Price. H - L: Difference between High and Low prices (H-L). O - C: Difference between Open and Close prices (O-C) (captures bullish or bearish sentiment). (H + L) / 2: Midpoint of High and Low prices. % Return of Close Prices: Daily percentage return of the Close prices. 3. Ensemble Model Design: XGBoost + LightGBM To improve the prediction accuracy, we will create an ensemble model combining predictions from XGBoost and LightGBM. Here's how the ensemble approach will work: XGBoost: Works well on non-linear relationships. Can handle imbalanced datasets effectively. Fast and scalable. LightGBM: Efficient on large datasets and high-dimensional data. Handles categorical features and missing values well. Optimized for speed and memory usage. 4. Ensemble Strategy Train both models separately: Train XGBoost and LightGBM using the same dataset and features. Combine Predictions: Use weighted averaging or voting to combine predictions from both models. Options for Ensemble Predictions: Weighted Average: Average the prediction probabilities from both models, with each model's contribution weighted. 𝑦 ^ = 0.5 × 𝑦 ^ 𝑋 𝐺 𝐵 𝑜 𝑜 𝑠 𝑡 + 0.5 × 𝑦 ^ 𝐿 𝑖 𝑔 ℎ 𝑡 𝐺 𝐵 𝑀 y ^ =0.5× y ^ XGBoost +0.5× y ^ LightGBM Voting: Use hard voting (majority vote) or soft voting (average of probabilities). 5. Workflow Overview Data Collection: Download historical stock data using yfinance. Data Preprocessing: Apply UKF smoothing to OHLC prices. Create derived features: H - L, O - C, (H + L) / 2, % Close Return. Model Training: Train XGBoost and LightGBM separately. Ensemble Prediction: Use weighted averaging or voting to combine predictions. Evaluation: Use accuracy, precision, recall, and F1-score to evaluate performance,CONFUSION MATRIX........NOW STOP YOUR REDUNDANCY AND CODE THIS THING ,,,IST READ AND THEN QRITE THE RULES BACK