Time-Series Correlation Models

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The most correlated data factors to stock performance—those most strongly linked to changes in stock prices—fall into several categories:

1. Fundamental Factors

Core financial metrics of a company:

• Earnings per share (EPS) and Profitability: Stock prices are highly sensitive to changes in earnings and profitability. EPS is a primary driver as it represents return to shareholders.
• Valuation multiples (e.g., P/E ratio): The price investors pay for each dollar of earnings strongly indicates stock performance. Changes in valuation multiples reflect shifts in investor sentiment about growth prospects or risk.
• Revenue growth and cash flow: Sustained growth positively correlates with long-term stock appreciation.

2. Macroeconomic Indicators

Broad economic data show strong correlations:

• Real GDP: Historical analysis shows very strong positive correlation between GDP growth and stock market performance, with R² of 0.9174.
• Consumer Price Index/Inflation: Stock prices often rise with inflation, though the relationship depends on interest rates and economic context. CPI had R² of 0.7597.
• Average Weekly Private Wages: Higher wages support consumer spending, corporate earnings, and stock prices (R² of 0.7045).
• Unemployment Rate: Weaker negative correlation with stock performance (R² of 0.2125), as lower unemployment supports economic growth.

3. Technical and Market Factors

• Overall market and sector movement: Research suggests up to 90% of a stock's movement is explained by overall market and sector movement, rather than company-specific news.
• Liquidity and trading volume: Highly liquid stocks are more responsive to news and trends, while illiquid stocks may be more volatile or discounted.
• Momentum and trends: Stocks that performed well recently tend to continue performing well short-term.

4. Market Sentiment and External Factors

• Investor sentiment: News, social media, and market mood drive short-term price swings.
• Macroeconomic events: Interest rates, inflation expectations, and geopolitical events trigger correlated moves across stocks and sectors.

5. Correlations Among Stocks

• Index and sector correlations: Stocks within the same index or sector move together due to shared economic drivers or investor behavior.
• Global market correlations: US and European stocks are more highly correlated with each other than with Asian stocks, reflecting economic ties and trading hours overlap.

Summary Table: Most Correlated Factors

In practice, combining these factors—especially macroeconomic indicators, earnings data, and market/sector trends—provides the most robust correlation with stock performance. Alternative data (like job postings or news sentiment) can add value for short-term or event-driven strategies, but the most statistically significant correlations remain with traditional fundamental and macroeconomic indicators.

Modeling Approaches

Prophet Model

• Uses Facebook Prophet with optimized parameters:
  • Increased seasonality complexity (higher Fourier orders for yearly, monthly, quarterly, biweekly).
  • Multiplicative seasonality mode.
  • More changepoints and wider changepoint range for flexibility.
  • Wider prediction intervals for uncertainty.
  • Custom seasonalities added for monthly, quarterly, and biweekly patterns.
• Adds multiple external regressors (weather and engineered features).
• Fits the model to training data and predicts on test and future data.

Ensemble Machine Learning Models

• Random Forest Regressor:
  • Tuned for more trees, deeper trees, and robust splitting criteria.
  • Uses all engineered features, including weather and rolling stats.
  • Trained on raw features.
• Ridge Regression:
  • Uses scaled features (RobustScaler for outlier resistance).
  • Regularization parameter tuned for reduced overfitting.
• Both models are trained and evaluated, and their predictions are compared.

Train-Test Splitting

• Splits data chronologically to preserve time series order, avoiding data leakage.

Prediction and Evaluation

Prediction Preparation

• Merges historical and future data to ensure continuity for rolling features.
• Ensures all required regressors are present for Prophet, filling missing ones with zeros if needed.

Evaluation Metrics

• Calculates MAE, RMSE, R², MAPE, accuracy percentage, average percent error, and data range for both actual and predicted values.
• Provides detailed printouts for model performance on both cross-validation and official prediction periods.

Result Saving and Reporting

• Saves final predictions (with confidence intervals and weather data) to JSON.
• Prints summary tables comparing model performance across all metrics.

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Summary Table of Feature Types

Summary of the Best XGBoost Parameters

XGBoost offers a wide array of parameters, which can be grouped into three main categories: general parameters, booster parameters, and learning task parameters. Below is a structured summary of the most important and commonly tuned parameters for optimal model performance.

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General Parameters

• booster: Type of model to run at each iteration. Options are gbtree (default), gblinear, or dart.
• device: Specify computation device (cpu or cuda for GPU acceleration).
• verbosity: Controls the amount of messages printed. Range: 0 (silent) to 3 (debug).
• nthread: Number of parallel threads used for running XGBoost.

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Tree Booster Parameters (for gbtree and dart)

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Learning Task Parameters

• objective: Specifies the learning task (e.g., reg:squarederror for regression, binary:logistic for binary classification, multi:softmax for multiclass).
• eval_metric: Evaluation metric for validation data (e.g., rmse, logloss, auc).
• seed: Random seed for reproducibility.

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Specialized Parameters

• DART Booster: Parameters like rate_drop, skip_drop, and sample_type control dropout behavior in the DART booster.
• gblinear Booster: Parameters like updater, feature_selector, and top_k control linear model fitting.
• Categorical Features: Parameters such as max_cat_to_onehot and max_cat_threshold manage categorical data handling.

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Parameter Tuning Tips

• Start with default values and tune the following for best results:
  • max_depth, min_child_weight (model complexity)
  • subsample, colsample_bytree (overfitting control)
  • eta (learning rate; lower values often require more boosting rounds)
  • gamma, lambda, alpha (regularization)
• For imbalanced datasets, adjust scale_pos_weight.
• Use tree_method=hist or gpu_hist for large datasets or GPU acceleration.

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Example of Good XGBoost Parameters

Typical Ranges for Key Parameters

Why These Parameters Work Well

• colsample_bytree/colsample_bylevel: Subsampling features helps reduce overfitting, especially in high-dimensional data[^1][^2].
• alpha/lambda: Regularization terms are crucial for controlling model complexity and preventing overfitting, especially with many trees or deep trees[^1][^2][^4].
• tree_method: 'approx' & grow_policy: 'lossguide': This combination enables efficient training on large datasets, and lossguide allows you to control complexity via max_leaves instead of max_depth[^1][^3].
• max_leaves: Directly limits the number of terminal nodes, which is effective for large or sparse datasets[^1][^3].
• eta: A moderate learning rate of 0.25 is a reasonable starting point; you can lower it (e.g., 0.05–0.1) for more conservative learning and increase nrounds if needed[^5].
• subsample: High subsampling (0.95) allows nearly all data to be used but still adds some randomness for regularization[^1][^2].
• early_stopping_rounds: Prevents unnecessary training if validation error stops improving[^1][^2].