Index
Time-Series Correlations
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
| Factor | Correlation Strength | Notes |
|---|---|---|
| Real GDP | Very High | R² ≈ 0.92 with S&P 500 |
| CPI/Inflation | High | R² ≈ 0.76 with S&P 500 |
| Average Wages | High | R² ≈ 0.70 with S&P 500 |
| Market/Sector Movement | Very High | Explains majority of stock movement |
| Company Earnings/EPS | High | Direct impact on valuation |
| P/E Ratio | High | Reflects investor sentiment/expectations |
| Unemployment Rate | Low/Negative | R² ≈ 0.21 with S&P 500 |
| Momentum | Moderate-High | Especially during market bubbles |
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.
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.
General Parameters
- booster: Type of model to run at each iteration. Options are
gbtree(default),gblinear, ordart. - device: Specify computation device (
cpuorcudafor GPU acceleration). - verbosity: Controls the amount of messages printed. Range: 0 (silent) to 3 (debug).
- nthread: Number of parallel threads used for running XGBoost.
Tree Booster Parameters (for gbtree and dart)
| Parameter | Default | Description | Typical Range |
|---|---|---|---|
| eta (learning_rate) | 0.3 | Step size shrinkage to prevent overfitting. Lower values make learning slower but safer. | [0.01, 0.3] |
| gamma | 0 | Minimum loss reduction required to make a split. Higher values make the algorithm more conservative. | [0, ∞) |
| max_depth | 6 | Maximum depth of a tree. Larger values increase model complexity and risk of overfitting. | |
| min_child_weight | 1 | Minimum sum of instance weight (hessian) in a child. Higher values make the algorithm more conservative. | |
| subsample | 1 | Fraction of training samples used per tree. Reduces overfitting. | (0.5, 1] |
| colsample_bytree | 1 | Fraction of features used per tree. | (0.5, 1] |
| colsample_bylevel | 1 | Fraction of features used per tree level. | (0.5, 1] |
| colsample_bynode | 1 | Fraction of features used per split. | (0.5, 1] |
| lambda (reg_lambda) | 1 | L2 regularization term on weights. | [0, ∞) |
| alpha (reg_alpha) | 0 | L1 regularization term on weights. | [0, ∞) |
| tree_method | auto | Algorithm for constructing trees: auto, exact, approx, hist, gpu_hist. | |
| scale_pos_weight | 1 | Controls balance of positive/negative weights for unbalanced classification. | [1, #neg/#pos] |
Typical Ranges for Key Parameters
| Parameter | Typical Range |
|---|---|
| eta | 0.01 – 0.3 |
| max_leaves | 16 – 256 |
| colsample_bytree | 0.5 – 1.0 |
| subsample | 0.5 – 1.0 |
| alpha/lambda | 0 – 10 |
| min_child_weight | 1 – 10 |
Why These Parameters Work Well
- colsample_bytree/colsample_bylevel: Subsampling features helps reduce overfitting, especially in high-dimensional data.
- alpha/lambda: Regularization terms are crucial for controlling model complexity and preventing overfitting, especially with many trees or deep trees.
- tree_method: 'approx' & grow_policy: 'lossguide': This combination enables efficient training on large datasets, and
lossguideallows you to control complexity viamax_leavesinstead ofmax_depth. - max_leaves: Directly limits the number of terminal nodes, which is effective for large or sparse datasets.
- 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
nroundsif needed . - subsample: High subsampling (0.95) allows nearly all data to be used but still adds some randomness for regularization.
- early_stopping_rounds: Prevents unnecessary training if validation error stops improving.
