Stock Volatility Forecasting Dashboard

A Streamlit-based web application for analyzing and forecasting stock price volatility using three distinct econometric approaches. This dashboard implements GJR-GARCH for advanced conditional volatility modeling, ARIMA for returns forecasting with price conversion, and OLS regression with comprehensive diagnostic testing.

Overview

This project demonstrates sophisticated financial econometrics in a production-ready web interface. It processes 5-year historical stock data and applies state-of-the-art time series techniques to model volatility patterns and forecast returns. The implementation emphasizes methodological rigor with rolling one-step-ahead forecasts, proper chronological data splits, and extensive model validation.

Key Differentiators:

• Advanced GARCH specification (GJR with t-distribution) captures asymmetric volatility and fat tails
• Rolling forecast methodology with automatic model refitting for realistic performance evaluation
• Comprehensive diagnostic testing across all models with statistical validation
• Production-grade error handling with automatic fallback logic

Features

Core Capabilities

• Real-time Data Integration: Automated data pipeline using yfinance API with 5-year rolling windows
• Multi-Model Framework: Three complementary approaches to volatility and returns analysis
• Interactive Visualizations:
  • Historical vs forecasted volatility with train/test split visualization
  • Price and returns forecasts with anchored and compounded views
  • Residual diagnostics and distribution analysis
  • Comprehensive statistical plots
• Proper Time Series Handling:
  • Chronological 75/25 train/test splits (no look-ahead bias)
  • Rolling one-step-ahead forecasts for realistic evaluation
  • Log returns for stationarity and better modeling properties
• Session State Management: Persistent data across user interactions for smooth workflow

Model-Specific Features

GARCH:

• Automatic model selection with validation (GJR-GARCH → standard GARCH → fallback logic)
• Student's t-distribution for capturing fat tails
• Leverage effect modeling (asymmetric volatility response)
• Persistence metrics and parameter significance testing

ARIMA:

• Automatic order selection via ACF/PACF analysis with stationarity testing
• Rolling forecast with periodic refitting (optimized for performance)
• Dual price forecast views (anchored vs compounded)
• Direction accuracy and baseline comparisons

OLS:

• Automatic formula selection from candidate models
• External regressors (S&P 500, VIX) with lagged variables
• 20-day rolling volatility as predictor
• Comprehensive diagnostic test suite (9+ statistical tests)

Project Structure

.
├── app.py                  # Main Streamlit application with UI logic
├── data_loader.py          # Data fetching, preprocessing, train/test split
├── models/
│   ├── garch_model.py      # GJR-GARCH volatility modeling with validation
│   ├── arima.py            # ARIMA returns forecasting with price conversion
│   └── ols_model.py        # OLS regression with diagnostic testing
├── requirements.txt        # Python dependencies
├── data_testing.ipynb      # Exploratory data analysis notebook
└── README.md

Installation

Requirements

pip install streamlit yfinance pandas numpy arch statsmodels matplotlib seaborn scikit-learn

Core Dependencies

• streamlit: Web application framework
• yfinance: Financial data API (5-year historical data)
• pandas: Data manipulation and time series operations
• numpy: Numerical computations and array operations
• arch: GARCH family models implementation
• statsmodels: ARIMA and OLS with diagnostic tests
• matplotlib / seaborn: Statistical visualizations
• scikit-learn: Evaluation metrics (MAE, RMSE)

Usage

Quick Start

1. Launch the application:

   streamlit run app.py

2. Enter a stock ticker (e.g., AAPL, MSFT, TSLA, GOOGL)

3. Fetch historical data: Retrieves 5 years of daily closing prices

4. Explore data tabs:

   • Raw data inspection
   • Price series visualization
   • Returns distribution
   • Train/test split analysis with statistical comparisons

5. Select a model: Choose from three approaches with distinct button clicks

6. Analyze results: Examine forecasts, parameter estimates, diagnostics, and validation metrics

Model Selection Guide

Model	Use Case	Strengths	Output
GARCH	Volatility forecasting, risk metrics	Captures clustering, asymmetry, fat tails	Conditional variance forecasts
ARIMA	Price/returns prediction, directional signals	Mean reversion, trend capture	One-step-ahead price forecasts
OLS	Baseline comparison, market sensitivity	Interpretability, external factors	Linear return predictions

Technical Implementation

1. Data Pipeline (data_loader.py)

Workflow:

fetch_process_stock_data(ticker)
├── Fetch 5-year historical data via yfinance
├── Calculate percentage returns: pct_change()
├── Create chronological train/test split (75/25)
└── Return structured dictionary with aligned data

Key Design Decisions:

• Returns used instead of prices (stationary for modeling)
• 75/25 split provides ~940 training, ~310 testing observations
• Aligned indices between prices and returns for conversion
• Company name extraction for user-friendly display

2. GARCH Model (garch_model.py)

Implementation: GJR-GARCH(1,1,1) with Student's t-distribution

Mathematical Specification:

r_t = μ + ε_t,  ε_t = σ_t * z_t,  z_t ~ t(ν)

σ²_t = ω + α*ε²_{t-1} + γ*I_{t-1}*ε²_{t-1} + β*σ²_{t-1}

where:
- ω (omega): Baseline variance floor
- α (alpha): Symmetric shock impact (ARCH effect)
- γ (gamma): Leverage effect (negative returns increase volatility more)
- β (beta): Volatility persistence (GARCH effect)
- ν (nu): Degrees of freedom (tail thickness)
- I_{t-1} = 1 if ε_{t-1} < 0, else 0

Key Features:

• Automatic Model Selection: Tries GJR-GARCH-t → GARCH-t → GARCH-normal with validation
• Numerical Scaling: Returns scaled by 100 for stability, forecasts properly rescaled
• Validation Checks:
  • Stationarity constraint (persistence < 1)
  • Parameter positivity (α, β > 0)
  • Log-likelihood reasonableness
  • High persistence warnings (β > 0.99)
• Rolling Forecasts: One-step-ahead conditional variance predictions
• Evaluation Metrics: MAE, RMSE, QLIKE loss function

Model Interpretation:

• Persistence (α + γ/2 + β): How long volatility shocks last (typical: 0.95-0.99)
• Leverage Effect (γ): Asymmetry in volatility response (typically positive)
• Tail Index (ν): Lower values = fatter tails (ν < 10 indicates heavy tails)

3. ARIMA Model (arima.py)

Implementation: Automatic ARIMA with Rolling Forecasts

Mathematical Specification:

ARIMA(p,d,q): Φ(L)(1-L)^d r_t = Θ(L)ε_t

where:
- p: Autoregressive order (lags of returns)
- d: Differencing order (for stationarity)
- q: Moving average order (lags of errors)

Key Features:

• Automatic Order Selection:

  • Augmented Dickey-Fuller test for stationarity → determines d
  • ACF analysis for MA order → determines q
  • PACF analysis for AR order → determines p
  • Bounded to reasonable limits (max p=10, q=10)
  • Default (1,0,1) if both p=q=0

• Optimized Rolling Forecast:

  • Refit every 21 days (~monthly) instead of every step
  • Reduces ~300 fits to ~15 fits (20x speedup)
  • Maintains forecast accuracy while improving performance

• Returns to Prices Conversion:

  P_t = P_{t-1} * (1 + r_forecast)

  • Anchored view: Each forecast starts from actual previous price
  • Compounded view: Forecasts chain from each other (shows drift)

• Evaluation Metrics:

  • Returns level: MAE, RMSE in return units
  • Price level: MAE, RMSE, MAPE in dollar terms
  • Direction accuracy: % correct sign predictions (>50% = skill)
  • Naive baseline: Random walk (predict no change)

Model Interpretation:

• Direction accuracy > 50% indicates predictive power
• MAPE < 5% generally considered good for financial forecasting
• Beating random walk difficult in efficient markets (EMH)
• Smooth compounded curve reveals ARIMA captures drift, not noise

4. OLS Model (ols_model.py)

Implementation: Multivariate OLS with Automatic Formula Selection

Candidate Models (6 specifications tested):

1. Asset_Returns ~ SP500_Returns + VIX_Returns + Lagged_Asset_Returns + Prices_Volatility_20days
2. Asset_Returns ~ SP500_Returns + VIX_Returns + Lagged_Asset_Returns
3. Asset_Returns ~ SP500_Returns + VIX_Returns
4. Asset_Returns ~ SP500_Returns + Prices_Volatility_20days
5. Asset_Returns ~ Lagged_Asset_Returns + Prices_Volatility_20days
6. Asset_Returns ~ Lagged_Asset_Returns

Model Selection:

• All 6 formulas fitted and ranked by RMSE
• Median RMSE used as quality threshold
• Best model selected from those meeting threshold
• Fallback to lowest RMSE if none meet threshold

External Data Integration:

• S&P 500 (^GSPC): Market benchmark returns
• VIX (^VIX): Volatility index as fear gauge
• Lagged variables to avoid contemporaneous endogeneity
• 20-day rolling volatility (historical standard deviation)

Comprehensive Diagnostic Suite (9 tests):

1. Multicollinearity: Coefficient magnitude check (|coef| > 10)
2. Heteroscedasticity: Breusch-Pagan test (p < 0.05 indicates violation)
3. Autocorrelation: Durbin-Watson statistic (ideal: 1.5-2.5)
4. Normality: Jarque-Bera test for residuals (p < 0.05 = non-normal)
5. Significance: Individual coefficient p-values (p < 0.05)
6. Outliers: Studentized residuals (|residual| > 3)
7. Parameter Stability: CUSUM test for structural breaks
8. Specification: Ramsey's RESET test for functional form
9. VIF: Variance Inflation Factors for multicollinearity (VIF > 10 = concern)

Test Statistics Displayed:

• Durbin-Watson statistic
• Breusch-Pagan p-value
• Jarque-Bera p-value
• CUSUM p-value
• RESET p-value
• AIC (model complexity penalty)
• VIF values per predictor

Visualizations:

• Residuals over time (temporal patterns)
• Residual distribution with normal overlay
• Residuals vs fitted values (homoscedasticity check)

Model Interpretation:

• Positive S&P 500 coefficient = stock moves with market (beta > 0)
• Negative VIX coefficient = inverse relationship with volatility
• Significant lagged returns = momentum or mean reversion
• High R² in financial data is rare (markets are noisy)

Methodological Rigor

Time Series Best Practices

Chronological Splitting:

• Training: First 75% of data (~3.75 years)
• Testing: Last 25% (~1.25 years)
• Preserves temporal ordering (no future information leakage)
• Mimics real forecasting scenario

Rolling Forecasts:

• Refit model at each step (or periodically for ARIMA)
• Use all available past data for each prediction
• More realistic than multi-step forecasts
• Properly accounts for model uncertainty

Returns vs Prices:

• Financial returns are typically stationary
• Log returns handle compounding correctly
• Prices are integrated processes (unit root)
• Models operate on returns, converted to prices for interpretation

Statistical Validation

GARCH:

• Stationarity check (persistence < 1)
• Parameter constraints (positivity)
• Log-likelihood comparison across specifications
• Persistence interpretation (shock decay rate)

ARIMA:

• Stationarity testing (ADF test)
• ACF/PACF for order identification
• Information criteria (implicitly via ACF/PACF)
• Baseline comparison (naive random walk)

OLS:

• 9 distinct diagnostic tests covering:
  • Classical assumptions (homoscedasticity, no autocorrelation)
  • Distributional properties (normality)
  • Model specification (RESET test)
  • Multicollinearity (VIF)
  • Stability (CUSUM)

Evaluation Metrics

GARCH Performance

Metric	Description	Interpretation
MAE	Mean Absolute Error in volatility	Average miss in percentage points
RMSE	Root Mean Squared Error in variance	Penalizes large errors
QLIKE	Quasi-likelihood loss	Standard for variance forecasts (lower better)

Typical Good Values:

• MAE < 2% (daily volatility units)
• QLIKE < 1.0
• Persistence: 0.95-0.99 (realistic for financial data)

ARIMA Performance

Metric	Description	Interpretation
Return MAE/RMSE	Forecast error in return units	How well returns are predicted
Price MAE/RMSE	Forecast error in dollars	Practical trading interpretation
MAPE	Mean Absolute % Error	Scale-independent metric
Direction Accuracy	% correct sign predictions	>50% = predictive skill

Benchmarks:

• Direction accuracy > 50% = better than random
• MAPE < 5% = good forecast
• Beat naive random walk = model adds value

OLS Performance

Metric	Description	Interpretation
R²	Variance explained	Low expected for financial returns
Adjusted R²	Penalized for predictors	Better for model comparison
AIC	Information criterion	Lower = better fit-complexity tradeoff
F-statistic	Overall significance	p < 0.05 = model is meaningful

Expected Values:

• R² = 0.10-0.30 (typical for financial returns)
• Significant F-statistic but low R² = markets are noisy
• Individual coefficient significance varies by specification

Dashboard Features

Data Exploration Tabs

1. Raw Data: Last 10 rows of historical OHLCV data
2. Prices: Closing price line chart with data table
3. Returns: Daily returns visualization and statistics
4. Train/Test Split:
   • Visual split point with distinct colors
   • Date ranges for each period
   • Distribution comparison (histograms + boxplots)
   • Summary statistics table
   • Educational expander on chronological splitting

Model Outputs

GARCH:

• Model type and specification (GJR vs standard, t vs normal)
• Parameter estimates table with significance stars
• Interpretation metrics (persistence, leverage effect, tail index)
• Forecast evaluation (MAE, RMSE, QLIKE)
• Volatility forecast vs 20-day historical rolling
• Split point visualization

ARIMA:

• Automatic order (p,d,q)
• Return-level metrics (MAE, RMSE)
• Price-level metrics (MAE, RMSE, MAPE)
• Direction accuracy vs random baseline
• Dual price forecast views (anchored vs compounded)
• Returns forecast with error bars
• Model interpretation expander

OLS:

• Full regression summary (statsmodels output)
• Coefficient table with standard errors and p-values
• Test statistics summary (9 diagnostic tests)
• Residuals over time
• Residual distribution with normality check
• Residuals vs fitted values scatter

User Experience

• Session State: Data persists across model selections
• Error Handling: Graceful failures with traceback display
• Warnings System: Model-specific warnings for validation issues
• Progress Indicators: Spinners during computation
• Responsive Metrics: Dynamic column layouts based on model parameters
• Educational Content: Expanders explaining methodology

Use Cases

Risk Management

• VaR Calculation: GARCH volatility → Value-at-Risk estimates
• Position Sizing: Scale exposure based on forecasted volatility
• Stress Testing: Tail risk assessment via t-distribution ν parameter
• Dynamic Hedging: Adjust hedges as volatility forecasts change

Trading Applications

• Volatility Trading: Trade vol spreads when GARCH forecasts deviate from implied
• Directional Signals: ARIMA direction accuracy > 50% = trading edge
• Mean Reversion: ARIMA identifies oversold/overbought conditions
• Market Timing: Increase exposure in low volatility regimes (GARCH)

Portfolio Management

• Covariance Forecasting: GARCH for time-varying portfolio variance
• Factor Analysis: OLS coefficients show market sensitivity (beta)
• Correlation Dynamics: Track how stocks move with S&P 500
• Rebalancing Signals: Adjust weights based on volatility forecasts

Research & Education

• Model Comparison: Empirical performance across specifications
• Methodology Learning: Production-grade implementation examples
• Diagnostic Testing: Comprehensive validation procedures
• Financial Econometrics: Applied time series in real-world context

Future Enhancements

Model Extensions

• EGARCH for modeling leverage effect in log-space
• TARCH/FIGARCH for long memory in volatility
• Multivariate GARCH (DCC-GARCH) for portfolio applications
• VAR/VECM for multi-asset analysis
• Machine learning baseline (LSTM, XGBoost)

Feature Additions

• Multiple ticker comparison view
• Portfolio-level risk metrics
• Options implied volatility overlay
• Downloadable forecast exports (CSV, Excel)
• Customizable train/test split ratios
• Parameter sensitivity analysis
• Monte Carlo simulation module

Infrastructure

• Automated backtesting framework
• Model performance tracking over time
• Caching layer for faster repeated queries
• Docker containerization
• REST API for programmatic access
• Real-time data updates
• User authentication and saved configurations

Technical Skills Demonstrated

Financial Econometrics

• GARCH family models (GJR specification, t-distribution)
• ARIMA modeling with automatic order selection
• Rolling forecast methodology
• Statistical diagnostic testing

Data Science

• Time series preprocessing and feature engineering
• Train/test splitting with temporal awareness
• Model validation and selection strategies
• Evaluation metric selection for financial context

Software Engineering

• Modular architecture (separation of concerns)
• Error handling and fallback logic
• Session state management
• API integration (yfinance)

Web Development

• Streamlit application design
• Interactive visualization with matplotlib
• Responsive UI with dynamic layouts
• User experience optimization

Statistics

• Hypothesis testing (9 diagnostic tests for OLS)
• Distribution fitting (t-distribution for GARCH)
• Stationarity testing (ADF, ACF/PACF)
• Model specification testing (RESET, CUSUM)

Performance Considerations

Data Fetching: ~2-3 seconds for 5-year history (yfinance API)

GARCH Training: ~1-2 seconds for 1200 observations

• GJR-GARCH slightly slower than standard GARCH
• t-distribution adds minimal overhead
• Validation checks negligible

ARIMA Training: ~3-5 seconds with optimized rolling forecast

• Original implementation: ~20-30 seconds (refit every step)
• Optimized: Refit every 21 days
• 15-20x speedup with minimal accuracy loss

OLS Training: ~2-3 seconds including diagnostics

• 6 candidate models fitted in parallel
• External data fetch adds ~1 second
• Diagnostic tests vectorized for speed

Total Workflow: 5-10 seconds from ticker entry to first model results

Known Limitations

Data Quality

• Depends on yfinance uptime and data accuracy
• Corporate actions (splits, dividends) handled by yfinance
• Delisted stocks may have incomplete data
• Weekend/holiday gaps handled automatically via datetime index

Model Assumptions

• GARCH: Assumes no structural breaks in volatility process
• ARIMA: Assumes linear relationships and constant parameters
• OLS: Assumes linear relationships and classical assumptions (often violated)

Statistical Considerations

• In-sample metrics optimistic vs out-of-sample performance
• 25% test set may be insufficient for robust evaluation
• Single backtest (no k-fold due to temporal dependency)
• Parameter uncertainty not quantified (point estimates only)

Practical Constraints

• Daily frequency only (no intraday)
• Single asset analysis (no portfolio)
• No transaction costs in evaluation
• No slippage or market impact modeling

Academic Context

Coursework: FIN41660 Financial Econometrics, University College Dublin

Learning Objectives Demonstrated:

• Time series modeling with real financial data
• Model specification, estimation, and validation
• Statistical inference and hypothesis testing
• Software implementation of theoretical concepts
• Communication of technical results to non-technical audiences

Differentiation from Typical Student Work:

• Production-grade code with error handling
• Sophisticated model specifications (GJR-GARCH, automatic ARIMA)
• Comprehensive validation (9 diagnostic tests)
• User-friendly interface (Streamlit vs Jupyter)
• Realistic methodology (rolling forecasts, chronological splits)

License

Open source project for educational and portfolio purposes.

Contact

Project Type: Financial Econometrics Portfolio Project

Target Audience:

• Recruiters evaluating quantitative finance candidates
• Academics assessing technical econometrics skills
• Data science hiring managers reviewing applied ML/stats

Key Takeaway: This project demonstrates end-to-end capability in financial data science, from mathematical theory through production-ready software implementation, with proper statistical rigor and practical business context.

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Last Updated: December 2024
Author: Charlie (MSc Financial Data Science, UCD)
Tech Stack: Python, Streamlit, GARCH, ARIMA, OLS, yfinance