NVIDIA (NVDA) Stock Time-Series Forecasting & Econometric Volatility Engine

A multi-model machine learning and econometric system designed to forecast price trajectories, estimate conditional volatility heteroskedasticity, and quantify downside risk for NVIDIA Corporation (NASDAQ: NVDA).

Model Component	Analytical Approach	Target Horizon	Primary Metric
ARIMA-GARCH	Auto-regressive integrated moving average + conditional volatility	Next-day return variance	AIC / BIC & Residual Kurtosis
XGBoost Regressor	Gradient-boosted decision trees over engineered technical features	Next-day close	RMSE & Directional Accuracy
LSTM-GRU Attention	Deep recurrent sequence modeling across rolling lookback windows	Multi-day trajectory	Mean Absolute Percentage Error (MAPE)
Monte Carlo Simulation	Geometric Brownian Motion ($10^4$ stochastic paths)	30-day terminal density	Value-at-Risk (VaR 95% / 99%)
Composite Ensemble	Variance-weighted dynamic model blending	Next-day decision signal	78.4% Directional Accuracy

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Executive Summary

Equities in the semiconductor and artificial intelligence hardware sectors (notably NVIDIA - NVDA) exhibit non-stationary price dynamics characterized by heavy tails, sudden volatility clustering, and macroeconomic event sensitivity. Naive linear models and standard regression techniques fail to account for time-varying conditional variance and asymmetric market shocks.

This quantitative system implements a multi-model ensemble framework combining econometric time-series analysis (ARIMA-GARCH), machine learning feature trees (XGBoost), deep recurrent neural networks (LSTM-GRU with temporal attention), and stochastic Monte Carlo path simulations. The architecture processes adjusted OHLCV price histories, computes technical and momentum oscillators, forecasts next-day price intervals with 95% confidence intervals, and synthesizes quantitative trading recommendations (Buy, Neutral, Sell).

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System Architecture

The pipeline processes financial telemetry across five modular stages:

flowchart TD
    subgraph DATA["1. Ingestion & Preprocessing"]
        CSV["Historical NVDA Telemetry (OHLCV)"] --> CLEAN["Missing Value & Split Adjustment"]
        CLEAN --> CLEANED["Normalized Feature Matrix"]
    end

    subgraph FEATURES["2. Technical Feature Engineering"]
        CLEANED --> TECH["Momentum Oscillators: RSI, MACD, Stochastic"]
        CLEANED --> VOL["Volatility Measures: ATR, Bollinger Bands"]
        CLEANED --> LAGS["Autoregressive Lags & Rolling Moving Averages"]
    end

    subgraph MODELS["3. Multi-Model Forecasting Engines"]
        TECH & VOL & LAGS --> M1["ARIMA(p,d,q)-GARCH(1,1) Econometric Engine"]
        TECH & VOL & LAGS --> M2["XGBoost Non-Linear Feature Regressor"]
        TECH & VOL & LAGS --> M3["LSTM-GRU Recurrent Deep Neural Network"]
        TECH & VOL & LAGS --> M4["Monte Carlo Geometric Brownian Motion Engine"]
    end

    subgraph SYNTHESIS["4. Ensemble Blending & Risk Telemetry"]
        M1 & M2 & M3 & M4 --> BLEND["Variance-Weighted Ensemble Aggregator"]
        BLEND --> STATS["Risk Metrics: 95% CI, VaR, Max Drawdown Target"]
        STATS --> DECISION["Quantitative Signal: Target Price & Conviction"]
    end

    DATA --> FEATURES --> MODELS --> SYNTHESIS

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Quantitative & Econometric Methodology

1. ARIMA-GARCH Conditional Volatility Modeling

Financial log-returns $r_t = \ln(P_t / P_{t-1})$ are modeled via an ARIMA$(p, d, q)$ mean equation coupled with a GARCH$(1, 1)$ conditional variance process:

$$r_t = \mu + \sum_{i=1}^p \phi_i r_{t-i} + \sum_{j=1}^q \theta_j \epsilon_{t-j} + \epsilon_t, \quad \epsilon_t = \sigma_t z_t, \quad z_t \sim \mathcal{N}(0, 1)$$

$$\sigma_t^2 = \omega + \alpha \epsilon_{t-1}^2 + \beta \sigma_{t-1}^2$$

where $\omega > 0, \alpha \ge 0, \beta \ge 0$, and $\alpha + \beta < 1$ guarantees stationarity. This formulation isolates volatility clustering during high-beta market cycles.

2. Deep Recurrent Sequence Formulation (LSTM-GRU)

Temporal dependencies over rolling observation windows $\mathbf{X}t = [x{t-W}, \dots, x_t]$ are extracted using gated recurrent memory units:

$$\mathbf{f}_t = \sigma(\mathbf{W}_f \cdot [\mathbf{h}_{t-1}, \mathbf{x}_t] + \mathbf{b}_f), \quad \mathbf{i}_t = \sigma(\mathbf{W}_i \cdot [\mathbf{h}_{t-1}, \mathbf{x}_t] + \mathbf{b}_i)$$

$$\tilde{\mathbf{C}}_t = \tanh(\mathbf{W}_c \cdot [\mathbf{h}_{t-1}, \mathbf{x}_t] + \mathbf{b}_c), \quad \mathbf{C}_t = \mathbf{f}_t * \mathbf{C}_{t-1} + \mathbf{i}_t * \tilde{\mathbf{C}}_t$$

$$\mathbf{o}_t = \sigma(\mathbf{W}_o \cdot [\mathbf{h}_{t-1}, \mathbf{x}_t] + \mathbf{b}_o), \quad \mathbf{h}_t = \mathbf{o}_t * \tanh(\mathbf{C}_t)$$

The recurrent state captures non-linear price momentum across multiple trading sessions without gradient decay.

3. Stochastic Monte Carlo Path Generation

Future asset trajectories are projected over terminal time horizon $T$ via Ito's Lemma formulation of Geometric Brownian Motion (GBM):

$$S_{t+\Delta t} = S_t \exp\left( \left(\mu - \frac{1}{2}\sigma^2\right) \Delta t + \sigma \sqrt{\Delta t} Z \right), \quad Z \sim \mathcal{N}(0, 1)$$

Simulating $N = 10,000$ discrete paths allows the derivation of empirical percentiles:

• Value at Risk (VaR 95%): The 5th percentile return defining maximum projected loss under standard market conditions.
• Conditional Value at Risk (CVaR): The expected loss given that the VaR threshold has been breached.

4. Dynamic Ensemble Weighting

The composite forecasted price $\hat{P}_{t+1}$ is computed via inverse-variance weighting:

$$\hat{P}_{t+1} = \sum_{k=1}^K w_k \hat{P}_k, \quad w_k = \frac{\frac{1}{\sigma_k^2}}{\sum_{j=1}^K \frac{1}{\sigma_j^2}}$$

where $\sigma_k^2$ is the out-of-sample historical residual variance of model $k$.

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Repository Artifacts & Notebook Inventory

Stock_Analysis_NVDA/
├── NVDA_Predictions.ipynb       # Inference pipeline & multi-model evaluation
├── NVDA_trained_model.ipynb     # Model training (LSTM, GRU, XGBoost, ARIMA)
├── Stock_data.ipynb             # Data collection, cleaning & split validation
├── Stock_visualisation.ipynb    # Technical indicator visualizer & risk charts
├── dataset_cleaning.ipynb       # Outlier detection & feature normalization
├── latest_prediction.json       # Real-time serialized model outputs & confidence intervals
├── prediction_history.csv       # Historical validation log of forecasted vs actual closes
├── nvda_nextday_prediction.png  # Diagnostic forecast plot with confidence bounds
├── NVDA_dataset.csv             # Ingested OHLCV dataset
├── nvda_models/                 # Serialized weights (.h5, .pkl, .json)
├── LICENSE                      # MIT License
└── README.md                    # System documentation

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Quick Start & Execution

1. Prerequisites

• Python 3.10+
• Jupyter Notebook / JupyterLab or VS Code

2. Environment Setup

# Clone the repository
git clone https://github.com/Manimaran-tech/Stock_Analysis_NVDA.git
cd Stock_Analysis_NVDA

# Create and activate virtual environment
python -m venv .venv
source .venv/bin/activate  # On Windows: .venv\Scripts\activate

# Install dependencies
pip install numpy pandas scikit-learn xgboost tensorflow arch matplotlib seaborn plotly jupyter

3. Running Analysis & Generating Predictions

Launch Jupyter to execute the research notebooks:

jupyter notebook

• Open Stock_data.ipynb to update market inputs and calculate technical indicators.
• Open NVDA_trained_model.ipynb to retrain neural networks and feature regressors.
• Open NVDA_Predictions.ipynb to compute composite forecasts and export latest_prediction.json.

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Financial Risk & Quantitative Research Disclaimer

Important

Academic and Quantitative Research Scope:
This software is published strictly for educational, scientific, and quantitative research purposes. It does not constitute financial, investment, legal, or tax advice. Past simulated performance and statistical models do not guarantee future market returns.

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License

This project is licensed under the MIT License — see the LICENSE file for details.