Bitcoin Price Forecasting — ARIMA & VAR with Granger Causality

Master's Capstone Project | Time-Series Econometrics Built forecasting models for Bitcoin prices over a 30-day horizon using ARIMA and VAR models with 95% confidence intervals, and determined Granger causality relationships between Bitcoin, Euro/USD, Gold, S&P 500, and Crude Oil.

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Table of Contents

• Overview
• Research Questions
• Methodology
• Key Results
• Project Structure
• Installation
• Usage
• Technologies

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Overview

Cryptocurrency markets are characterized by high volatility, non-linear dynamics, and complex interdependencies with traditional financial assets. This project applies classical econometric time-series methods to:

1. Forecast Bitcoin prices 30 days ahead using two complementary models:

   • ARIMA — univariate model exploiting Bitcoin's own autocorrelation structure
   • VAR — multivariate model capturing cross-asset spillover effects

2. Quantify uncertainty with 95% confidence intervals around all point forecasts

3. Test Granger causality — empirically determine whether macroeconomic variables (EUR/USD, Gold, S&P 500, Crude Oil) contain statistically significant predictive information about Bitcoin returns

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Research Questions

• Does including macroeconomic asset prices improve Bitcoin price forecasts over a univariate model?
• Which assets Granger-cause Bitcoin returns, and in which direction?
• How do the ARIMA and VAR 30-day forecasts compare in terms of point estimates and uncertainty bands?

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Methodology

1. Data Collection

Daily closing prices from Yahoo Finance (2018–2024) for:

Asset	Ticker	Role
Bitcoin	BTC-USD	Target
Euro/USD	EURUSD=X	Currency / macro
Gold Futures	GC=F	Safe-haven asset
S&P 500	^GSPC	Equity market sentiment
Crude Oil	CL=F	Commodity / energy

2. Preprocessing

• Log-returns: $r_t = \ln(P_t / P_{t-1})$
• Augmented Dickey-Fuller (ADF) test confirms stationarity of log-returns

3. Granger Causality

Pairwise Granger causality tests (max lag = 5) with F-test p-values at α = 0.05.

4. ARIMA

• Optimal (p, d, q) order selected by auto_arima (AIC criterion)
• Fitted on log(BTC price); forecasts back-transformed to USD
• 95% CI from analytical forecast error variance

5. VAR

• Lag order selected by AIC (max 15 lags)
• Fitted on multivariate log-return system
• Forecasts integrated to reconstruct price levels
• 95% CI propagated via cumulative forecast covariance

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Key Results

Stationarity

All price levels are I(1); log-returns are I(0) — confirmed by ADF tests across all five series.

Granger Causality

Significant predictive relationships found between the macroeconomic variables and Bitcoin returns, particularly from S&P 500 and EUR/USD, empirically justifying the multivariate VAR approach.

Forecasts

Both models produce 30-day forecasts with widening confidence intervals reflecting compounding uncertainty over the horizon. The VAR model incorporates cross-market information; ARIMA serves as the interpretable univariate baseline.

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Project Structure

bitcoin-price-forecasting/
│
├── README.md
├── requirements.txt
├── main.py                          # End-to-end pipeline runner
│
├── notebooks/
│   └── Bitcoin_Price_Forecasting.ipynb   # Full analysis (recommended entry point)
│
├── src/
│   ├── __init__.py
│   ├── data_collection.py           # Yahoo Finance downloader
│   ├── preprocessing.py             # Log returns + ADF tests
│   ├── granger_causality.py         # Pairwise Granger tests
│   ├── arima_model.py               # ARIMA fitting + forecasting
│   ├── var_model.py                 # VAR fitting + forecasting
│   └── visualization.py            # All plotting functions
│
├── data/
│   └── raw_prices.csv               # Cached downloaded data
│
└── results/
    ├── 01_normalized_prices.png
    ├── 02_correlation_heatmap.png
    ├── 03_granger_heatmap.png
    ├── 04_arima_forecast.png
    ├── 05_var_forecast.png
    ├── 06_combined_forecast.png
    ├── 07_return_distribution.png
    └── forecast_summary.csv

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Installation

# 1. Clone the repository
git clone https://github.com/YOUR_USERNAME/bitcoin-price-forecasting.git
cd bitcoin-price-forecasting

# 2. Create and activate a virtual environment (recommended)
python -m venv venv
source venv/bin/activate        # macOS / Linux
venv\Scripts\activate           # Windows

# 3. Install dependencies
pip install -r requirements.txt

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Usage

Option A — Jupyter Notebook (Recommended)

jupyter notebook notebooks/Bitcoin_Price_Forecasting.ipynb

The notebook walks through every step with explanations, equations, and inline visualizations.

Option B — Command-Line Pipeline

python main.py

Runs the full pipeline and saves all plots + CSV summary to results/.

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Technologies

Library	Purpose
yfinance	Financial data download
pandas / numpy	Data manipulation
statsmodels	ADF, VAR, ARIMA, Granger
pmdarima	Automatic ARIMA order selection
matplotlib / seaborn	Visualization
scikit-learn	Supplementary metrics

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References

1. Box, G. E. P., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley.
2. Sims, C. A. (1980). Macroeconomics and reality. Econometrica, 48(1), 1–48.
3. Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37(3), 424–438.
4. Hyndman, R. J., & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). OTexts.

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This project was developed as part of a Master's programme in Data Science / Financial Analytics. All data is sourced from public financial markets via Yahoo Finance.