ARIMA-ARCH Bitcoin Price Forecasting

This project forecasts Bitcoin prices in US$ using ARIMA for trend modeling and ARCH for volatility, leveraging daily data sourced from Kaggle.

Overview

• Objective: Predict Bitcoin prices, incorporating volatility.
• Dataset: Bitcoin BTC-USD Stock Dataset on Kaggle

Tools:

• ARIMA modeling in Minitab
• ARCH modeling in R

Methodology

1. Data Preparation:
   • Log transformation and first-order differencing to achieve stationarity.
2. ARIMA Model:
   • Selected ARIMA(2,1,0) based on ACF/PACF analysis using Minitab.
3. ARCH Model:
   • Fitted ARCH(8) model in R to capture conditional heteroscedasticity in residuals.
4. Forecasting:
   • Generated 95% one-step ahead forecast intervals using the ARIMA-ARCH model.

Results

• ARIMA-GARCH vs ARIMA: ARIMA-ARCH provides narrower, more precise forecast intervals.
• Model Accuracy: 5.63% forecast failures, consistent with a 95% prediction interval.

Plot

Below is the plot of the historical Bitcoin prices along with the ARIMA-ARCH one-step ahead 95% forecast intervals.