Estimating and forecasting bitcoin daily prices using ARIMA-GARCH models

Abstract

PurposeThe goal of the study is to offer important insights into the dynamics of the cryptocurrency market by analyzing pricing data for Bitcoin. Using quantitative analytic methods, the study makes use of a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and an Autoregressive Integrated Moving Average (ARIMA). The study looks at how predictable Bitcoin price swings and market volatility will be between 2021 and 2023.Design/methodology/approachThe data used in this study are the daily closing prices of Bitcoin from Jan 17th, 2021 to Dec 17th, 2023, which corresponds to a total of 1065 observations. The estimation process is run using 3 years of data (2021–2023), while the remaining (Jan 1st 2024 to Jan 17th 2024) is used for forecasting. The ARIMA-GARCH method is a robust framework for forecasting time series data with non-seasonal components. The model was selected based on the Akaike Information Criteria corrected (AICc) minimum values and maximum log-likelihood. Model adequacy was checked using plots of residuals and the Ljung–Box test.FindingsUsing the Box–Jenkins method, various AR and MA lags were tested to determine the most optimal lags. ARIMA (12,1,12) is the most appropriate model obtained from the various models using AIC. As financial time series, such as Bitcoin returns, can be volatile, an attempt is made to model this volatility using GARCH (1,1).Originality/valueThe study used partially processed secondary data to fit for time series analysis using the ARIMA (12,1,12)-GARCH(1,1) model and hence reliable and conclusive results.