Data-Driven Forecasting of Liquor Sale in Ranchi, Jharkhand: Insights from ARIMA, SARIMA, and Prophet Models

Abstract The ability to accurately forecast time-dependent data is essential for informed decisionmaking in various domains, including supply chain management, finance, and public policy. This study presents a detailed comparative analysis of three widely adopted time series forecasting models—Autoregressive Integrated Moving Average (ARIMA), Seasonal ARIMA (SARIMA), and Prophet—applied to liquor Sale data from Ranchi. The dataset is examined at two distinct temporal resolutions, namely daily and monthly, to evaluate the sensitivity of each model to data granularity. The models are assessed using multiple performance indicators, including Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Symmetric Mean Absolute Percentage Error (SMAPE). The results indicate that ARIMA demonstrates superior performance for aggregated monthly data due to its effectiveness in modelling stable trends, whereas Prophet yields better results for daily data owing to its flexibility in capturing irregular fluctuations and multiple seasonal patterns. The study also identifies limitations in the use of MAPE for datasets with zero or near-zero values and emphasizes the importance of selecting appropriate evaluation metrics. Keywords— Time Series Forecasting, ARIMA, SARIMA, Prophet, Liquor Sale, RMSE, SMAPE, Sale Forecasting