Statistical Modelling of Monthly Petroleum Product Sales: Trend, Seasonality and Stationarity Analysis of Premium Motor Spirit and Automotive Gas Oil in Plateau State, Nigeria
Reliable statistical modeling of petroleum product sales requires a thorough understanding of their underlying trend, seasonal behavior, and stationarity characteristics before forecasting models can be appropriately specified. While previous studies have largely focused on crude oil prices and national-level petroleum indicators, empirical evidence on depot-level sales dynamics in Nigeria remains limited. This study statistically examines the trend, seasonality, and stationarity properties of monthly sales of Premium Motor Spirit (PMS) and Automotive Gas Oil (AGO) at the Nigerian National Petroleum Company (NNPC) Limited Plateau Depot, Nigeria, using 72 monthly observations covering January 2020 to December 2025. Descriptive statistics, graphical time series analysis, classical seasonal decomposition, and the Augmented Dickey–Fuller (ADF) unit root test were employed to identify the underlying characteristics of the series and determine the appropriate transformations required for statistical time series modeling. The results revealed that PMS sales exhibited a significant upward trend until early 2022, followed by a gradual decline, together with pronounced annual seasonality and non-stationarity. In contrast, AGO sales fluctuated around a relatively stable mean, indicating level stationarity despite exhibiting clear seasonal variations associated with agricultural and commercial activities. The ADF test confirmed that first differencing was necessary to achieve stationarity for PMS, whereas AGO remained stationary at level but required seasonal differencing for seasonal model development. These findings establish the statistical properties and transformation requirements necessary for robust ARIMA and SARIMA modeling, while providing valuable insights for petroleum inventory management, demand planning, and operational decision-making. The study contributes to the limited literature on depot-level petroleum sales analysis in Nigeria and provides a statistical foundation for subsequent forecasting of petroleum product demand.
Keywords: Petroleum product sales; Statistical time series modeling; Trend analysis; Seasonal decomposition; Stationarity; Augmented Dickey–Fuller test; Premium Motor Spirit; Automotive Gas Oil; Nigeria.
