Time series modeling of fertiliser demand in kenya

Abstract

The agricultural sector is the backbone of the Kenyan economy, contributing approximately 33% of the Gross Domestic Product. The agriculture sector employs more than 40% of the total population and 70% of the rural population. However, agricultural productivity has stagnated recently due to various constraints, including poor agronomic practices such as fertiliser application. One of the major constraints in crop production is the timeliness of fertiliser application. If fertilisers are applied too early or too late, plants might not absorb the nutrients efficiently, leading to reduced growth and lower yields. Understanding the patterns of fertiliser demand helps in better planning and management of fertiliser supply chains, ensuring that farmers have access to the right types and amounts of fertilisers when they need them most. Therefore, there is need to understand the demand for fertiliser across different agroecological zones and its timely delivery to the farming communities. The objective of this study was to apply time series forecasting techniques to model fertiliser demand in Kenya based on the secondary monthly data from 2010 – 2023. The data was obtained from the Ministry of Agriculture and Livestock Development headquarters in Nairobi, Kenya. R- Studio software (version 2023.12.1+402) was utilised to analyse data for descriptive statistics, fertiliser demand variability, and model fitting. The Box-Jenkins method was used to model and forecast fertiliser demand variability. The findings of this study indicated that the demand for fertilisers is seasonal. In addition, fertiliser demand in Kenya experiences significant demand fluctuations over time due to the seasonality of the agricultural practices. STL decomposition was applied to separate the time series data into trend, seasonal, and residual components, allowing for a clear analysis of seasonal patterns and underlying trends. This study also found that the demand for various types of fertilisers varied from month to month, and the demand was high during the months of March, April, July, August, October and November. The Akaike Information Criterion (AIC) test was used to compare different SARIMA models, with lowest AIC values indicating better model fit and complexity balance. The study's findings revealed that the demand for different types of fertilisers can be modelled by the following Seasonal Autoregressive Integrated Moving Average (SARIMA) models: Calcium nitrate; SARIMA (1,1,1) (0,0,1)[2], Diammonium Phosphate; SARIMA (0,0,0) (2,0,0)[12], Muriate of potash; SARIMA (1,1,4) (0,0,1)[12], NPK; SARIMA (2,0,0) (2,0,0)[12], Calcium ammonium nitrate; ARIMA (0,0,0)w/mean, Urea; ARIMA (0,1,1) and total fertiliser demand SARIMA; (1,1,4) (0,0,1)[12]. Most fertilisers, especially Diammonium Phosphate, Muriate of Potash, and Nitrogen, Phosphorus and Potassium Fertiliser, exhibited clear yearly seasonal patterns, likely corresponding to specific planting or growth seasons. Some fertilisers, such as Urea and Muriate of Potash, exhibit trends and short-term fluctuations, while others like Calcium Ammonium Nitrate are more stable. Fertilisers such as Muriate of Potash and total demand have complex demand dynamics, requiring more sophisticated models to capture both seasonal and non-seasonal components. The study recommends exploring other forecasting methods, such as machine learning models and SARIMAX models that account for seasonal and non-seasonal components and external factors in the model.