Robust Estimation of Single Exponential Smoothing through Kalman Filter: An Application to Agricultural and Allied Commodities - Amit Saha; K.N. Singh; Bishal Gurung; Achal Lama; Santosha Rathod; Ravindra Singh Shekhawa (Journal of the Indian Society of Agricultural Statistics, 2025)
Time series modelling utilizes previous values to forecast the future values. Exponential smoothing is one of the approaches to make forecast as well as to smooth the time series data. Among the various exponential smoothing model, Single Exponential Smoothing (SES) is the most popular model in time series due its simplicity of understanding and implementation. On the other hand, state space methodology is a very useful technique to solve various problems in time series which is required to improve a system over time. This state space methodology can be used to represent various time series models including Autoregressive Integrated Moving Average (ARIMA). Kalman filter technique is an approach to estimate the time-dependent parameters. One heartening feature of Kalman filter is that it provides the minimum mean squared error (MSE) estimates for linear model. In present study, an attempt has been made to represent the SES in state space form and parameters are estimated using Kalman filter in conjunction with prediction error decomposition form of the likelihood function. An illustration has been given with different applications in agricultural domain. It has been seen that state space form of SES provides lower MSE compared to traditional SES. This integration of SES with state space formulations in agricultural domain will open a new era in agricultural modelling and forecasting.