Comparing the Forecasting Power of ARIMA, SARIMA, and Holt-Winters Models.
Chapter 1: Introduction
1.0: Background of the study
Forecasting is the technique of obtaining future information based on the past and present information. Forecasting is widely applied in business organizations and companies. Most business firms and production companies use time series as the forecasting tool. Time series can be defined as a sequence of events taken over time. Time series analysis has four components that are trend, cyclical, seasonality, and irregular component.
ARIMA, SARIMA, and Holt-Winters are time series models that are widely used in forecasting. ARIMA (Auto-Regressive Integrated Moving Average) model is also called the Box-Jenkins model because it was developed by Box and Jenkins in 1960 (George E. P. Box, Gwilym M. Jenkins, Gregory C. Reinsel, Greta M. Ljung, 1993). ARIMA model assumes non-zero autocorrelation between the successive values of a time series data. ARIMA model is applicable only when the series is stationary. If the series is not stationary, then it has to be made stationary through differencing. A stationary time series is the one which is independent of time that is mean and variance are constant over time.
ARIMA prediction equation for a stationary time series is always linear. The exponential smoothing model, random walk, and autoregressive models are a special case of the ARIMA model. ARIMA model is denoted by ARIMA. ARIMA is called the autoregressive process of order p also denoted as AR and ARIMA is the moving average process of order q also denoted as MA. ARIMA is called the random walk process denoted by
.
SARIMA (Seasonal Autoregressive Integrated Moving Average) model is a stochastic linear model that models seasonal time series. SARIMA model is an extension of the ARIMA model. It was proposed by Box and Jenkins for seasonal time series. It is appropriate for stationary time series that is mean, variance, and autocorrelation function are constant over time (Mathenge, 2019). Seasonal differencing of appropriate order is performed to remove non-stationarity.
1.1: Problem Statement
Forecasting is the technique of making projections about the future based on past and present information. In time series we obtain future information by using models like ARIMA, SARIMA, Holt-Winters, ARFIMA, and ANN. Forecasting is mainly done in business firms and production companies. In business, forecasting is done to obtain future information about sales whereas, in production, forecasting is done to obtain more information about future output. Due to improving the forecasting accuracy, a lot of studies and researches have been done to determine the best model that can improve the forecasting accuracy.
The idea behind determining the best model that improves forecasting accuracy formed a basis for this research work. I was therefore motivated to compare the forecasting power of ARIMA, SARIMA, and Holt-Winters models in order to determine the best forecasting model that can be used by business organizations and production companies to obtain accurate future information.
1.2: Objectives
1.2.1: General Objective
The general objective of the study is to compare the forecasting power of ARIMA, SARIMA, and Holt-Winters models to determine the best forecasting model that improves forecasting accuracy.
1.2.2: Specific Objectives
- To develop ARIMA, SARIMA, and Holt-Winters models.
- To determine the best forecasting model by comparing between ARIMA, SARIMA, and Holt-Winters models.
1.3: Research Hypothesis
SARIMA model is more accurate than the ARIMA model.
ARIMA model is more accurate than the Holt-Winters model.
1.4: Research Question
Which forecasting model is more accurate between ARIMA, SARIMA, and Holt-Winters models?
1.5: Justification
The forecasting technique is widely applied in business organizations and manufacturing companies. Accurate sales forecasting is the best tool to acquire a good estimate of future demand. It enables business firms to monitor sales and avoid unnecessary spending. The best sales forecasting helps companies avoid overstocking and stock-out situations, it enable an individual to start a new business. Also with accurate forecasting of revenue, sales, and expenses enable business organizations to maximize profit. Accurate demand forecasting helps manufacturers maintain their competitive position in the growing market.
Since accurate forecasting is viewed as the backbone of successful business companies and production firms, thus the best model has to be identified in order to give accurate forecasted results. Therefore the urge to compare the forecasting power of ARIMA, SARIMA and Holt-Winters models to determine the best model that can be used by business organizations and companies to give accurate forecasting results.
1.6: Scope of the study
The study is centered on time series modeling with an aim to compare the forecasting power of ARIMA, SARIMA, and Holt-Winters models. The study will make use of the petrol sales dataset which will be collected from the Total petrol station Kitale town, Trans-Nzoia County.