Mathematics and Statistics 7(4A): 29-40, 2019 http://www.hrpub.org DOI: 10.13189/ms.2019.070705 Application of ARIMAX Model to Forecast Weekly Cocoa Black Pod Disease Incidence Ling, A. S. C. 1,* , Darmesah, G. 2 , Chong, K. P. 2 , Ho, C. M. 2 1 Malaysian Cocoa Board, Wisma SEDCO, Locked Bag 211, 88999 Kota Kinabalu, Sabah, Malaysia 2 Faculty of Science and Natural Resources, Universiti Malaysia Sabah, Jalan UMS, 88400 Kota Kinabalu, Sabah, Malaysia Received July 1, 2019; Revised September 8, 2019; Accepted September 23, 2019 Copyright©2019 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of the Creative Commons Attribution License 4.0 International License Abstract The losses caused by cocoa black pod disease around the world exceeded $400 million due to inaccurate forecasting of cocoa black pod disease incidence which leads to inappropriate spraying timing. The weekly cocoa black pod disease incidence is affected by external factors, such as climatic variables. In order to overcome this inaccuracy of spraying timing, the forecasting disease incidence should consider the influencing external factors such as temperature, rainfall and relative humidity. The objective of this study is to develop a Autoregressive Integrated Moving Average with external variables (ARIMAX) model which tries to account the effects due to the climatic influencing factors, to forecast the weekly cocoa black pod disease incidence. With respect to performance measures, it is found that the proposed ARIMAX model improves the traditional Autoregressive Integrated Moving Average (ARIMA) model. The results of this forecasting can provide benefits especially for the development of decision support system in determine the right timing of action to be taken in controlling the cocoa black pod disease. Keywords ARIMAX, Black Pod, Climate, Cocoa, Forecasting 1. Introduction Black pod or Phytophthora pod rot is the most economically important and widespread disease of cocoa, Theobroma cacao L. in Malaysia. The losses due to Phytophthora exceed $400 million worldwide [1]. Among the Phytophthora spesies which attacked the cocoa, Phytophthora palmivora is the most widely distributed in the world and it caused global yield loss of 20-30% and tree deaths of 10% annually [1]. The intensity of black pod disease in cocoa was influenced by numerous climatic parameters such as rainfall, temperature and high humidity as reported by Thorold [2,3], Dakwa [4], Wood [5] and Mpika [6]. Both rainfall and relative humidity has strong correlation which encourages pathogen sporulation by reproduction of zoospores to infect the cocoa pods while the optimum temperature is propitious to black pod symptom development [2-6]. It is important to quantify the black pod disease fluctuations due to the real effect of climatic parameters. Understanding the effect of the climatic variables on the cocoa black pod incidence can identifying the suitable management options such as fungicide spraying and culture practices to control the disease incidence under projected climate change scenario. The time-fractional partial differential equation was widely used in study the mathematical biology including the description of plant disease epidemic [7] but need the numerical approach to solve the equation. Another approach was developing the time series model especially auto-regressive moving average (ARIMA) described by Box and Jenkins [8] that widely used in forecasting where it used the historical sequences of observations to do the forecasting. In agriculture, ARIMA model used to forecast the annual production of several crop in countries that relied the crop for daily life or economy, for example production of rice [9], wheat [10], coffee [11] and cocoa [12]. As for the disease monitoring program, ARIMA model was used to predict Botrytis cinerea spore concentrations that caused grey mould in Spain and assist in deciding number of treatments needed [13]. In cocoa, it is very useful in forecasting the cocoa black pod incidence to understand the effect of previous incidence on the current incidence. However, ARIMA model along can’t quantify the effect of climate variables on the cocoa black pod disease incidence and help in decision making process. The key problem is how to incorporate the climate information into the forecasting process and subsequently into the decision making process. When an ARIMA model CITE THIS PAPER [1] Ling, A. S. C. , Darmesah, G. , Chong, K. P. , Ho, C. M. , "Application of ARIMAX Model to Forecast Weekly Cocoa Black Pod Disease Incidence," Mathematics and Statistics, Vol. 7, No. 4A, pp. 29 - 40, 2019. DOI: 10.13189/ms.2019.070705.