Akintunde mutairu oyewale
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Journal 04JOURNAL 08
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Further Applied Mathematics, 1 (2) (2021): 1-10 www.furthersci.com ON FORECASTING MALARIA INFECTION USING AUTOREGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA) MODELS. AKINTUNDE MUTAIRU OYEWALE Department of Statistics, Federal Polytechnic, Ede, Osun State Received: 11 April 2021; Accepted: 6 may 2021; Published: 12 May 2021 Abstract The study examines the forecast performance of ARIMA model with reference to monthly malaria data obtained from the record of federal Polytechnic, Ede Osun state from 2015 to 2019. The stationarity conditions of the series were examined using Augmented Dickey-Fuller test. At first difference the data become stationary, indicating that the malaria infection data is integrated of order 1. Twelve models were fitted which make up of six different specifications from each class of models. Akaike and Bayesian information criteria were used as benchmark to select optimal models. The optimal models comprise of from the group models and from the group models. ARIMA (1,1,3) and ARIMA (3,1,1) were compared using performance measure indices (RMSE, MSE, MAPE, MAE, and Theil U-inequality), with ARIMA (3,1,1) having better in-sample and out-of-sample forecast measures. Keywords: models, in and out of sample, forecast accuracy, correlogram, unit root, , 1. Introduction The need to project into the future is critical in all human endeavors, because a combination of a very excellent record of yesterday and today will reveal what the future will look like. Forecasting is the science of seeing into the future. Any model(s) that can't project into the future won't be effective for policymaking, and thus won't survive the test of time. When forecasting future situations, time series models remain an invaluable asset that could project into the future. Autoregressive integrated moving average model was applied by [7] for the determination of the seasonal variation of demand by making use of historical data and verified these models by checking its forecast performance. In enhancing forecast accuracy [10] combined seasonal factors in their model and calculated the seasonal factors using multiplicative model. [11] elongated [10] research utilized different connections between trend and seasonality within the context of seasonal ARIMA hypothesis. [3] explained Forecasting as an operation of making guess(es) into the future values of variables under study. ARIMA model is a classical or traditional model with so many applications in stock market data [12]. The approaches of statistical and artificial intelligence techniques are used to generate this model [12]; [2]. ARIMA model are applied in so many fields of human endeavour for example ARIMA models was applied by [14] to demonstrate time correlation and probability distribution to decide wind-pace time collection information problem. ARIMA model architecture was applied by [13] to forecast electricity price. [8] devised ARIMA model in the software program reliability. Several researchers have improved forecasting models prominent among models so improved are exponential method, regression model, GARCH model and many others. However, in the present study only related works that made use of ARIMA model in forecasting stock market data are cited, for more details one may consult [9]; [4]; [5]; [6]; [12]. In this paper the author used ARIMA model for forecasting malaria infection data, from which some results of forecasting were obtained. The results obtained from analysed data pointed to the potential asset of ARIMA model in offering potential academia, policy analyst and other would-be users the forecasting model that could assist in decision making. ARIMA model is divided into three components: The autoregressive component ( ), the differencing component ( ), and the moving average component ( ). The objective of this study is to forecast malaria infection at federal Polytechnic, Ede. Monthly data were obtained from the health record of the institution for the period 2015-2019. The remaining part of the paper is organized as follow section 2 covers mathematical specification of ARIMA model and stationarity test. Section 3 Empirical analysis with malaria data, illustration of stationarity test, results and discussion. Parameter estimation of ARIMA model, within and out of sample forecast performance of the model fitted. Section 4 and 5 are Conclusion and References. MATHEMATICAL SPECIFICATION OF THE MODEL USED ARIMA model in time series analysis is an extension of an autoregressive moving average model by introducing integration order. ARIMA models are fitted to time series data either to enhance the data performance or to forecast the future point. They are applied in cases when series are chaotic, volatile and not stable. The model is commonly referred to as the , where parameter p d, and q are positive integers that refer to the order of the autoregressive, integrated and moving average parts of the model respectively. ARIMA Model’s form is a very important part of the Box-Jenkins approach to time series modeling. The Autoregressive Integrated Moving Average Process is represented using the model Where and If and then the general model may be written as 2.2 STATIONARITY TEST Augmented Dickey Fuller test was employed to examine the stationary condition of the series used. This is defined as Where is a constant, is the coefficient on a time trend and is the lag order of the autoregressive process. The following is the hypothesis of the Augmented Dickey-Fuller test: : The data is stationary and does not need to be differentiated : The data is non-stationary and must be differentiated to achieve stationarity. 3,0 EMPIRICAL ANALYSIS WITH MALARIA DATA The study relied on monthly malaria data obtained from the records of the Federal Polytechnic in Ede, Osun state, from 2015 to 2019. 3.1 STATIONARITY TEST Tables 1 and 2 show the results of the series' stationarity tests (Malaria infection). We reject the null hypothesis that the data is stationary and does not require differentiation at any level because both AIC and BIC are less than the critical value. However, at the first difference, an alternative hypothesis was accepted, implying that the series is non-stationary and should be differentiated as such. TABLE 1: STATIONARITY TEST AT LEVEL
TABLE 2: STATIONARITY TEST AT FIRST DIFFERENCE
3.2 RESULTS AND DISCUSSION After determining the series' stability at the first difference, we proceeded to analyze the series. Six different and six different models were fitted. The optimal models are from the class of models and from the class of models, as shown below.: TABLE 3: AIC AND BIC VALUES FOR FITTED
TABLE 4: AIC AND BIC VALUES FOR FITTED
3.3 PARAMETER ESTIMATION FOR THE ARIMA MODEL FITTED and ARIMA are fitted and their parameters are estimated in tables 5 and 6 below. TABLE 5: MODEL PARAMETER ESTIMATES
The mathematical specification of the model fitted is stated below TABLE 6: MODEL PARAMETER ESTIMATES
In the same way as given above the mathematical specification of the model fitted is stated below 3.4 WITHIN-SAMPLE FORECAST PERFORMANCE OF AND MODELS To evaluate the within-sample forecast performance of the models fitted, indices such as RMSE, MSE, MAPE, MAE, and Theil U-inequality were used. The performances of the two models are competitive based on the eight performance indices used, but outperformed ) as shown below: TABLE 7: IN-SAMPLE FORECAST PERFORMANCE OF AND MODELS
3.5 IN-SAMPLE FORECAST PERFORMANCE OF AND MODELS The same performance measure indices that were used previously were used to evaluate the out-of-sample forecast performance of the models and In this case, eight performance indices were used; the performances of the two models are comparable, but ) outperformed as illustrated in table 8 below: TABLE 8: OUT- OF SAMPLE FORECAST PERFORMANCE OF AND MODELS
CONCLUSION This paper focuses on modeling and forecasting Malaria infection using ARIMA models. The series' stationarity was examined and found to be stable at first difference using the Augmented Dickey- Fuller test. Following that, we analyzed the data using ) and . These models were chosen based on how well they fit the series under study. The model fitted for in and out of sample forecast performance results show that ) performed better than for the two forecast scenarios (the in and out of samples forecast). It should be noted that the two models are competitive; in the absence of ), we can make do with Download 165.69 Kb. Share with your friends:
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