A New Model of Poverty Index Prediction Using Triple Exponential

Smoothing Method

Kristoko Dwi Hartomo Faculty of Information Technology, Satya Wacana Christian University,

Salatiga, Indonesia kristoko@uksw.edu

Sri Yulianto Faculty of Information Technology, Satya Wacana Christian University,

Salatiga, Indonesia sri.yulianto@uksw.edu

Asni Valentina Faculty of Information Technology, Satya Wacana Christian University,

Salatiga, Indonesia 672013143@student.uksw.edu

Abstract—High poverty rate has been a main problem of Indonesia, especially in the Central Java Province. The province itself set a target to reduce its poverty rate by 6.84% or 1.36% per year. However, it only managed to reduce poverty rate less than 1% per year. Based on this problem, this research predicts poverty index using Triple Exponential Smoothing: Brown's One – Parameter Quadratic. The spatial model of this research aims to map the actual and predicted figures of poverty index in the Central Java Province. Our prediction results of poverty index using Triple Exponential Smoothing show relatively small error value with accuracy of 85.38%. This research contributes to provincial governments in distributing aids to poor population and eventually in reducing poverty rate.

Index Terms—Poverty Prediction; Triple Exponential Smoothing; Spatial Model; Accuracy.

I. INTRODUCTION

Poverty is a fundamental problem of developing countries around the world. Accelerating the poverty alleviation requires concerted efforts that consists of target setting, program design and coordination, monitoring and evaluation, and budget effectiveness of these programs [1][2]. One of the main causes of high poverty rate is delayed aid distribution to poor areas that eventualy is driven by less accurate prediction of poverty index and the absence of spatial model of poverty index prediction as the basis of aid distribution by related local government units [3][[4][5].

The Multidimensional Poverty Index (MPI) has been published by the HDRO in the annual Human Development Report since 2010. Up until the 2013 Human Development Report (see below), it was based on an index developed by Alkire & Santos at the Oxford Poverty and Human Development Initiative (OPHI) [6]. It is a particular form of a class of multidimensional poverty indices using a dual cut-off approach to identify the multidimensionally poor [7]. Since its introduction, there has been a vigorous debate on the conceptual and empirical merits and problems of the MPI [8][9]. It is impossible to do justice to all the points that have been raised. In particular, it is very difficult to come to definitive judgments on some of the conceptual issues surrounding the MPI. Many of the points raised in this discussion are essentially value

judgments about the desirable and undesirable features of the MPI, relative to potential ‘competitors’.

This paper use UML to develop spatial model of poverty index spatial using triple exponential smoothing : brown’s one-parameter quadratic. The model produced can determine regional poverty level in the Central Javaprovince. This research facilitates poor areas prediction and mapping that will be visualized into Central Java Province thematic map so that stakeholders are better able to monitor poor areas and implement poverty alleviation program better and more effectively.

II. THE PROPOSED METHOD The first step of our research is identifying poverty

problems, government tend to pay less attention to potentially poor regions because there is no spatial prediction model of poverty index in the Central Java Province. Next, the second stage is the literature review and data analysis. We conduct short-term poverty index prediction (one-period-ahead) using the Triple Exponential Smoothing: Brown’s One-Parameter Quadratic method [10][11].

We predict the 2015 poverty rate based on the historical data of 2006-2014 for all regencies and cities in the Central Java Province. The initialization on exponential quadratic smoothing of brown can be very simple, if S′1 = S′′1= S′′′1. Prediction starts from period 2. It then can be said that in period 2 the value of S′2 , S′′2 dan S′′′2 can be determined using the first smoothing process of the equation 1 and followed by the second and third smoothing using the equation 2 and equation 3. In order to generate the smoothing value of a certain value, we use the equation 4 and 5. The results of smoothing process from the equations are then used to generate predicted value by using the equation 6. = + (1 − ) (1) = + (1 − ) (2) = + (1 ) (3) = 3 − 3 + (4) = ( ) ( − 2 + ) (5) = + + (6)

Fig. 1. The Proposed Model

We obtain our research data from Central Statistical Bureau of Central Java Province [2]. More specifically, we use the following data: macro data that consist of Head Count Index – P0 is the percentage of population living below poverty line, Proverty Gap Index – P1 measures the average expenditure gap of each poor resident toward poverty line. Higher index value implies wider expenditure gap of poor population relative to poverty line and index. The third data is the Proverty Severity Index-P2 that indicates expenditure distribution among poor population. Higher index value implies higher expenditure gap between poor population [2].

Figure 1 shows the first stage of data preprocessing, our experiment uses poverty index data of 35 regencies/ cities in Central Java Province. We use Index P0 or poverty percentage, P1 or poverty depth index, and P2 or poverty severity index in 2014. The next process is data cleaning by doing replace missing value to clear the poverty data of noise and distortion values [12]. The second stage is poverty index data prediction using triple exponential smoothing method. The third phase of testing the model, tests using the test size ME, RMSE, MPE, MAPE, MASE, and Euclidean Error to search results prediction error value [12].

Our research object is 35 regencies/ cities in the Central Java Province. We use three poverty indicators as suggested by BPS: Percentage of Poor Population (P0), poverty depth index (P1), and poverty severity index (P2). Our third stage involves model design and user interface design using Unified Modeling Language (UML). Figure 2 displays use case diagram.

Fig. 2. Use case diagram

Figure 2 shows functional design for users. The design has a function to further see poverty index data of each region (regency or city) in the Central Java Province in the form of Central Java Province thematic map. Besides the thematic map of the Central Java Province, we also present our data in the form of table and graphic. Graphic facilitates users in comparing data between regencies/ cities.

The next functions are extend. Users can download data in the table form with extension of .xls. However, if users only want to look at available data, they do not have to download the data. Here, admin’s role is processing predicted and actual data such as adding new data each year, converting data if there are mistakes in data inputting, and deleting unused data. User can also see regional mapping according to predicted index value, and prediction results one year ahead.

Activity Diagram at Figure 3 displays user admin’s activities operating model. The diagram indicates that admin will process all data in model. Initially, admin has to fill in the form of Login. If she mistypes username and password, she will be redirected to form Login page. However, if she types username and password correctly, she will enter the main page. The main page of user admin exhibit several functions, such as displaying data, adding actual data and prediction results, data conversion, and data deletion. Admin can opt available functions. Converted data will be processed further for being updated and updated data will be immediately displayed in the form of thematic map.

The fourth stage involves testing, testing process, and analysis of prediction results of poverty index with the method Triple Exponential Smoothing: Brown’s One-Parameter Quadratic that looks at error terms of prediction results. We use the test size ME, RMSE, MPE, MAPE, MASE, and Euclidean Error to search prediction results error value. The smaller the error value the more accurate the prediction results [10].

Design Of Spatial Model Of Poverty Index Prediction Using Triple Exponential Smoothing Method

Fig. 3. Admin’s Activity Diagram

We then classify regions into three groups with different

colors to represent the level of poverty percentage. Red color represents regions with high poverty percentage. Yellow for regions with medium poverty percentage, and green for regions with low poverty percentage [13]. In classifying the regions based on the poverty percentage, we refer to the data from Subdistrict Social Welfare Agency - Badan Tenaga Kesejahteraan Sosial Kecamatan [14].

GEODATA application requires two types of data, the attribute data obtained from the observation process regularly, includes data pests and rainfall data. Spatial data in form of vector is data entered at the time of application development and permanent. Vector data in the form of map data is in shape format files (ESRI format) [15].

Trend pattern and seasonal data will be more accurate with the use of Winters Exponential Smoothing which consists of : (1) exponential smoothing series, (2) trend estimation, (3) seasonal estimation, and (4) the following period forecasting [16].

III. EXPERIMENTAL RESULT

Based on Table 1, error value of prediction results with the Triple Exponential Smoothing method use error tests ME, RMSE, MAE, MPE, MAPE, and EE. The average error is relatively small (approaching 0), we perform accuracy test using constan value α=0.2 and our results indicate a good fit. The results of average of error value prediction test (ME) of 0.183 shows that the TES Brown’s One-Parameter Quadratic method can be used to predict povery index data. The average of prediction error tested with the Euclidean Error method is 14.623, implying that prediction accuracy is 85.38.

TABLE 1. Tests of average error of prediction results of P0, P1 dan P2 index in Central

Java Province 2015

Poverty Index ME RMSE MAE MPE EE

P0 -0.52 3.47 2.93 -9.73 9.20 P1 0.01 0.44 0.38 -7.53 8.86 P2 0.02 0.18 0.16 -22.93 25.81

Figure 4 is the spatial model of actual data of poverty depth index 2014. There are 16 regencies/ cities with low poverty percentage, namely: Jepara, Pati, Kudus, Tegal, Wonogiri, Sukoharjo, Boyolali, Batang, Temanggung, Semarang, Magelang, Surakarta, Salatiga, Semarang, Tegal, and Pekalongan. There are 9 regencies/ cities with moderate poverty percentage, namely Pekalongan, Blora, Sragen, Purworejo, Demak, Karanganyar, Kendal, Pekalongan, dan Klaten. Lastly, there are 10 regencies/ cities with high poverty percentage, namely Rembang, Grobogan, Wonosobo, Kebumen, Cilacap, Banyumas, Purbalingga, Pemalang, Brebes, dan Banjarnegara.

Fig. 4. Spatial model of poverty depth index data 2014

Fig. 5. Spatial model of predicted poverty index data 2015

Figure 5 is the spatial model that displays predicted poverty index one year ahead (2015) and visualized in the form of thematic map of the Central Java Province. Spatial model at Figure 5 shows that most regions (28 regencies/ cities) in the Central Java Province exhibit high poverty percentage. There are only two regions with moderate poverty category and 5 regencies/ cities with low poverty category. This prediction can be executed not only in regencies/ cities within the Central Java Province, but also all regencies/ cities throughout Indonesia so that each regency/ city can be classified based on its predicted value of poverty index.

IV. CONCLUSION AND SUGGESTION

The spatial model of predicted data of poverty index using

the method of Triple Exponential Smoothing: Brown’s One-Parameter Quadratic can produce prediction results of poor regions one year ahead. Governments can immediately distribute aids to potentially poor regions so that poverty rate decreases.

It is expected that further studies could increase the prediction accuracy by using ARIMA or kriggin spatial prediction methods and increase object details in the spatial models from village level to sub-village level (dusun).

ACKNOWLEDGMENTS

This research was conducted using Featured Grant PTUPT from Directorate General of Higher Education, Ministry of National Education Republic Indonesia year 2019 - 2021.

REFERENCES

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