Human Development Index Forecasting with Moving Average, Simple Exponential Smoothing and Naïve Method

,


INTRODUCTION
Human is the real nation's resources [1].Economic development viewed from the side of trade, investment, and technology sees humans as a tool to achieve growth, not as the purpose of development [2].Human development have seen all the issues in society simultaneously: the balance between economic growth, environment quality and social welfare [3] also cover the other important issue, which is gender [4].Therefore, human development pays attention to the social sector, and is a comprehensive approach from all sectors [2].United Nations for Development Programme (UNDP) introduced the measurement of human development in 1990 [5].UNDP introduced a new idea for measuring human development, the Human Development Index (HDI).Since then, HDI has been publicized periodically in the annual Human Development Report (HDR).HDI explained how the public can access development results in obtaining income, health, education, etc.According to UNDP, Human Development Index (HDI) measures human development achievement based on some basic life quality components.As the measurement of life quality, HDI is built through a basic 3-dimensional approach.These dimensions include: 1. a long and healthy life; 2. knowledge; and 3. a decent standard of living [2][6] [7].
The measurement of HDI is also performed in Indonesia, both at the country, provincial, and regency/city levels.West Nusa Tenggara's (NTB) HDI level is on the 29th out of 34 provinces in Indonesia [8].The NTB province consist of 10 regencies/cities [9].The lowest HDI is occupied by North Lombok Regency (KLU) [8], so it is interesting to forecast to assist the government in determining policy.Based on the HDI category set by [5], KLU's HDI is in the medium category [10].One of the steps that can be taken to determine a policy related to HDI is to forecast the HDI value [11].Based on [12] forecasting is a prediction about what will happen in the future using past and present data, while according to [13] forecasting is the result of prediction from future events that can be obtained from systematic process or intuition, thus it can be concluded that forecasting is a prediction of future events by processing the data of past and present time.
There are many methods of forecasting [14].Some initial steps to determine the right forecasting method are considering the amount of data, making the data plot to see the data or performing a preliminary analysis of the data [15].There are 13 past data on North Lombok Regency's HDI data [16], so there are several methods to forecast the HDI which is moving average (MA), simple exponential smoothing (SES) and Naïve method that can be used to forecast the future data with the limited amount of the past data.Furthermore, these methods have the advantage, which is the simplicity of forecasting calculation [17] [18].For example, the Naïve method that can forecast the tomorrow data only with one data today because in the Naïve method, tomorrow forecast is the actual value today.Moving average (MA), simple exponential smoothing (SES), or Naïve method have been used on the previous researches to forecast the HDI value.The previous researches were conducted by Mandailina et al in 2018 [19], Sucipto et al in 2018 [20], and Irawan et al in 2019 [21].In the research conducted by [15], [16] and [17] have the Mean absolute percentage error (MAPE) under 10%, even below 2%, dimana metode dengan MAPE yang dibawah 10% indicating that these methods is suitable and has high accuracy to forecast the HDI.
The of this research is to forecast North Lombok Regency's HDI using the Moving Average (MA), simple exponential smoothing (SES) and Naïve methods.The smallest MAPE will select the best method from these three methods.The best method will be used to forecast the North Lombok Regency's HDI value.It is expected that the HDI forecasting value in the coming year will assist the local government of North Lombok Regency in increasing the effectiveness of Policy-making associated with health, education and decent life society to increase the value of the regional HDI.

Data Time Series
Time series data consists of the variables collected according to time sequence in a certain period for a certain category or individual.When time is seen as discrete (time can be seen as continuous), the collecting frequency will always the same (equidistant).In discrete case, the frequency can be in seconds, minutes, hours, days, weeks, months, years, etc [22].This research will try to forecast the future data of North Lombok Regency's HDI by using the time series data of North Lombok Regency's HDI from 2010 until 2022, using three methods, which is Moving Average (MA), Simple Exponential Smoothing (SES) and Naïve method.The three methods' accuracy will be compared using Mean Absolute Percentage Error (MAPE).The method with the smallest MAPE will be chosen as the best, which will be used later to forecast the North Lombok Regency's HDI in 2023.

Moving Average (MA) Method
Moving Average method is the forecasting method which is done by taking a group of observation values to find the average value as the predition for the next period.This method is called the moving average because every time new data is available, a new average is calculated and used as the forecast value [23] [24].The advantage of this method is that it is very easy to understand and use in forecasting calculations compared to using trendline analysis, while the disadvantage is that the moving average method is slow to respond to data changes that often occur in the market [25].
There are several types of moving average methods:  Simple Moving Average (SMA) Simple Moving Average (SMA) is the simplest Moving Average and does not use weighting in forecasting calculations.Even though it is simple, SMA is effective enough to determine the trend that happened in the market.Even the data is convenient to read.Simple Moving Average (SMA) is calculated by collecting the average values from the HDI over a certain period of time [23].
[26] [27].Description:   = actual data from a certain period (t) n = amount of data  Weighted Moving Average (WMA) Weighted Moving Average (WMA) is an enhanced form of Simple Moving Average (SMA) which is giving more wight (  )to newer data than the older data.Means that the most recent data is more influential than older data in determining forecasting values.The weight factor is calculated from the number of days used in the time series data, also known as the number of digits [23][28].The newest data in EMA get the highest weight and every data values get less weight when we go back chronologically.It means that the most recent data is more influential than older data in determining forecasting values, but unlike WMA, in EMA, the weight for each old data point decreases exponentially, so it never reaches zero [23].

Simple Exponential Smoothing (SES)
Unlike the moving average, simple exponential smoothing put more pressure on the current time series through the use of a smoothing constant.Smoothing constant is possibly larger from 0 but smallest than 1.The value that closer to 1 put most pressure to the current value, while the value that closer to 0 put more pressure to the previous data point [23] [30].

Naïve Method
Naïve method is a simple forecasting method.whereas this method is often used as a comparison, because of the convenience in obtaining forecasting results.

Accuracy Measurement of the Forecasting Method
Data is often divided into two parts in time series analysis; data in sample and data out sample.The best model is the model with the minimum error.It is certainly expected to be the best model to fitting data in sample and also the good model to forecast data out [35].According to [36], the accuracy measurement of the model can use the calculation of Mean Absolute Percentage Error (MAPE) with the following equation [37]: Not accurate [38].

The Forecasting Algorithm
The algorithm used in this forecasting is as follows:

Data Tabulation and Descriptive Statistics
The discussion will being with tabulating data and making descriptive statistics as follows: The information obtained from the table 2 is North Lombok Regency's average HDI value is 61.57,where the data spread by 3.61 from the average.The lowest HDI in North Lombok Regency is 56.13 and the highest is 65.70, with the kurtosis value -1.18, so it can be said to be a platykurtic curve, which is a destribution that has an almost flat peak (kurtosis value < 3).On a platykurtic curve, the peaks of the curve are below the normal distribution, so that it can be said that the frequency of the modus values are close to the minimum or maximum frequency values.
Skewness also showed negative value -0.43 or the values is concentrated to the right side (located on the right side of Mo), so that the curve has a tail that extend to the left, its mean the average value is smaller than the mode value.

 Simple Moving Average (SMA)
The method used in this research is SMA MA3 and SMA MA5.SMA MA3 forecasted the HDI today by calculating the average value of 3 time series of the past HDI: 3(  ) =  −1 +  −2 +  −3 3 while SMA MA5 is the SMA method that forecasted the HDI values today by calculating the average values from 5 HDI's data in the past: For example if we want to forecast value at 2015 using SMA MA3 we have to calculating the average actual data from 2012 to 2014.But if we use SMA MA5 we have to calculating the average actual data from 2010 to 2014.The results of forecasting and MAPE SMA MA3 and SMA MA5 is as follows:

 Exponential Moving Average (EMA)
The MA method that used on this research are EMA MA3 and EMA MA5.The first calculation of   is using the equation ( 1) and followed by using the equation ( 3) to determine   on EMA method, both on MA MA3 and MA MA5.

Metode Simple Exponential Smoothing (SES)
This method used two  value, which are  = 0.1 and  = 0.9.On SES method with  = 0.1 (closer to 0) means the forecast put emphasis on the past data point.On the contrary, SES method with  = 0.9 (closer to 1) means the forecast put emphasis on the newest data point.The calculation of this method used the equation ( 4).

Naïve Method
The calculation of Naïve method forecasting results using the equation ( 5), which is the today forecasting results is the actual value of yesterday.The following is the results of forecasting and MAPE from North Lombok Regency's HDI using Naïve method.

Choosing the Best Method
The following is the list of method with the MAPE value, sorted from the method with the smallest to the highest MAPE.On the table 9, it can be seen that all of the methods has MAPE below 10%.This means that based on the category from table 1, the accuracy measurement scale on all of the nine method can be classified as highly accurate because of having MAPE below 10%.However, the Naïve method has been chosen as the best out of the nine methods because this method obtained the smallest MAPE.Thus, Naïve is used to forecast the HDI of North Lombok Regency in 2023.

North Lombok Regency's HDI Forecasting in 2023
Forecasting value   of North Lombok Regency's HDI based on Naïve equation method is: =  −1

Table 4 .
(2)ecasting and MAPE results from SMA MA3 and SMA MA5 Method The WMA method that being used is WMA MA3 dan WMA MA5, using the equation(2).The difference of WMA MA3 and WMA MA5 is the amount of data used on forecasting.WMA MA3 used 3 past data, while WMA MA5 used 5 past data.This is the forecasting calculation (  ) of HDI 2015 using WMA MA3 (and

Table 5 .
Forecasting and MAPE results from WMA MA3 dan WMA MA5

Table 6 .
Forecasting and MAPE results from EMA MA3 and EMA MA5 Method 1 :

Table 8 .
Forecasting and MAPE results from Naïve Method

Table 9 .
MAPE list from MA, SES and Naïve Method

Time Series Plot of Actual HDI Data vs Data According to the Naïve Method
⇒  2023 =  2022 = 65.7 Time Series Plot of North Lombok Regency's HDI in 2010-2022, Data According to HDI in 2010-1022, and forecasting result in 2023 using Naïve methodCONCLUSIONSThe best method to forecast HDI in North Lombok Regency is the method with the smallest MAPE, which is Naïve method with 1.32% as the amount of MAPE.This method is in the model category with high accuracy because it has a MAPE below 10%.The results of HDI in North Lombok Regency in 2023 using Naïve method generate a forecast of 65.7 which means that the HDI in North Lombok Regency has not changed.HDI in North Lombok Regency stay on middle level.It is necessary to adopt a policy that can increase the level of HDI in North Lombok Regency.