Seemingly Unrelated Regression Approach for GSTARIMA Model to Forecast Rain Fall Data in Malang Southern Region Districts


CAUCHY - JOURNAL OF PURE AND APPLIED MATHEMATICS 
Volume 4(2) (2016), Pages 57-64 
 

Submitted: 17 February 2016 Reviewed: 1 March 2016 Accepted: 1 May 2016 
 

Seemingly Unrelated Regression Approach for GSTARIMA Model to Forecast Rain Fall 
Data in Malang Southern Region Districts  

Siti Choirun Nisak 

Department of Statistics, Faculty of Mathematics and Natural Sciences, Brawijaya University, Malang, 
Indonesia 

 

Email: nisak.statistika@gmail.com  

ABSTRACT 

Time series forecasting models can be used to predict phenomena that occur in nature. Generalized Space 
Time Autoregressive (GSTAR) is one of time series model used to forecast the data consisting the elements 
of time and space. This model is limited to the stationary and non-seasonal data. Generalized Space Time 
Autoregressive Integrated Moving Average (GSTARIMA) is GSTAR development model that accommodates 
the non-stationary and seasonal data. Ordinary Least Squares (OLS) is method used to estimate parameter 
of GSTARIMA model. Estimation parameter of GSTARIMA model using OLS will not produce efficiently 
estimator if there is an error correlation between spaces. Ordinary Least Square (OLS) assumes the 
variance-covariance matrix has a constant error 𝜀𝑖𝑗 ~𝑁𝐼𝐷(𝟎, 𝝈

𝟐) but in fact, the observatory spaces are 

correlated so that variance-covariance matrix of the error is not constant. Therefore, Seemingly Unrelated 
Regression (SUR) approach is used to accommodate the weakness of the OLS. SUR assumption is 
𝜀𝑖𝑗 ~𝑁𝐼𝐷(𝟎, 𝚺) for estimating parameters GSTARIMA model. The method to estimate parameter of SUR is 

Generalized Least Square (GLS). Applications GSTARIMA-SUR models for rainfall data in the region Malang 
obtained GSTARIMA models ((1)(1,12,36),(0),(1))-SUR with determination coefficient generated with the 
average of 57.726%.  

Keywords: Space Time, GSTARIMA, OLS, SUR, GLS, Rainfall. 

 

INTRODUCTION   

Time series data is data based on the sequence of time within a certain time span and 
modeled by time series models either univariate or multivariate [1]. If the data consists of the 
elements of time and space is modeled using multivariate models of space-time. One of the 
multivariate models are most often used for data modeling space-time is a Generalized Space-
Time Autoregressive (GSTAR) model introduced by [2]. GSTAR has limitations that can only be 
used for data space-time that are stationary and non-seasonal. This condition tends to not be met 
at the data that is not stationary and containing a seasonal pattern. 

GSTARIMA first implemented by Sun, et al. (2010) for forecasting traffic flow data in 
Beijing. GSTARIMA is the development of GSTAR model for data non-stationary and seasonal. 
GSTARIMA more flexible and practical for every space observatory has its own real-time 
parameter and not influenced by other changes in the observation location. 

A method that can be used in parameter estimation of GSTARIMA include Ordinary Least 
Square method (OLS) and approach to the system of equations Seemingly Unrelated Regression 
(SUR). OLS assumes the variance-covariance matrix has a constant error. Thus, the equations 
system of Seemingly Unrelated Regression (SUR) is used to overcome the weakness of the OLS. 

mailto:nisak.statistika@gmail.com


Seemingly Unrelated Regression Approach for GSTARIMA Model to Forecast Rain Fall Data in Malang 
Southern Region Districts 

Siti Choirun Nisak   58 
 

SUR equations system is used because it can accommodate correlations between space of the 
rainfall observatories. Parameter estimation of SUR can use the Generalized Least Square (GLS) 
method. Discussion and implementation of the model GSTARIMA still a bit to do so in this research 
will be modeling GSTARIMA approach SUR forecasting rainfall data in the region Malang with an 
observation location Jabung, Tumpang, Turen, Tumpuk Renteng, Tangkilsari, Wajak, Blambangan, 
Bululawang, Tajinan and Poncokusumo. 

 

LITERATURE REVIEW 

GSTAR (Generalized Space Time Autoregressive) Model 

GSTAR with order autoregressive (p) and spatial order (𝜆𝑝), or represented by GSTAR 

(𝑝, 𝜆𝑝) can be written in the equation: 

𝒛(𝒕) = ∑ [𝜱𝒌𝟎𝑾
(𝟎)𝒛(𝒕−𝒌) + ∑ 𝜱𝒌𝒔

𝜆𝑝

𝑠=1

𝑾(𝒔)𝒛(𝒕−𝒌)] + 𝒆(𝒕)

𝑝

𝑘=1

 (1) 

 
where : 

𝒛(𝒕)  : vector of location 𝑚 at time t 

𝜆𝑝  : spatial order from form of autoregressive p 

𝑾(𝑠)  : weighted matrix with size of 𝑚 ×  𝑚 
 𝜱𝒌𝒔   : autoregresive parameter at time lag 𝑘 and spatial lag 𝑠 
𝒆(𝒕) : error vector with white noise and normal multivariate distribution  

 
 

GSTARIMA (Generalized Space Time Integrated Autoregressive and Moving 
Average) Model 

Min, et al. (2010), defines the model GSTARIMA as follows: 
 

∆𝒅𝒛(𝒕) = ∑ ∑ 𝚽𝒌𝒍 𝑾
(𝒍)

𝝀𝒌

𝒍=𝟎

𝒑

𝒌=𝟏

∆𝑑 𝑧(𝑡 − 𝑘) − ∑ ∑ 𝚯𝒌𝒍𝑾
(𝒍)𝜖

𝒎𝒌

𝒍=𝟎

𝒒

𝒌=𝟏

(𝑡 − 𝑘) + 𝝐𝒕 (2) 

 

 

 
with: 

𝚽𝒌𝒍 = 𝑑𝑖𝑎𝑔(𝜙𝑘𝑙
1

, 𝜙𝑘𝑙
2

, … 𝜙𝑘𝑙
𝑁

) = [
𝜙𝑘𝑙

1

⋮
0

…
⋱
…

0
⋮

𝜙𝑘𝑙
𝑁

] 

𝚯𝒌𝒍 = 𝑑𝑖𝑎𝑔(𝜃𝑘𝑙
1

, 𝜃𝑘𝑙
2

, … 𝜃𝑘𝑙
𝑁

) = [
𝜃𝑘𝑙

1

⋮
0

…
⋱
…

0
⋮

𝜃𝑘𝑙
𝑁

] 

where, p and q is the order of the autoregressive and moving average, 𝜆𝑘  and 𝑚𝑘  is the spatial 
order k to autoregressive and moving average, and ∆𝒅𝒛(𝒕) is the observation vector 𝒛(𝒕) in order 
differencing to d. 𝝓𝒌𝒍  and 𝜽𝒌𝒍  are autoregressive and moving average parameters on the lag time 

to spatial lag k and l. 𝑾(𝒍) is the weighted matrix of size N x N and 𝝐(𝒕) is the vector of the 
residual that is random and normal with size n x 1. 
 

Seemingly Unrelated Regression (SUR) 

Seemingly Unrelated Regression (SUR) is an equation parameter estimation using General 
Least Square (GLS). SUR Model with m equations stated, 



 

Siti Choirun Nisak   59 

(

𝒚𝟏
𝒚𝟐
⋮

𝒚𝒎

) = (

𝑿𝟏
𝟎
⋮
𝟎

𝟎
𝑿𝟐
⋮
𝟎

…
…
⋱
…

𝟎
𝟎
⋮

𝑿𝒎

) (

𝜷𝟏
𝜷𝟐
⋮

𝜷𝒎

) + (

𝜺𝟏
𝜺𝟐
⋮

𝜺𝒎

) = 𝑿𝜷 + 𝜺 (3) 

 
The assumption of the model is a residual 𝜀𝑖𝑟  is independent at all times, but between 

equality / contemporary correlated location. 𝐸[𝜀𝑖𝑟 𝜀𝑗𝑠|𝑋] = 0 when r≠s and 𝐸[𝜀𝑖𝑟 𝜀𝑗𝑟|𝑋] = σij. 

Variance-covariance matrix is denoted by Ω. 

𝛀 = [

σ11𝐈𝑅 σ12𝐈𝑅 … σ1𝑚𝐈𝑅
σ21𝐈𝑅 σ22𝐈𝑅 … σ2𝑚 𝐈𝑅

⋮
σ𝑚1 𝐈𝑅

⋮
σ𝑚2 𝐈𝑅

⋱
…

⋮
σ𝑚𝑚 𝐈𝑅

] = 𝚺 ⊗ 𝐈𝑅 (4) 

 
SUR estimation by adding variance covariance matrix residual is stated as follows, 
 

�̂� =  (𝑿′(�̂�−𝟏 ⊗ 𝐈𝑹)𝑿)
−𝟏𝑿′(�̂�−𝟏 ⊗ 𝐈𝑹)𝐘 (5) 

 

With 

𝑟(�̂�) = 𝐸 [(�̂� − 𝜷)
𝟐

]

= 𝐸[(�̂� − 𝜷)(�̂� − 𝜷)′]

= 𝐸[{(𝑿′𝑿)−𝟏𝑿′𝜺}{(𝑿′𝑿)−𝟏𝑿′𝜺}′]

= 𝐸 [(𝑿′𝑿)−𝟏𝑿′𝜺𝜺′𝑿(𝑿
′𝑿)

−𝟏

]

= (𝑿′𝑿)−𝟏𝑿′𝑬[𝜺𝜺′]𝑿(𝑿′𝑿)−𝟏

= (𝑿′𝑿)−𝟏𝑿′𝛀𝑿(𝑿′𝑿)−𝟏

= (𝑿′𝛀−𝟏𝑿)
−𝟏

.

 

assuming 𝜺~𝑵(𝟎, 𝚺). SUR estimators use the information system more efficient than OLS because 
of the diversity in each equation is smaller, [3]. 
 

The precision model with MSE and R2 

Criteria for the good of the model can be determined based on the residual is the Mean 
Square Error (MSE). 

𝑀𝑒𝑎𝑛 𝑆𝑞𝑢𝑎𝑟𝑒 𝐸𝑟𝑟𝑜𝑟 (MSE) =
1

N
∑ et

2

N

t=1

 (6) 

 
where et = Zn+1 − �̂�𝑛(𝑙) and N is account of data. 

The coefficient of determination stating how great the diversity of the dependent variable 
(Y) can be explained by the independent variable (X). According Makridakis, et al. (1999), R2 is 
obtained from, 
 

𝑅2 = 1 −
∑ (∑ (𝑍𝑖(𝑡) − �̂�𝑖(𝑡))

2𝑇
𝑡=1 )

𝑁
𝑖=1

∑ (∑ (𝑍𝑖(𝑡) − �̅�𝑖(𝑡))
2𝑇

𝑡=1 )
𝑁
𝑖=1

 (7) 

where : 
𝑍𝑖(𝑡)     : dependen variable i 

�̅�𝑖(𝑡)     : mean of 𝑍𝑖(𝑡) 



Seemingly Unrelated Regression Approach for GSTARIMA Model to Forecast Rain Fall Data in Malang 
Southern Region Districts 

Siti Choirun Nisak   60 
 

�̂�𝑖(𝑡)     : predicted value of 𝑍𝑖(𝑡) 
 

METHODOLOGY 

Location of the study is the rainfall observatory stations in the in malang southern region 
districts. The stations are Tumpang, Wajak, Tajinan, Jabung, Poncokusumo, Turen, Tumpuk 
Renteng, Tangkilsari, Blambangan, and Bululawang. Data used is 10 days period of rainfall 
(dasarian) since the beginning of the dry season is determined based on the amount of rainfall in 
a single dasarian (10 days) of less than 50 mm and is followed by several subsequent dasarian. 
Meanwhile, the beginning of the rainy season is determined based on the amount of rainfall in a 
single dasarian (10 days) is equal or more than 50 mm and is followed by several subsequent 
dasarian [4]. 

Rainfall data used to build GSTARIMA-SUR model is a sample data for forecasting 
(insample). The insample data is dasarian rainfall data for the period may 2000 to April 2015. The 
other data is called outsample data that is used to validate the GSTARIMA-SUR models of the data 
in the period May-June 2015. 

Steps taken to form GSTARIMA-SUR model is started by exploration of rainfall data in the 
ten rainfall observatory stations, identification of univariate model (ACF and PACF) and 
multivariate model (MPACF and MCCF) to determine the order GSTARIMA, determination 
parameters of the model, model validation, and the last is forecasting rainfall data in the malang 
southern region districts and the surrounding region. 

 

RESULTS AND DISCUSSION 

Exploration data is used to easy for viewing the information on the data. exploration data 
can be presented in the form of graphs and descriptive data. Graph data movement precipitation 
10 locations this year May 2000 to April 2015 is shown in the form of a time series plot as in Figure 
4.1 below. 
 

 
Figure 4.1. Time series Plot of Rainfall data 

 

Based on Figure 4.1, known that movement pattern of rainfall data in 10 locations tend to 
be similar. High and low altitude change of rainfall data recorded in each period indicates the same 
pattern every year. 

Identification of the model is used to find the order of autoregressive and moving average 
for GSTARIMA model. The order of autoregressive lag is obtained from the identification of the 
real MPACF and the order of moving average lag is obtained from the identification of the real 
MACF, then from some real lag is chosen the best use of AIC. Lag which has the smallest AIC value 
will be used as the order of autoregressive and moving average for GSTARIMA model. Moreover 
to identification seasonal pattern use univariate identification by seeing ACF and PACF plot. 
Results of identification rainfall in malang southern region districts is 
GSTARIMA((1)(1,12,36),(0),(1))-SUR. 



 

Siti Choirun Nisak   61 

Estimation of parameters is done by inserting a weighted into the equation to describe the 
spatial relationship between the location of the post of rain. The weight of the locations used in 
this study is the inverse distance weighting location. 

 
 

Table 4.1 Inverse Distance Weighted Value 10 Pos Rain 

 
 

GSTARIMA-SUR models for rainfall in the Malang southern region districts can be 
expressed as follows: 

 
𝒁(𝒕) = 𝚽𝟎𝟏

(𝟏)𝒁(𝒕 − 𝟏) + 𝚽𝟏𝟏
(𝟏)𝑾𝒁(𝒕 − 𝟏) + 𝚽𝟎𝟏

(𝟐)𝒁(𝒕 − 𝟏𝟐) + 𝚽𝟏𝟏
(𝟐)𝑾𝒁(𝒕 − 𝟏𝟐) + 𝚽𝟎𝟏

(𝟑)𝒁(𝒕 − 𝟑𝟔)

+ 𝚽𝟏𝟏
(𝟑)𝑾𝒁(𝒕 − 𝟑𝟔) + 𝒆(𝒕) − 𝛉𝟎𝟏

(𝟏)
𝒆(𝒕 − 𝟏) + 𝛉𝟏𝟏

(𝟏)
𝑾𝒆(𝒕 − 𝟏) 

 
 

Based on the results of parameter estimation GSTARIMA ((1)(1,12,36),(0),(1))-SUR to 
Tumpang rain post is as follows: 

 

�̂�1(𝑡) = 0.236𝑧1(𝑡−1) + 0.102𝑧2(𝑡−1) + 0.038𝑧3(𝑡−1) + 0.024𝑧4(𝑡−1) + 0.015𝑧5(𝑡−1) + 0.007𝑧6(𝑡−1)
+ 0.05𝑧7(𝑡−1) + 0.026𝑧8(𝑡−1) + 0.037𝑧9(𝑡−1) + 0.041𝑧10(𝑡−1) + 0.026𝑧1(𝑡−12)
+ 0.009𝑧2(𝑡−12) − 0.017𝑧3(𝑡−12) + 0.003𝑧4(𝑡−12) + 0.005𝑧5(𝑡−12) − 0.004𝑧6(𝑡−12)
+ 0.005𝑧7(𝑡−12) − 0.002𝑧8(𝑡−12) − 0.004𝑧9(𝑡−12) + 0.001𝑧10(𝑡−12) + 0.147𝑧1(𝑡−36)
+ 0.121𝑧2(𝑡−36) + 0.023𝑧3(𝑡−36) + 0.007𝑧4(𝑡−36) + 0.006𝑧5(𝑡−36) + 0.02𝑧6(𝑡−36)
+ 0.029𝑧7(𝑡−36) + 0.014𝑧8(𝑡−36) + 0.022𝑧9(𝑡−36) + 0.019𝑧10(𝑡−36) + 𝑒1(𝑡)
+ 0.081𝑒1(𝑡−1) + 0.009𝑒2(𝑡−1) + 0.019𝑒3(𝑡−1) + 0.002𝑒4(𝑡−1) + 0.004𝑒5(𝑡−1)
− 0.005𝑒6(𝑡−1) + 0.011𝑒7(𝑡−1) + 0.012𝑒8(𝑡−1) + 0.003𝑒9(𝑡−1) + 0.015𝑒10(𝑡−1) 

 

Rainfall in the Tumpang Rain Post is influenced by the rain heading more in ten days and 
twenty days earlier and was influenced by weighting the location. In addition there is seasonality 
in the rainfall in the period a quarter of the year and annually. 

Based on the above model prediction results can be obtained in the data sample for the 
Tumpang rain post as follows: 

 

 
Figure 4.2 Forecasting using GSTARIMA((1)(1,12,36),(0),(1))-SUR in Tumpang Rain Post 

Pos Hujan turen
tumpuk 

renteng
wajak tumpang jabung

poncokus

umo
bululawang tajinan tangkilsari blambangan

turen 0 0.286 0.140 0.057 0.044 0.068 0.103 0.087 0.092 0.122

tumpuk renteng 0.226 0 0.179 0.055 0.041 0.067 0.111 0.098 0.101 0.121

wajak 0.123 0.200 0 0.082 0.055 0.118 0.097 0.130 0.103 0.090

tumpang 0.059 0.073 0.097 0 0.191 0.223 0.075 0.128 0.090 0.064

jabung 0.063 0.074 0.089 0.260 0 0.141 0.083 0.121 0.097 0.072

poncokusumo 0.072 0.090 0.141 0.227 0.105 0 0.078 0.129 0.090 0.069

bululawang 0.068 0.093 0.073 0.048 0.039 0.049 0 0.115 0.280 0.235

tajinan 0.069 0.099 0.117 0.098 0.068 0.097 0.138 0 0.218 0.097

tangkilsari 0.062 0.087 0.080 0.059 0.046 0.058 0.288 0.187 0 0.133

blambangan 0.099 0.125 0.084 0.050 0.041 0.053 0.290 0.100 0.159 0



Seemingly Unrelated Regression Approach for GSTARIMA Model to Forecast Rain Fall Data in Malang 
Southern Region Districts 

Siti Choirun Nisak   62 
 

 

Inspection accuracy of the model or the model validation is done by looking at the value 
of RMSE and R2 of the model. 
 

Table 4.2 Accuracy Test Model of GSTARIMA ((1),(1,12,36)(0)(1))-SUR Model in ten Rain Post  

Location RMSE R2 Prediction 

Tumpang 5.668 0.5052 

Tajinan 5.51 0.5716 

Poncokusumo 5.916 0.5146 

Blambangan 5.697 0.5935 

Bululawang 5.175 0.5805 

Wajak 5.899 0.5136 

Tumpuk Renteng 6.007 0.6476 

Jabung 5.337 0.5671 

Turen 6.119 0.6308 

Tangkilsari 5.263 0.6481 

 

R2 prediction for 10 observation locations is more than 50%. The greater the value of R2 
prediction obtained the greater, model can explain the rainfall distribution. The biggest prediction 
of R2 is Tangkilsari, that is equal to 0.6481. It can meaned that about 64.81% in Tangkilsari rainfall 
distribution can be explained by the model GSTARIMA ((1), (1,12,36) (0) (1))-SUR. 

The lowest R2 prediction is in Tumpang Area rainfall, but the prediction obtained R2 can 
still be said to be good for rainfall prediction for prediction obtained R2 values> 50%. If viewed 
from the RMSE and R2 prediction can be said that the rainfall distribution in ten observation 
locations have the same result by using modeling GSTARIMA ((1) (1,12,36) (0) (1))-SUR. 

 
Result forecast rainfall using GSTARIMA ((1),(1,12,36)(0)(1))-SUR model is: 

 
Table 4.3 Forecasting Rainfall Period of May-June 2015 

Month May June 

Locations 1 2 3 1 2 3 

Tumpang 7.157 8.254 6.642 5.503 3.241 1.438 

Tajinan 3.318 15.397 10.754 1.504 1.842 1.495 

Poncokusumo 5.702 3.069 6.390 6.610 3.309 1.179 

Blambangan 1.180 1.515 1.100 1.382 1.259 0.397 

Bululawang 9.392 2.592 6.521 4.620 3.943 0.490 

Wajak 1.509 1.143 1.343 1.401 1.468 0.031 

Tumpuk Renteng 5.360 3.440 3.025 4.704 2.654 1.073 

Jabung 5.981 1.204 1.291 0.851 1.090 0.962 

Turen 8.348 7.754 3.159 5.744 3.885 1.703 

Tangkilsari 7.406 1.766 2.010 1.669 1.947 1.160 

 



 

Siti Choirun Nisak   63 

 
Figure 4.3 Forecast for Period May-June 2015 in Malang Southern Region Districts 

 

Model validation is done by comparing the actual data of rainfall dasarian the period from 
May to June 2015 on the results of data using models forecasting GSTARIMA ((1),(1,12,36)(0)(1))-
SUR. If seen from Figure 4.3 can be said that result of forecasting data can approach the actual 
data. To better know the data equation then done two paired samples t test. Based on the results 
of two sample paired t test obtained by value t amounted to 1,958 with significant value 0095. t 
table with db = 59 values obtained 2,301, for t <t table (1.9585 <2,301) and the p-value is more 
than 0.05 (0095> 0.05) it was decided to accept H0. The conclusion of this validation test is that 
the rainfall dasarian data forecasting results do not differ significantly from the actual data, so the 
model GSTARIMA-SUR formed from in sample data can be used for forecasting rainfall dasarian 
next period. 

 

CONCLUSION 

Our analysis found that the GSTARIMA ((1)(1,12,36)-SUR model can be used to forecast 
the dasarian seasonal rainfall in the Malang Southern Region Districts. By using seasonal patterns 
in lag 1,12,36 more accurate forecasting result is obtained. To validate the model, MSE and R2 
prediction can be used. In this research, the largest R2 prediction is 57.726%. 
 

REFERENCE 

 

[1]  J. Rosadi, Pengantar Analisis Runtun Waktu, Diktat Kuliah, Program Studi Statistika, Fakultas 
Matematika dan Ilmu Pengetahuan Alam, Universitas Gajah Mada, Yogyakarta, Universitas Gajah Mada, 
2006.  

[2]  S. Borovkova, H. Lopuhaa and B. Ruchjana, "Generalized STAR model with experimental weights," in 
Proceedings of the 17th International Workshop on Statistical Modelling, 2002.  

[3]  H. R. Moon and B. Perron, "Seemingly unrelated regressions," The New Palgrave Dictionary of 
Economics, pp. 1-9, 2006.  

[4]  BMKG, Modul Diklat Badan Meteorologi Klimatologi dan Geofisika Karangploso Malang, BMKG, 2000.  

[5]  A. Zellner, "An efficient method of estimating seemingly unrelated regressions and tests for aggregation 
bias," Journal of the American statistical Association, vol. 57, no. 298, pp. 348-368, 1962.  

[6]  P. E. Pfeifer and S. Jay Deutsch, "Stationarity and invertibility regions for low order starma models: 
stationarity and invertibility regions," Communications in Statistics-Simulation and Computation, vol. 9, 
no. 5, pp. 551-562, 1980.  

[7]  X. Min, J. Hu and Z. Zhang, "Urban traffic network modeling and short-term traffic flow forecasting 
based on GSTARIMA model," in Intelligent Transportation Systems (ITSC), 2010 13th International IEEE 
Conference on, 2010.  



Seemingly Unrelated Regression Approach for GSTARIMA Model to Forecast Rain Fall Data in Malang 
Southern Region Districts 

Siti Choirun Nisak   64 
 

[8]  A. Iriany, Suharningsih, B. N. Ruchjana and Setiawan, "Prediction of Precipitation data at Batu Town 
using the GSTAR (1,p)-SUR Model," Journal of Basic and Application Scientific Research, vol. 3, no. 6, pp. 
860-865, 2013.  

 
 





 
 

 
 

 


	ABSTRACT
	INTRODUCTION
	LITERATURE REVIEW
	GSTAR (Generalized Space Time Autoregressive) Model
	GSTARIMA (Generalized Space Time Integrated Autoregressive and Moving Average) Model
	Seemingly Unrelated Regression (SUR)
	The precision model with MSE and R2

	METHODOLOGY
	RESULTS AND DISCUSSION
	CONCLUSION
	REFERENCE