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© 2017 Conscientia Beam. All Rights Reserved. 

FORECASTING GOAT MILK PRODUCTION IN TURKEY USING ARTIFICIAL NEURAL 
NETWORKS AND BOX-JENKINS MODELS   

 

 

 Ferhan KAYGISIZ1+ 

 Funda Hatice 

SEZGİN2 

 

1Istanbul University, Faculty of Veterinary Medicine, Department of Animal 
Breeding and Husbandry, Avcılar, Istanbul, Turkey 

 
2Istanbul University, Faculty of Engineering, Department of Industrial 
Engineering, Avcılar, Istanbul, Turkey 

 
  

(+ Corresponding author) 

 ABSTRACT 
 
Article History 
Received: 9 October 2017 
Revised: 20 December 2017 
Accepted: 26 December 2017 
Published: 29 December 2017 
 
 

Keywords 
Artificial neural networks model 
Box - Jenkins model 
Forecasting 
Goat milk.  
Time series 
Milk production 
 

The demand for goat milk has gradually increased in Turkey in recent years and dairy 
goat breeding began to be seen as an alternative investment area. The aim of the study 
is to create the data that will contribute to policy formulation in the stockbreeding 
industry by making a 10-year forecast of output pertaining to the goat milk production 
in Turkey. In the study, the annual data of the goat milk production in Turkey during 
the time period 1961 and 2016 obtained from Turkish Statistical Institute and Food and 
Agriculture Organization was utilized. Box-Jenkins estimation models and artificial 
neural networks model were used to forecast the production of goat milk. It was 
identified that artificial neural networks model gave the best result and prospective 
estimations were made through this model. As a result of the study, the projected value 
of milk production for 2026 was found to be 495,536.1 tons. Following the forecasts, it 
was calculated that the average rate of increase in the goat milk production will be 
0.12%. 
 
 

Contribution/Originality: The study was conducted to estimate the amount of goat milk production in Turkey 

until 2026. Box-Jenkins and artificial neural networks models were used as prediction models. The results of this 

study contribute in the literature about the goat breeding production policies.  

 

1. INTRODUCTION 

Goat breeding is a traditional animal production branch usually practiced in underdeveloped and developing 

countries. Aforementioned production branch constitutes a significant source of living and nutrition for the families 

with low income living in rural and forested lands [1]. Goat breeding has made a significant progress in the world 

since the late 20th century in consequence of the development in agriculture, consumer demands related to social 

and economic indicators, the need for quality and healthy food products [2, 3]. Goat breeding is maintained as 

either in an agricultural enterprise or as village herds, transhumance or migratory herds. However, intensive 

businesses making cheese or providing milk for cheese making dairies have also been operating in Western Anatolia 

in recent years [4]. The amount of goat milk production which was 192,210 tons in Turkey in 2009 increased to 

479,401 tons in 2016 by rising 2,5 times and the share of goat milk in the total milk production in Turkey was 

2.59% [5]. 

In Turkey, goat milk and products have economically gained importance by means of their taste, aroma, and 

quality, and goat cheese has begun to be demanded more and more with the urban growth and the development of 

tourism [1]. Goat plays a significant part in the domestic and foreign trades as well as contributing to the 

Animal Review 
2017 Vol. 4, No. 3, pp. 45-52 
ISSN(e): 2409-6490 
ISSN(p): 2412-3382 
DOI: 10.18488/journal.ar.2017.43.45.52 
© 2017 Conscientia Beam. All Rights Reserved. 

 
 
 

 
 

 
 

https://orcid.org/0000-0003-4939-7849
https://orcid.org/orcid-search/quick-search?searchQuery=Funda%20Hatice%20SEZGİN
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Animal Review, 2017, 4(3): 45-52 

 

 
46 

© 2017 Conscientia Beam. All Rights Reserved. 

nurturing of people, textile industry, and employment. Especially, the fact that EU (European Union) has not 

reached sufficiency in sheep-goat products creates a potential market for Turkey [1]. Therefore, it is important to 

promote goat breeding by implementing economic policies. 

The significance of consistent estimations for creating realistic prospective policies regarding livestock sector is 

a fact. While forming consistent estimations, a sound data system and time series analysis methods modeling this 

data are necessary [6].  

Researchers used Box-Jenkins [7-10] models successfully in analyses made with time series in agricultural 

output. It is observed that artificial intelligence methods have an increasing usage rate in recent years. Around the 

world and in Turkey, there is research that artificial neural networks method was used in the studies of estimating 

milk yield in livestock [11-13]. However, a limited number of studies [14] using artificial neural networks method 

in the estimation analyses of the amount of agricultural production were found in Turkey. This study was 

conducted to guide the policies which will be implemented in the field of livestock production by estimating the 

amount of goat milk production for the period of 2016-2026. 

 

2. MATERIAL AND METHODS 

2.1. Material  

The material of the study consists of the goat milk production data between 1961 and 2016. The statistical data 

used in the study were obtained from TSI (Turkish Statistical Institute) and FAO (Food and Agriculture 

Organization) [5, 15].  

 

2.2. Statistical Analysis 

In this study, future forecasts for goat milk production data were made and their compatibility was assessed by 

ARMA (Autoregressive Moving Average) which is one of the Box-Jenkins models frequently used in time series 

analyses and applied to level data, and ARIMA (Autoregressive Integrated Moving Average) methods applied to 

differentiated data along with ANN (Artificial neural networks models). 

Box-Jenkins which is an analysis and estimation method in time series is based on discrete, linear stochastic 

processes. AR (Autoregressive), MA (Moving Average), ARMA and ARIMA are Box-Jenkins estimation models. 

While AR (p), MA (q) and their combination ARMA (p, q) models are applied to stationary processes, ARIMA (p, d, 

q) models are applied to non-stationary processes [16]. ARMA (p, q) models are the most general stationary 

stochastic process models and are a linear function of past observations and past error terms [17]. ARMA (p, q) 

models are usually as demonstrated below: 

     (1) 

In the equation above; 

Yt-p   : is the past observation values, 

Ф1, Ф2,…, Фp  : is the coefficient for past observation values, 

δ   : is the constant value, 

at, at-1, at-p  : is the error term, 

θ1, θ2,…,θq  : is the coefficients regarding error terms [16]. 

In situations where time series is stationary, namely in situations where the average, variance, and covariance 

of the process is not changing depending on time and therefore series does not fluctuate, ARMA (p, q) or AR (p) or 

MA (q) models which are particular states of ARMA (p, q) can be used. However, the fluctuation of the average and 

variance of time series depending on time is frequently observed in reality. This situation is referred to as the non-

stationary situation. This kind of time series can only be appropriate for the use of ARMA (p, q) models when they 

are made stationary. 



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47 

© 2017 Conscientia Beam. All Rights Reserved. 

The process of stabilizing can be done with differencing processes and differencing the time series which has a 

linear trend at first degree makes the time series stationary. However, the time series which demonstrate 

curvilinear trend can be stationary with the process of second differencing [16-18]. The models applied to the new 

series resulting from the process of stabilizing the non-stationary series by differencing is called “non-stationary 

linear stochastic models” or “integrated models”. In this situation, the model is denoted as ARIMA (p, d, q). Where 

“d” is the stabilizing parameter of the series [19]. Namely, it states in which degree the series was differenced.  

ANN was developed as a result of the studies of modeling the biological neural system mathematically. ANN 

(Artificial Neural Networks) produced by being inspired by the functions of the human brain is a method which 

provides learning and generalization by testing. The aforesaid method is used to make estimations as a result of its 

constant output production [20]. ANNs produce quite successful results in complicated estimations for the fact that 

it is a technique which has a high power of calculation and the ability to generalize.  

ANN consists of stratified, feed-forward and interrelated artificial neural networks or nodes. Hence the 

network is feed-forward, unidirectional flow is provided and loop or return is not allowed. ANN model formed by 

the connection of numerous cells in various forms has a parallel distributed structure and the information which the 

network obtains is scattered on all the connections in the network. Therefore, the fact that some of the connections 

and cells of a trained ANN model become neutralized does not affect the accuracy of the information that the 

network produces significantly [21].  

 

3. RESULTS AND DISCUSSION 

Various models were tested to determine the most appropriate model for a ten-year prospective estimation 

using goat milk production data between 1961 and 2016 and an estimation method was developed by comparing 

them. First, correlogram test was applied to the data and it was observed that the result showed a slow decline 

indicating the unit root. ADF (Augmented Dickey-Fuller) test validated that the level data includes unit root, that 

it's non-stationary. While estimating the goat milk data which was observed to become stationary by first 

differencing, difference data was used firstly. 

Notation for ARIMA (p, d, q) model is as follows: p: standard autoregressive level of the model; d: the degree of 

the difference that will make the series stationary; q: standard moving average degree. In this study, d=1 was used 

because it was differentiated from the first degree in order to make the series stationary. While choosing the most 

appropriate model among the calculated potential estimation models, the model having a lower SC (Schwarz 

criterion) value (SC = n Log (SEE) + k Log (n)), a lower SEE (Sum squared of regression) value and a higher R2 (R-

squared) value was determined to be more suitable and meaningful compared to other models. 

 
Table-1. Estimation criteria of ARIMA models 

ARIMA MODEL SC R2 SEE 

(1, 1, 0) 22.939 0.178 21933.62 
(2, 1, 0) 23.054 0.090 23214.14 
(1, 1, 1) 23.011 0.179 22131.10 
(1, 1, 2) 22.991 0.196 21911.41 
(0, 1, 1) 23.258 0.164 25749.31 
(0, 1, 2) 23.331 0.101 26707.91 

(2, 1, 1) 22.913 0.205 21908.42 
(2, 1, 2) 23.124 0.094 23395.55 

                                             Source: Table was constitute from analyzed data of current study 

 

With reference to Table 1, considering SC, R2, SEE values; the model of (2, 1, 1) which was differentiated from 

first degree and with AR (2) and MA (1) added was decided to be the most appropriate ARIMA model. Estimation 

was tried to be made with ARIMA models on goat milk production data which was made stationary by 

differentiating from the first degree. Estimation results on the data which was not differentiated (level) were added 



Animal Review, 2017, 4(3): 45-52 

 

 
48 

© 2017 Conscientia Beam. All Rights Reserved. 

to the study to make a comparison. ARMA models and AR and MA models which are specific versions of ARMA 

models were used on level data and their tests were carried out. 

 
Table-2. Examination criteria of ARMA models 

ARMA MODEL SC R2 SEE 

(1, 0) 23.340 0.935 26824.74 
(2, 0) 24.227 0.840 41774.48 
(1, 1) 23.221 0.945 24600.48 
(1, 2) 23.294 0.941 25516.06 
(0, 1) 24.893 0.722 58352.38 
(0, 2) 25.122 0.651 65419.26 
(2, 1) 23.145 0.948 23663.21 
(2, 2) 24.088 0.868 37916.80 

                                               Source: Table was constitute from analyzed data of current study 

 

The subjects to be considered while choosing the most appropriate model among the potential estimation 

models calculated for ARMA models are similar to the ones with ARIMA models. ARMA (2, 1) model which has 

the lowest SC and SEE values and the highest R2 value among the given models was decided to be the most 

appropriate model (Table 2). 

The ANN model set up in this study serve as a non-linear regression model. Minimum-maximum (min-max) 

normalization which is frequently used in literature for data normalization was made and input vector was the years 

between 1961 and 2016 and the output vector was annual goat milk production. LM (Levenberg Marquardt) model 

was chosen as the training method for the ANN model which was set as feed-forward, back-propagated and 70% 

was used in training, 15% used in validation and 15% in the testing stage. The interlayer number was taken as 10 

and delay number was taken 2. These values were kept stabilized for the performance of the model was at the 

desired level. 

Goat milk estimation performance of the network trained with LM method can be seen in Figure 1. 

Performance graph, input, and target data consist of three lines as they are divided into three sets. As seen in the 

figure, it declined to nearly zero error in 12th iteration. MSE (mean squared error) represents the proportional 

value of the difference between the values in the artificial neural network and estimated values. In this study, the 

training stops when the MSE value drops below 0.01. This value represents that the difference between the actual 

values and the estimated values will be 1% maximum. 0.05 and 0.01 values are frequently used in the literature 

[22]. For the reason that the error dropped below 0.01 in the training set, it can be said that the results are at an 

acceptable level. The training stopped when the verification error started to increase, at 100th iteration. A 

remarkable sign of memorization is not observed until the 12th iteration where the best verification performance is 

present because the error rate in the verification and test set does not increase as of this iteration. As verification 

error and test set error show similar characteristics and a significant memorization has not occurred, the 

performance of the network is at an acceptable level. In addition to this, MSE result of the goat milk production of 

the model is 0.0075064. As a result, error rate acquired and predetermined and acceptable performance target has 

been achieved. R correlation coefficient indicates how good the variations in outputs are explained by targets. 

The fact that the R-value approaches 1 signifies that the relationship strengthens and that it approaches zero 

signifies that the relation weakens [22]. Figure 2 shows the correlation between outputs and targets. It represents 

a good compatibility that R-value is quite close to 1. Training data shows a quite good harmony. While R 

correlation coefficient is 0.99 for training data, R correlation coefficient values which are above 0.97 are acquired for 

test and verification data. Scatter graph is important in that the particular data points show a weak harmony. When 

training, verification and test graphs are examined; it can be observed that there is no significant inconsistency 

between the actual value and network inputs. 20-years of the output of ANN, ARIMA and ARMA models used for 

estimation and the actual output of last 10 years are as given in Table 3. 



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Table-3. Values of 2007-2016 and estimation results for 2007-2026 

DATE ACTUAL YSA ARIMA ARMA 

2007 237487 220867.1 223829.0 348809.0 
2008 209570 216894.4 202292.4 348265.9 
2009 192210 235414.8 188506.3 347764.5 
2010 272811 282890.3 270884.3 347301.6 
2011 320588 335389.6 320005.4 346874.2 
2012 369429 377973.5 371207.2 346479.7 
2013 415743 420999.0 419396.1 346115.4 
2014 463270 460443.2 468105.2 345779.2 
2015 481174 484143.5 487482.0 345468.7 
2016 479401 494410.3 486374.4 345182.1 
2017  443125.0 485491.5 344917.5 
2018  446462.5 485484.6 344673.2 
2019  472664.7 485493.9 344447.6 
2020  466844.8 485481.3 344239.4 
2021  455216.3 485498.3 344047.2 
2022  474135.0 485475.5 343869.7 

2023  485646.4 485506.1 343705.9 
2024  495665.7 485464.9 343554.6 
2025  490479.1 485520.3 343415.0 
2026  495536.1 485445.9 343286.0 

                                Source: Table was constitute from analyzed data of current study 

 

 
Figure-1. Performance graph of the network 

     Source: Figure was constitute from analyzed data of current study 

 

MSE and MAPE (mean absolute percentage error) methods were applied to choose the estimation method 

which gives the best result among the models and the results were given in Table 4. 

 
Table-4. Error results for the estimation models 

 MSE MAPE 

ARMA 6028086102 0,21251266 
ARIMA 274473715 0,028086212 
YSA 209308290 0,028060791 

                                                   Source: Table was constitute from analyzed data of current study 

 

While MAPE values of which estimation values below 10% were regarded to be at high accuracy degree, 

models between 10% and 20% were classified as accurate estimation model [23, 24]. As a result of the error tests 

demonstrated in Table 4, MAPE value of the ARMA model was found as 0.212, MAPE value of the ARIMA model 



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© 2017 Conscientia Beam. All Rights Reserved. 

and ANN model which were quite close to each other was found as 0.028. When MSE values, another comparison 

measure, were examined, the model with the least error rate was found to be the model established by ANN. It is 

indicated that it is necessary to work with over 70 data for Box-Jenkins methods which include ARIMA and ARMA 

models subject to this study [19]. ANN is a method used frequently in time series estimations and it produces quite 

successful results. It allows working with less data by nature. However, despite the number of the data is not 

sufficient in this study, it is observed that ARIMA model resulted well with a close degree to ANN. Estimation 

model made with ANN was the model which gave the most accurate result among examined time series estimation 

methods. When regression outputs of the model were examined, it was observed that it showed good compatibility 

and MAPE value was found at an accurate estimation level. 

 

 
Figure-2. Regression output of the network 

                              Source: Figure was constitute from analyzed data of current study 

 

In this study, various estimation models with Box-Jenkins and ANN were tested by using the data of the 

goat milk produced between the years 1961-2016 and the models built were compared to each other. According to 

ANN results, forecasted value of the milk production belonging to 2026 is 495,536.1 tons. According to the forecast 

values in Table 4, it was forecasted that a fair amount of milk decrease will be observed in goat milk amount 

starting from 2017 when compared to the production amount of 2016; however, it was forecasted that the 

production will increase as of 2023. Following the forecasts, it was calculated that annual average rate of increase in 

the goat milk production will be 0.12%. 

 

 



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4. CONCLUSION 

The aim of the study is to obtain the data that will contribute to forming a policy in the field of animal 

production by making a 10-year forecast of output belonging to the goat milk production in Turkey. As a result of 

the estimation, it was concluded that ANN models are more successful and goat milk production will follow an 

upward trend in 10 years. 

In recent years both around the world and in Turkey, the demand for goat products have increased gradually 

with the rising significance of the goat milk with regards to nutrition. It is necessary to take a number of measures 

in terms of increasing the production of goat products and its sustainability in line with this development. Direct 

and indirect government interventions with technical measures will play an important role in production policies in 

improving goat breeding. Subventions and regulations regarding the price formation of meat, milk, and mohair are 

compulsory within production policies. On the other hand, legal regulations which will promote breeder to organize 

under cooperatives must be implemented and measures protecting goat health must be taken for Turkey to compete 

with other countries in exportation [4]. When the measures are taken regarding the technical and economic 

problems that producers encounter, goat breeding will contribute greatly to the national economy. 

 

Funding: This study received no specific financial support.  
Competing Interests: The authors declare that they have no competing interests.  
Contributors/Acknowledgement: Both authors contributed equally to the conception and design of the 
study.  

 

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