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African Journal of Agricultural Marketing ISSN 2375-1061 Vol. 8 (4), pp. 001-007, April, 2020. Available online at 
www.internationalscholarsjournals.org © International Scholars Journals 

 

Author(s) retain the copyright of this article. 
 

 

Full Length Research Paper 

 

Prediction of added value of agricultural 
subsections using artificial neural networks: Box-

Jenkins and Holt-Winters methods 

 
Elham Kahforoushan1*, Masoumeh Zarif1 and Ebrahim Badali Mashahir2

 
 

1
Department of Agricultural Economics, Faculty of Agricultural Engineering, University of Zabol, Zabol, Iran. 

2
Tarh Ab Araz Consulting Engineers Company, Iran. 

 

Accepted 11 January, 2020 
 
Added value of agricultural sub sectors is affected by many factors such as quantity production per 
agricultural sub sectors and selling price of producers and is related to some factors such as government 
investment and monetary and financial policies. This study examines the performance of artificial neural 
network, Box-Jenkins and Holt-Winters-no-seasonal models in forecasting added value of agricultural sub 
sectors in Iran. It compares error criterions for determining the best model. Results showed that Box-Jenkins 
and artificial neural network are appropriate and artificial neural network indicated good result relatively in 
learn stage, but Box-Jenkins model gave better results in forecasting of unseen data. Holt-Winters model had 
the lowest mean absolute percent error in both of model fitting and model validation stages. 
 
Key words: Artificial neural network, Box-Jenkins, Holt-Winters, added value of agricultural sub sectors. 

 
INTRODUCTION 

 
Agricultural sector is regarded as one of the most 
important economical parts of Iran. It holds a special 
position considering production, employment, food 
security, foreign exchanges and relative advantages and 
plays a key role in economical development process. 
Added value of agricultural section includes added value 
of each of agronomy, animal husbandry, fishery and 
forestry subsections. The percentage portion of added 
value of agricultural section is about 13% in combination 
of national economy (Database of Central Bank of Iran). 
Determining added value in agricultural section is 
considered as one of the necessities of econo-mical 
calculations which is required for different decision 
makings and specifying important policies in investment, 
employment, income and principally development 
planning and the likes and also in the evaluation of five-
year program for agricultural development. So it is 
calculated to satisfy above mentioned requirements 
through study of amount of production of agricultural  
 
 

 
*Corresponding  author.  E-mail:  e_kahforoushan@yahoo.com. 
Fax: +984115248613. 

 
 
 

 
subsections, sale prices of producers of agricultural 
section, gross value of products of each of agricultural 
subsections, middleman costs of each of subsections, 
added value of each of subsections and finally added 
value of all of agricultural section at constant and current 
costs.  

Several studies refer to relations between state 
investment and added value and also long-term relations 
between fiscal and monetary policies and added value of 
agricultural section. Having exact information from future 
events is necessary for appropriate short and long-term 
planning on added value since choosing appropriate poli-
cies is required for formation of agricultural section as an 
effective section in economical development. Nowadays, 
prediction of future events has attracted attention of 
researchers in different aspects and a variety of methods 
has been innovated, among them, we can refer to non-
regression methods such as simple average, moving 
average, exponential adjustment and regression methods 
including GARCH, ARCH, ARIMA and artificial neural 
network methods (Najafi and Tarazkar, 2006). Added 
value of agricultural subsections has been forecasted 
through using three Holt-Winters, ARIMA and artificial 
neural network methods at this study, aim of which is 

file:///C:\Users\user\Documents\REPUBLICATION\AGRICULTURAL%20SCIENCES\AppData\Local\Temp\www.internationalscholarsjournals.org


 
 
 

 

which is comparing accuracy of these methods with error 
criteria. 
 

 

Background 

 

Several studies have been done on different economic 
variables alongside many predictions, and different 
methods have been used in each of them with different 
outcomes resulting. We refer to some samples in order to 
compare and have a more complete understanding of the 
subject. Henry et al. (2007) compared efficiency of 
artificial neural network with seasonal Holt-Winters and 
ARIMA models for prediction of rice exporting of Thailand 
and concluded that Holt-Winters model is an appropriate 
and satisfactory one in prediction of rice monthly export at 
modeling stage. But they weakly performed in prediction 
of future unspecified amounts.  

In contrast, ANN demonstrated the seasonal and non-
linear effects relatively well. Deetae (1991) applied 
analysis and Box-Jenkins methods for evaluation of rice 
price in the farm and the efficiency of Box-Jenkins model 
became obvious. Kerdsomboon (1999) used preliminary 
statistic prediction models in order to study rice 
production and demonstrated the better performance of 
Box-Jenkins method. Sangpattaranate (2005) applied 
four additive Holt-Winters's prediction techniques, Box-
Jenkins and regression analysis for Thailand rice prices 
and made it clear that despite of relatively well 
performance of analysis model, the Box-Jenkins model 
was the best. Baki Billah et al (2006), in a study under 
title of choosing exponential smoothing model for 
prediction, introduced MAPE criterion as an appropriate 
method for model choosing at model evaluation stage. 
The method with procedure is appropriate for annual data 
and seasonal method is appropriate for time series less 
than annual from among three single exponential 
smoothing, with time and seasonal procedure methods. 
Hyndman (2001) used single exponential smoothing 
method in his study and demonstrated that its 
performance is better than ARIMA. Nadjafi and Tarazkar 
(2006) applied artificial neural network and ARIMA 
procedure for prediction of pistachio export of Iran and 
compared the results. The study results demonstrated 
that feed-back neural network has better performance 
comparing with other neural networks and ARIMA proce-
dure and is able to anticipate the amount of pistachio 
exports more exactly. Sadrolashrafi and Nassabian 
(2002) in a study on effects of difference of optimized and 
complied added value of agricultural subsections on 
optimized GDP through using input-output table of 1991 
concluded that the government can achieve 57 and 71% 
from the complied added values of animal husbandry and 
forestry subsection and also 37 and 45% of the complied 
added values of agronomy and fishery subsections 
considering population annual growth rate and domestic 
gross production annual growth rate scenario in the third 

 
 
 
 

 

development program. Kopahi and Kiani (2000) 
forecasted the amount of required investment in 
agricultural section from 2000 - 2004 through finding a 
relation between state investment and added value of 
agricultural section.  

An investment function with a time interval has been 
used in this regard. Akbari et al. (2003), in a study on the 
effects of the government's expenditures on added value 
of agricultural subsection, introduced learning and 
research charges of the government as the most effective 
variable on added value of agricultural section. Civil 
charges occupy the next place. Current costs and sub-
sides paid to the producers of this section has statistically 
meaningful effect on added value of agricultural section. 
Torkamani and Bagheri (2002), through study of the 
relation between private and state investment and growth 
of added value in agricultural section demonstrated that 
variables of the ratio of private and state investment to 
added value and growth of export in agricultural section 
have a positive effect on the growth of this section and 
variables of growth of agricultural import and growth of 
employment have a negative effect. Growth of added 
value variable of agricultural section just has a bilateral 
relationship with private and state investment and a 
unilateral relationship with other variables. Co-integration 
relations have been estimated through Johansson' co-
accumulation test and use of VAR model. 
 

 
METHODOLOGY 
 
In this study, added value of agricultural subsections has been 
forecasted through using three Holt-Winters, ARIMA and artificial 
neural network methods. Its goal is to compare the accuracy of 
these methods with error criteria such as MAPE (Mean Absolute 
Percent Error), MSE (Mean Square Error), MAE (Mean Absolute 
Error) and ME (Mean Error). Time series of 1936 - 2005 years of 
four agricultural subsections is the data used in this study. Data of 
1959 - 2005 years has been extracted from database of Central 
Bank of Iran and the statistics of 1936 - 1958 years has been 
extracted from research plan of domestic gross production 
estimation for 1936 - 1958 years done by bank and monetary 
research institute of Central Bank (Khavarinezhad, 2001) and real 
prices of 1997 have been used in order to omit inflation effects from 
statistics. 

 

Exponential smoothing 
 
This method began with the work of Holt-Winters in 1950. 
Afterwards, the main model exposed to many changes and several 
studies has expressed its exceptional performance. Bowerman and 
O’connell (1979) stated that this model is on the basis of an 
autoregressive statistical model in which the information in the 
relation with forecasted series is just used and in contrary to 
regression models predictions using constant factors, the 
predictions of this model adjusted according to the previous 
predictions errors (Hyndman, Koehler, Snyder and Grose, 2002) 
classified exponential smoothing.  

Each method consisted of one of five types of trend (none, 
additive, damped additive, multiplicative and damped multiplicative) 
and one of three types of seasonality (none, additive and 



 
 
 

 
multiplicative). Among the 15 different exponential smoothing 
methods, the best known are simple exponential smoothing (no 
trend, no seasonality), Holt’s linear method (additive trend, no 
seasonality), Holt-Winters’ additive method (additive trend, additive 
seasonality) and Holt-Winters’ multiplicative method (additive trend, 
multiplicative seasonality) (De Gooijer et al., 2006). Gardner and 
McKenzie (1988) provide some simple rules based on the variances 
of differenced time series for choosing an appropriate exponential 
smoothing method. Hyndman et al. (2002) also proposed an 
information criterion approach, but using the underlying state space 
models.  

Different methods of smoothing require primary estimation of 
parameters related to (α) level, (β) trend and (γ) seasonal indices 
(Hyndman, 2002). In eviews software, parameters are estimated by 
minimizing sum of error squares and in QSB software, error criteria 
is selected by the researcher and the software chooses the best 
parameter considering error criteria. These parameters have been 
defined between zero and one. Theory of the method used in this 
study will be discussed later. 

 

Single exponential smoothing 
 
This is a single-parameter method and is appropriate for series 
randomly move around a constant mean. If the parameters are 
estimated close to one, means that this procedure is a random step. 
Parameter α is related to level (mean), β to the trend and γ to the 
seasonality. These parameters have been defied between zero and 
one.  

If the smoothed series is ŷt and the main series is yt, ŷt is 
randomly obtained from the following relation: 
 

ŷt= α yt  + (1-α) ŷt-1 (1) 
 

In which, 0 ≤ α ≤1 is the smoothing factor, ŷt series are smoothing. 
We can rewrite the relation (1) through repetitive replacements:  

 

ŷt  =α (2) 
 
This relation states the reason of calling this method as exponential 

smoothing. yt prediction is a weight mean of previous yt values in 
which weights reduces exponentially with time. These predictions 
have been proved for all future observations. This constant is 
obtained through following relation: 
 

yt+k= yt for k>0 
 
Where t = end of the sample. We require a value for α and an initial 

value for yt in order to begin repeat procedure. Bowerman and 
O’connell (1979) suggested that α values around 0.01 to 0.3 
perform relatively well. 

 

No-seasonal Holt-Winters 
 
No-seasonal Holt-Winters used in this research is a double-
parameter method and is appropriate for series with time trend and 
without seasonal pattern. In this method, predictions are made with 
trend and without seasonal fluctuations. 
 

yt+k= a+bk 
a(t)=αyt+(1-t)[a(t-1)+b(t-1)] 
 
Intercept =a, b(t)= β[a(t)-a(t-1)]+1-βb(t-1) 
 
Trend = b in which β<0, α>0 are smoothing factors. This is a 
smoothing method with two parameters and predictions are made 
through following relation: 

 
 
 
 

 

yt+k= a(t) + b(t)k 
 
located on trend with a(t) intercept and b(t) slope. 

 

Box-Jenkins 
 
Stationary time series can be modeled in different ways. If a time 
series become stationary after d times of difference then modeled 
by ARIMA procedure, the main time series will be called integrated 
moving average autoregressive time series in which p is the order 
of autoregressive and q is the rank of moving average process: 
 

ARIMA (p, d, q):  yt= θ+α1Yt-1+β0Ut+β1Ut-1 
 
Box-Jenkins has four stages; the first stage is the identification 
stage in which the real values of p, d, q is determined by a single 
root test or correlogram. At the second stage the parameters of the 
model are estimated. Third stage is called recognition control 
sought after choosing of a special model of ARIMA and estimation 
of its parameters in order to determine that whether it appropriately 
fits the data since it is possible another ARIMA model fits better. For 
this purpose, we can use function of Box-Pieres (Q) and Lijang-Box 
(LB) tests. At the fourth stage the estimation is done with the best 
selected model. The predictions resulted from this model is 
especially for short-term predictions and in most cases, is more 
reliable than traditional modeling method of econometrics. Of 
course, it is necessary to separately judge about each special case 
(Abrishami, 2006). 

 

Artificial neural network 
 
The structure of artificial neural networks is like human's brain 
including a set of connected neurons. Each set is called a layer. For 
example, an ANN consists three neural layers (node):  

Input layer, which receives outside information and acts as an 
independent variable. So, the number of neurons of input layer is 
determined on the basis of nature of the problem and depends on 
the number of independent variables. The last layer is the output 
layer, from which the solution of the problem results.  

Several numbers of middle layers have separated input and 
output layers which is called hidden layers and are merely an 
intermediate result in calculation process of output value. The 
nodes have been connected in adjacent of the layers from lower 
layers to upper ones by a rotative arch. There is no theoretical 
principle for determining appropriate number of hidden units or 
layers in a network. Researchers have used different relations 
including n/2, n, 2n, 2n+1 in order to determine number of hidden 
neurons. In these relations, n is number of input neurons. Trial and 
error is the best way for determining number of hidden nodes 
(Zhang et al., 1999). Figure 1 shows the simplest node in which 
sum of N harmonious inputs enters the network. In this research we 

used feed-back network in which F is output function, β0 is bias unit 

(equivalent to 1), G is output function of j units of hidden layers, γkj 

refers to input weight of k of j neuron, βj is output weight from 
hidden layers in output layers unit and X is the input vector. 

F Fβo ∑j
 

1 β j G∑k
 1 γk j X j 

j  k  

 
Activation function determines the relationship between inputs and 
outputs of a node and a network. It is possible that a network have 
different activation functions for different nodes at the same or 
different layers, but nowadays almost all researchers use similar 
activation functions for nodes at the same layers (Zhang et al., 
1998). Neural network helps the smallest error of prediction of 
learning set through using criteria such as mean square error and 



  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
Figure 1. One type of feed-back neural network. 

 
 

 
the data should be normalized for presentation by using following 
formula: 
 

Ni= 0.8 ×[Xi-Xmin/Xmax- Xmin]+ 0.1 
 

Ni and Xi represent normalized and main data: Xmin and Xmax 

represent minimum and maximum of data (Haykin, 1994). Data 
normalization at the meaning of preprocessing and post processing 
improves the performance of the network. Data are usually 
preprocessed before learning of the network meaning exercising 
some conversions on inputs and outputs of the network in order to 
extract the properties from the inputs and change of the output to a 
more understandable form for the network. Inputs of the network 
are changed to their primary form, referred to post processing, after 
learning and extraction of results from the network. 
 

 
Compare of prediction methods 
 
Criteria such as MAPE and MAE are used for examining of  
prediction power. 
Mean Absolute Error   

MAE  ∑ e i  
n 

 
Mean Square Error 
 

MSE   ∑ 
e

i
2     n 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
Mean Absolute Percent Error 
 

n y    
 

n ∑    
 

MAPE  
1

 e i    
 

i1 
 

i 
 
In these relations, n is the number  

  
  

of predictions,  is the prediction error obtained from the difference 
between predicted and real values. A MAPE criterion is one of the 
percent error criterions which is more desired and is one of the 
most applied unit-less criteria. A single error criterion such as 
MAPE is mostly used for comparing several time series with 
different measures (Najafi and Tarazkar, 2006). 

 

RESULTS AND DISCUSSION 

 

Exponential smoothing model 

 

Single exponential smoothing with linear trend method 
has been used in this study which is the same as Holt-
Winters' non-seasonal method. This method has been 
selected considering nature of data which is annually with 
a linear trend and also MAPE criterion at the evaluation 
stage of the model by WinQSB. Modeling has been done 
considering data of the period 1936 to 1996; smoothing 
parameters and error criteria have been listed in Table 1.  

The goal of model validation is to show that the 
constructed model has the capability for producing data 
acceptable for future. Data used in this stage relate to 



 
 
 

 
Table 1. Smoothing parameters and error criteria of modeling and model validation stages.  

 
 Sub sector α (Average) β (Trend) MAP MSE MAE 

 Agronomy 0.92 0.08 8.9 547149.6 544.33 

 Animal husbandry 0.85 0.61 5.01 113588.1 225.012 

 Fishery 1 0.19 10.6 11707 57.13 

Model fitting Forestry 1 0.01 14.9 1585.24 22.49 

 Agronomy 0.92 0.08 6.3 4385428 1761.22 

 Animal husbandry 0.85 0.61 2.4 222237.7 368.82 

 Fishery 1 0.19 15.3 38277.46 182.45 

Model validation Forestry 1 0.01 13.1 11214.39 83.63 
 

 

1997 - 2005 period which was regarded as out of sample 
data at modeling stage. Considering the less amount of 
mean absolute value percent error, it is evident that 
exponential smoothing method has presented very good 
results in both stages. 

 

Box-Jenkins model 
 
Augmented Dickey-Fuller test statistic was used in order 
to survey the static mode of time series. In this test, the 

equation ∆yt= α +βt+δyt-1+Vt is tested through adding ∆y 
breaks in order to omit correlation of estimation disorder 
sentences and being zero of α, β, δ. Results of the test 
demonstrate that none of the variables are at static level 
but they reach static level after one time of differentiation 
(Noferesti, 1999).  

We determine the number of autoregressive sentences  
(p) and number of motion mean sentences (q) in order to 
predict with ARIMA procedure after determination of 
static level of the variables which requires trial and error 
and examining of different models. Schouarts-Bazin 
values is one of the criteria that helped us in choosing the 
model, the best model is selected considering the smaller 
values and also remainders test by Q Box-Pieres test 
function. Also, it is necessary to take into account the 
meaningfulness of AR and MA correlations and also the 

value of R
2
. After estimation of ARIMA models for each of 

the agricultural subsections by using sample period of 
1936 - 1996, prediction was made for out of sample data 
until 2005 and error criteria of modeling stage were 
estimated. Then, error criteria of model validation stage 
were calculated again through using real available data 
for 1997 - 2005 periods. The results have been shown in 
Table 2. Considering MAPE in these two stages, it can be 
observed that modeling of out of sample data predictions 
are more accurate. 

 

Artificial neural network 

 
The result were tested for feed-back neural network 
having 2, 3, 4 and 5 layers and finally the best evaluation 

with a higher criterion of R
2
 was specified for each 

subsection and error criteria were calculated in both 

 

 

network learning and its test in both stages which have 
been shown in Table 3. As it can be observed, mean 
absolute value percent error in learning stage was higher 
than network testing stage in all subsections and this 
demonstrates the better performance of neural network in 
prediction of future data. 
 
 
SUMMARY AND CONCLUSION 

 

In this study, artificial neural network, Box-Jenkins and 
Holt-Winters methods compared with each other in order 
to predict the added value of each of the agricultural 
subsections. The form of primary time series and single 
root tests demonstrated that time series of all four 
sections have procedure and non-seasonal Holt-Winters 
(single exponential smoothing with time trend) and Box-
Jenkins models were selected to be compared with 
artificial neural network because of their capability in 
description of time series data trend.  

The non-seasonal Holt-Winters model requires 
estimation of parameters of level and trend solved with 
trial and error and minimizing criterion of mean absolute 
value percent error. It is possible that a prediction model 
shows better results at modeling stage but has not a 
good performance at prediction stage. Table 4 
demonstrates the error criteria of models at modeling and 
validation stages. The results manifest that non-seasonal 
Holt-Winters model has performed very well in both 
stages and mean absolute value percent error was less 
than 15%, while artificial neural network performed better 
than Box-Jenkins at modeling stage. The mean absolute 
value percent error was less than 42% for all groups 
through using artificial neural network at this stage, while 
this criterion was less than 62% for Box-Jenkins. The 
performance of Box-Jenkins was better than artificial 
neural network at testing and validation stage of models 
and mean absolute value percent error was less than 
23% while it has been calculated as less than 36% for 
artificial neural network.  

Although, according to MAP criteria, artificial neural 
network has more errors then ARIMA model considering 
test section, this can not lead to conclusions with regard 
to weakness of artificial neural network. Remember that 



 
 
 

 
Table 2. ARIMA process and error criteria of modeling and model validation stages.  

 
Sub sector MAP MSE MAE ARIMA 

 

Agronomy 44.3 6610041 2324 (3,1.3) 
 

Animal husbandry 57.8 4141225 1802 (1,1.3) 
 

Model fitting 
61.3 39521 165 (1,1.3) 

 

Fishery 
 

Forestry 49.9 33014 112 (2,1,2) 
 

Agronomy 15.1 23653394 4453 (3,1.3) 
 

Animal husbandry 6.03 906821 904 (1,1.3) 
 

Model validation 
13.8 28880 167 (1,1.3) 

 

Fishery 
 

Forestry 22.8 6004 57 (2,1,2) 
 

 

 

Table 3. Error criteria of test and learn stages of artificial neural network.  
 

Sub sector ME MAE MSE MAP 
 

Agronomy 2377.18 20517.48 16824029.06 30.1 
 

Animal husbandry 1474.25 1503.08 3332469.13 27.9 
 

Learn 
83.93 93.47 12616.74 22.8 

 

Fishery 
 

Forestry 52.99 54.32 6073.41 41.7 
 

Agronomy 1157.49 3559.09 20714114.72 16.6 
 

Animal husbandry 160.83 1366.22 2866854.61 11.3 
 

Test 
272.5 360.71 199898.44 35.9 

 

Fishery 
 

Forestry 7.46 68.035 7029.43 14 
 

 

 

Table 4. Comparison of Holt - Winters and Box - Jenkins and artificial neural network mean absolute value percent error.  
 

 Model Model fitting Model validation 

 Agronomy   

 Exponential smoothing 8.9 6.3 

 Box-Jenkins 44.3 15.1 

 Artificial neural network 30.1 16.7 

 Animal husbandry   
 Exponential smoothing 5.01 2.4 

 Box-Jenkins 57.8 6.3 

 Artificial neural network 27.9 11.4 

 Fishery   
 Exponential smoothing 10.6 15.3 

 Box-Jenkins 61.3 13.8 

 Artificial neural network 22.8 35.9 

 Forestry   
 Exponential smoothing 14.86 13.1 

 Box-Jenkins 49.9 22.8 

 Artificial neural network 41.7 14 
 

 

neural networks need more data for learning and 
examination. So, changes in number of learning and 
examinational data may have different results. Other 

 

 

criteria (Tables 2 and 3) demonstrate that artificial neural 
network operates better than ARIMA at learning stage, 
that is, identification and description of relations in 



 
 
 

 
Table 5. Predicted value using best model until 2011.  

 
 Year Agronomy Animal husbandry Fishery Forestry 

 2006 35613.35 17368.90 1375.09 725.62 

 2007 36534.39 17770.16 1405.05 742.51 

 2008 37455.43 18171.42 1435.00 759.40 

 2009 38376.46 18572.68 1464.96 776.30 

 2010 39292.50 18973.93 1994.91 793.19 

 2011 40218.54 19375.19 1524.87 810.08 
 

 

agricultural subsections. The outcomes demonstrate tha 
use of several study criteria can lead to obtaining more 
reliable results because in some cases, results of 
prediction criteria are different. Also, normalizing of data 
plays a significant role in improving of function of artificial 
neural network. Predictions made for the next year have 
been demonstrated in Table 5.  

The government should take actions for increasing of 
added value growth through appropriate planning in order 
to maintain annual growth rate of Iran economy which is 
about 6% and considering almost 2.5% growth predicted 
for added value of agriculture section in spite of 
continuing of ascending process of added value of 
agricultural subsections. Considering that each of the 
economical sections should obtain part of their added 
value through promoting of productivity, it is necessary to 
provide opportunity for growing of added value through 
required planning by the country's planning and 
management authorities in order to promote productivity 
of this section. 
 

 
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