Forecasting Models for Thailand’s Electrical Appliances Export Values
SOMSRI BANDITVILAI, YUWADEE KLOMWISES
Department of Statistics
King Mongkut’s Institute of Technology Ladkrabang
Bangkok 10520
THAILAND
Abstract: - This research aimed to study forecasting models for Thailand’s electrical appliances export values.
Thailand’s monthly electrical appliances export values were gathered from the Information Technology and
Communication Center, Ministry of Commerce, from January 2006 to November 2022. The data from January
2006 to December 2021 were used to construct and select the forecasting models, and the remaining were used
for measuring the model’s accuracy. Since the electrical appliances export values showed trends and seasonal
variation, the researcher selected the Holt-Winters method with various initial settings, the Box-Jenkins
method, and Long Short-Term Memory Neural Networks (LSTM) for constructing models. The forecasting
models were chosen by minimum Root Mean Square Error (RMSE) as a criterion. Mean Absolute Percentage
Error (MAPE) was employed to measure the accuracy of the forecasting model. The study revealed that the
Box-Jenkins model gave the appropriate forecasting model for Thailand’s electrical appliances export values
and gained a MAPE of 8.0%.
Key-Words: - Forecasting, Electrical Appliances Export Values, Holt-Winters Method, Box-Jenkins Method,
Long Short-Term Memory Neural Networks
Received: July 29, 2022. Revised: March 22, 2023. Accepted: April 13, 2023. Published: May 19, 2023.
1 Introduction
Electrical appliances have become an essential
factor that plays an important role in daily life.
Electrical appliances help the well-being of the
people in the houses, communities, and societies to
be more comfortable. Thailand’s electrical
appliances industry produces electrical appliances
for domestic sales and export to foreign countries.
Thailand is an important electrical appliance
manufacturing base in Asia. As the government has
a policy to promote foreign investment in the
electrical appliances industry and the development
of electrical appliances parts since 1972, it also has
a policy to support the production of electrical
appliances in Thailand during the year 2016-2020,
[1]. According to the Office of Industrial Economics
report in 2020, Thailand's electrical appliances
exports 65-70% of the total electrical appliances
production. The main export products are air
conditioners, televisions, radios, refrigerators,
washing machines, and compressors. The export
value of electrical appliances was 889,541.55
million baht or 11.06% of the total export value of
the country, [2]. Since exports drive investment
expansion and increase labor demand, it also assists
in importing foreign currency and causing efficient
use of resources, and creating added value to
resources.
Accurate forecasting enables businesses to plan
their production and exports better. As a result, the
inventory is lower and the production costs and
export costs are decreased. It also helps the
government formulate trade policies supporting
exports to help businesses grow faster.
Currently, the most widely used forecasting
method is time series analysis. Time series analysis
constructs models or equations to guide future value
predictions. The method uses historical data
collected in an order of time to study the patterns,
and data correlation to build models. This study will
construct a model to forecast the export values of
electrical appliances in Thailand
The Holt-Winters method is simple and easy to
use. They are best suited for time series that tend to
be linear and fluctuate seasonally. The different
settings of levels, trends, and seasonal variations
affect the Holt-Winters forecasting performance,
[3]. This has led to extensive studies of different
default levels, trends, and seasonal factors. The
study of [4], found that significantly MAPE values
change resulting from different initial settings. In
[5], the author employed Extended Additive Holt-
Winters and Holt-Winter methods with four initial
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settings to construct the forecasting models for
Thailand’s crude palm oil production and crude
palm oil price. The results from both forecasting
methods confirmed that different initial settings
gave significantly different MAPE values. In [6],
the author proposed a new default setting for the
multiplicative Holt-Winters model compared to the
original Holt-Winters setting and Hansun’ s initial
settings, [7]. The study showed that the proposed
initial settings gave the best result for all ten
datasets. Therefore, this research will examine
various initiations that are proposed by the different
studies.
Box-Jenkins method is reputable for providing
high accuracy in short-term prediction. In [8], the
author predicted the total imports and exports in
Saudi Arabia by employing ANN and ARIMA
models. It was found that both methods are
appropriate for forecasting the total annual imports
and exports of Saudi Arabia kingdom. Box-Jenkins
method was applied to forecast the imports and
exports of paper products in Turkey, [9].
Autoregressive with seasonal dummies and Box-
Jenkins were employed to forecast the imports and
exports of Pakistan and it was found that Box-
Jenkins provided better accuracy for the exports and
autoregressive with seasonal dummies demonstrated
more precision for the imports, [10].
In recent years, Long Short-Term Memory
Neural Networks (LSTM) gained popularity in time
series forecasting. LSTM and ARIMA models were
used to forecast Ecuador’s imports of household
appliances. The results revealed that the LSTM
produced a better fit and improved predictions than
the ARIMA model, [11]. The LSTM was used to
forecast the total trade volume of China Shandong
Province’s imports and exports. The results revealed
that the LSTM outperformed the cubic exponential
smoothing method, [12]. In [13], the authors
employed ARIMA, ETS, TBATS, SVR, RFR,
LASSO, MLP, XGB, and HDL methods to predict
the global trade of ten major countries. The results
revealed that the Hybrid Deep Learning method
provides the best performance. Therefore, this study
employs the Holt-Winters Exponential Smoothing
method with various initial settings, the Box-Jenkins
method, and LSTM in the prediction of the
electrical appliance export values of Thailand.
2 Data Collection and Methodology
Thailand’s electrical appliances monthly export
values are collected from the Information
Technology and Communication Center, Ministry of
Commerce from January 2006 to November 2022.
The data from January 2006 to December 2021 were
used to construct and select the forecasting models,
and the remaining were used for measuring the
model’s accuracy. Three forecasting methods which
are the Holt-Winters method with various initial
settings, the Box-Jenkins method and LSTM are
employed to construct the forecasting models.
2.1 Holt-Winters Method
The Holt-Winters exponential smoothing method is
an analytical method that is suitable for time series
with a linear trend and seasonality. It is often used
for short-term forecasting. The Holt-Winter method
deals with three smoothing parameters:
,,
tuning levels, trends, and seasonal factors. The
tuning parameters must have values between 0 and
1. The Holt-Winters method has two models: the
additive model and the multiplicative model. The
additive model is suitable for constant seasonal
influences and the multiplicative model is fit for
seasonal influences which variate to the trend value,
[14].
2.1.1 Additive Holt-Winters Model
In the case of time series that has a linear trend, a
constant slope
1
()
, and a constant seasonal
fluctuation
()
t
S
. Equation (1) is used to describe the
time series with an additive model, [15].
01
()
t t t
Y t S
(1)
For the additive model,
1t
T
and
t
T
are the time
series level at time t-1 and t.
1t
T
and
t
T
are defined
as
1 0 1( 1)
t
Tt
, and
01
.
t
Tt
1
is the
slope from time t to time t+1.
t
Y
,
t
are the real data
and the error at time t.
ˆ
ˆ,,
t t t
T b S
are the estimated
level, slope, and seasonality at time t.
11
ˆ,
tt
Tb
are the
estimated level and slope at time t-1.
ˆtL
S
is the
estimated seasonality at time t-L and L is the
number of seasons in a year. The smoothing
equations (2)-(4) are used to update
ˆ
t
T
,
t
b
,
ˆt
S
from
time t-1 to time t, [13].
11
ˆˆ
t t t t
T T b e
(2)
1t t t
b b e
(3)
ˆˆ (1 )
t t L t
S S e
(4)
2.1.2 Multiplicative Holt-Winters Model
In the case of time series has a linear trend with a
constant slope
1
and a variate seasonal fluctuation.
The equation (5) is used to describe the
multiplicative model.
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01
()
t t t
Y t S
(5)
The smoothing equations (6)-(8) are used to update
ˆ
t
T
,
t
b
,
ˆt
S
from time t-1 to time t for the
multiplicative model.
11
ˆˆ t
t t t
tL
e
T T b S
(6)
1
t
tt
tL
e
bb S
(7)
(1 )
ˆˆ t
t t L
t
e
SS T
(8)
2.1.3 Holt-Winters Model with Different Initial
Settings
The different initial settings provide different
accuracy of the Holt-Winters model. This research
divides the initial settings into two categories. The
first category consists of seven different patterns.
The seasonal influence patterns 1-6 for the additive
model are given by equation (9), and for the
multiplicative model are given by equation (10).
The seasonal influence patterns 7 are computed by
using the ratio to moving average method to
decompose the time series and get
01
,bb
for level,
slope, and
ˆt
S
seasonal factor, then using only
seasonal factor, [6].
ˆˆ; 1,
i i L
S Y T i L
(9)
ˆ; 1,
ˆ
i
i
L
Y
S i L
T
(10)
The level component of patterns 1-5 for both the
additive model and multiplicative model is given by
equation (11).
12
()
ˆL
LY Y Y
TL
(11)
The level component for patterns 6-7 is defined as
equation (12), [6].
11
( 1) ( 1)
ˆ(12)
( 1) ( 1)
L L L m
L
LY L Y L m Y
TL L L m
Pattern 1: [16], [17], suggested the growth
component as equation (13).
1
1Li L i
Li
YY
bLL
(13)
Pattern 2: [4], [18], advised the growth component
as equation (14).
21L
b Y Y
(14)
Pattern 3: [4], [18], suggested the growth
component as equation (15).
2 1 3 2 4 3
( ) ( ) ( )
3
L
Y Y Y Y Y Y
b
(15)
Pattern 4: [4], [18], proposed the growth component
as equation (16).
1
1
L
LYY
bL
(16)
Pattern 5: [4], [18], recommended the growth
component as equation (17).
0
L
b
(17)
Pattern 6-7: [7], suggested the growth component as
equation (18).
2 2 1 2 1
2
1 2 1
2 (2 1) ( 2) ( 1)
2 (2 1) ( 2) ( 1)
1
( 1) 2
( 1) 2 1
L L L L
LLL
LY L Y L Y L Y
L L L L
bLY L Y Y Y
L
LL
(18)
The second category employs the data from the first
2-15 years (K=2,…,15) to calculate label, trend, and
seasonal components by using the ratio to moving
average method to decompose the time series. Then
get
01
,bb
for level and slope of a linear trend and
ˆt
S
seasonal factor, and calculates
ˆ
t
T
by applying
equation (19)-(20). t denotes the number of data
used in calculating initial settings.
01
ˆ
t
T b b t
(19)
1L
bb
(20)
This research employed the Solver module in
Microsoft Excel to estimate the smoothing
parameters:
,,
to obtain the minimum RMSE.
2.2 Box-Jenkins Method
The Box-Jenkins method is widely used in modeling
and forecasting. The Box-Jenkins method defines a
predictive model by first checking whether it is
stationary. Stationary time series have a constant
mean and variance. If the time series has a trend, it
will be converted to stationary by taking the
difference. If the time series has seasonal influences,
it is converted to stationary by seasonal difference.
In case of time series have an inconstant variance,
taking a log is performed to make the time series
stationary. Once the stationary time series is
established, there are four steps to analyze, [15]:
Step 1. Find models that are expected to be suitable
by considering the correlogram of the
Autocorrelation Function (ACF) and Partial
Autocorrelation Function (PACF) of the time series
which are similar to the ACF and PACF of the
population.
Step 2. Estimate parameters of the model from time
series data.
Step 3. Check whether the model set in Step 1 is
suitable, by performing various tests. If the model
fails, then adjust the model and return to Step 2.
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Step 4. If the model passes all the tests in Step 3, the
model can be used for forecasting, then Equation
(21) is used to predict future values.
The Box-Jenkins model is defined as follows, [19]:
0
( ) ( ) ( ) ( )
LL
a A t b B t
B B Z B B
(21)
when
2
12
( ) (1 )
a
aa
B B B B
2
12
( ) (1 )
L L L AL
A L L AL
B B B B
2
12
( ) (1 )
b
bb
B B B B
2
12
( ) (1 )
L L L BL
B L L BL
B B B B
(1 ) (1 )
d L D
tt
Z B B Y
The d regular difference and D seasonal difference
are taken to make the time series stationary. The
real data at time t are defined by
t
Y
. The constant
term is defined by
0
. The order of the non-seasonal
autoregressive model is defined by
()
aB
. The order
A of the seasonal autoregressive model is defined by
()
L
AB
. The order b of the non-seasonal moving
average model is defined by
()
bB
. Order B of the
seasonal moving average model is defined by
()
L
BB
. L is the number of seasons in a year. The
error at time t is defined as
t
which has a normal
distribution with zero mean and constant variance
and
t
is statistically independent.
Minitab 21.1.0 was used to analyze the Box-Jenkins
model in this research.
2.3 Long Short-Term Memory Networks
(LSTM)
Artificial Neural Networks (ANN) are built to
imitate the human brain to create the capability of
learning patterns, recognition, and the extraction of
new knowledge, [20].
Neural Networks are a branch of Artificial
Intelligence. Neural Networks use backpropagation
algorithms to simulate human-like learning. There
are two methods of learning. Supervised learning is
the process of training computers to solve problems
by providing information and target outcome.
Unsupervised learning is the algorithm of training a
computer by giving unspecific data and letting the
computer learn the relationship between them.
LSTM is a recurrent neural network in which
the output layer can be fed back into the network.
LSTM introduces a memory cell and three gates:
input, output and forget gates. The input gate
accepts the new data to enter the cell state. The
forget gate determines whether the data that enters
the cell state should be kept or discarded. The
selected data is evaluated from the input data of that
node plus the results of the previous node. The
output gate prepares data for output.
The data from January 2006 to December 2021
are separated into 70:30. The electrical appliance
export values from January 2006 to February 2017
are employed as the training set used for training
LSTM. The electrical appliance export values from
March 2017 to December 2021 are employed as the
test set. The data from January 2022 to November
2022 are used as the validation set. This research
employs Python in modeling LSTM. The number of
nodes in the input layer is set to 12, 13, 14, 15, and
16 nodes because this time series has both trends
and seasonal influences. This research varies the
hidden neurons from 2-15 nodes and varies epochs
from 100, 200, 300, 400, and 500 epochs. Adam
optimizer is used with a learning rate of 0.001 and a
momentum of 0.9.
3 Criterion for Model Selection
The forecasting model with the smallest root mean
square error was chosen. Then mean absolute
percentage error was used to calculate the model’s
accuracy.
2
1
1
1(22)
1100 (23)
m
t
t
mt
tt
RMSE e
m
e
MAPE mY
4 Results
The Holt-Winters models with different initial
settings, Box-Jenkins models, and LSTM models
are built for Thailand’s electrical appliances export
values.
4.1 The Holt-Winters Method
The results from Holt-Winters models with various
initial settings were shown in Tables 1 and 2.
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Table 1. RMSE of Holt-Winters models with seven
different settings
Pattern
Additive
model
Multiplicative
model
1
3,963.13**
4,103.39**
2
4,098.47**
4,160.79**
3
4,492.53**
4,431.10**
4
4,012.42**
4,113.16**
5
3,972.70**
4,102.35**
6
3,970.68
4,101.46**
7
3,634.90**
3,673.52
** Residuals have normal distribution at
0.01a=
Table 2. RMSE of Holt-Winters models with
different settings from the decomposition method.
Number of
years (K)
Additive
model
Multiplicative
model
2
4,118.17
4,303.69*
3
3,697.96*
3,892.27*
4
3,851.76*
4,672.54*
5
3,716.52
3,811.19
6
3,794.90
3,828.32
7
3,548.65*
3,596.57*
8
3,519.28*
3,647.69*
9
3,717.16*
3,849.71*
10
3,778.39*
3,864.07*
11
3,843.95
3,910.68*
12
4,007.99
4,017.87*
13
4,028.65*
4,033.21*
14
4,007.01
3,993.70*
15
5.623.00*
5,478.79*
*Residuals have normal distribution at
0.05a=
From Table 1, the Holt-Winters models with initial
settings pattern 7 obtained the smallest RMSE for
both additive and multiplicative models, where the
additive model yielded the minimum RMSE of
3,634.90. This result confirmed that the Holt-
Winters method with the initial setting proposed by
[6], could be a choice to estimate the initial settings
for the Holt-Winters method. Residuals from all
settings did not have a normal distribution
0.05a=
, but some had a normal distribution
0.01a=
.
From Table 2, the additive Holt-Winters with
the initial values from the decomposition method,
which the initial settings computed from the first
eight years of data gained the minimum RMSE of
3,519.28. The initial settings computed from the
first seven years of data gave the minimum RMSE
for the multiplicative Holt-Winters model. It was
found that the residuals from nearly every model
had a normal distribution. Therefore, the initial
settings from the decomposition method are suitable
for the Holt-Winters method.
4.2 Box-Jenkins Method
Fig. 1: Thailand’s electrical appliances export
values from January 2006 to December 2021
From Figure 1, Thailand’s electrical appliances
export values showed a non-linear trend and
seasonal fluctuation. To make the time series
stationary, one regular difference (d=1) and one
seasonal difference (D=1) were taken. According to
Autocorrelation Function (ACF) in Figure 2 and
Partial Autocorrelation Function (PACF) in Figure
3, ACF were decreasing after lag 3 and PACF were
decreasing after lag 4. Then it was proposed to be a
(3,1, 4)ARIMA
model. In the seasonal part, ACF at
lag 12, 24, 36,… were decreasing rapidly and PACF
was cut off at lag 48. Then it was suggested to be a
seasonal model
12
(4,1,0)SARIMA
. Unfortunately, the
residuals of the model correlate with each other. The
model
12
(3,1,3) (4,1,0)ARIMA SARIMA
was
suggested.
Fig. 2: ACF of Thailand’s electrical appliances
export values with d=1 and D=1
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Fig. 3: PACF of Thailand’s electrical appliances
export values with d=1 and D=1
Table 3 showed all parameters of the model
12
(3,1,3) (4,1,0)ARIMA SARIMA
were statistically
significant from zero (p-value was less than 0.05).
From the Box-Ljung test, the residuals of the model
for all lags were statistically independent (the p-
value was larger than 0.05). Therefore,
the
12
(3,1,3) (4,1,0)ARIMA SARIMA
model passed the
diagnostic check. In addition, the residuals of Box-
Jenkins models needed to have a normal
distribution. The Anderson-Darling test was
employed to test the normality of residuals. Figure
4, showed residuals of the model
12
(3,1,3) (4,1,0)ARIMA SARIMA
had a normal
distribution because the p-value was greater than
0.05 (p-value = 0.162). Some other models passed
the diagnostic checking but the residuals did not
have a normal distribution. Therefore, the model
12
(3,1,3) (4,1,0)ARIMA SARIMA
was the only model
that fitted Thailand’s electrical appliances export
values.
Table 3. Minitab output of the model
12
(3,1,3) (4,1,0)ARIMA SARIMA
Type
Coef.
SE.
Coef.
t-value
p-value
1
0.8198
0.0868
9.44
0.000
2
-0.7280
0.1280
-5.67
0.000
3
0.4840
0.1090
4.44
0.000
12
-0.6652
0.0773
-8.61
0.000
24
-0.5773
0.0878
-6.57
0.000
36
-0.5555
0.0868
-6.40
0.000
48
-0.5518
0.0778
-7.09
0.000
1
1.1032
0.0458
24.09
0.000
2
-1.0167
0.0886
-11.47
0.000
3
0.8907
0.0711
12.53
0.000
Modified Box-Pierce(Box-Ljung) Chi-Square
statistic
Lag
12
24
36
48
Chi-
Square
5.71
13.23
32.08
48.07
DF
2
14
26
38
p-value
0.079
0.595
0.173
0.129
Fig. 4: Anderson-Darling normality test for residuals
of the
12
(3,1,3) (4,1,0)ARIMA SARIMA
model
4.3 Long Short-Term Memory Networks
(LSTM)
Increasing the input nodes, the RMSE of the
training set was decreasing significantly. On the
contrary, the RMSE of the testing set was
increasing. To avoid overfitting, the selected model
should have the RMSE of the training set and
testing set, which have similar values with minimal
RMSE. The optimal model of LSTM was 14-5-1
with 300 iterations. The RMSE of the model was
shown in Table 4.
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Table 4. The RMSE of the training set, test set, and
validation set
Model
RMSE
Training set
Test set
Validation
set
14-5-1
3,566.07
3,545.14
3,570.35
Table 5. The RMSE from three predicting methods
Forecasting model
RMSE
The additive Holt-Winters model
with initial setting 7
3,634.90
The additive Holt-Winters model
with the initial setting from the
decomposition method
(The initial settings computed from
the first eight years of data)
3,519.28
12
(3,1,3) (4,1,0)ARIMA SARIMA
3,415.49
LSTM
3,545.14
4.4 Model Selection and Performance
Measure
From Table 5, the Box-Jenkins model obtained the
smallest RMSE. The additive Holt-Winters method
with initial settings from the decomposition method,
which have the initial settings computed from the
first eight years of data, gave the minimum RMSE
for the Holt-Winters method. Therefore, the Box-
Jenkins method was the most appropriate
forecasting method for Thailand’s electrical
appliance export values and obtained a MAPE of
8.0%. The actual, fits and forecasts from the Box
Jenkins method are presented in Figure 5.
Fig. 5: Actual, fits and forecasts from Box-Jenkins
method
5 Conclusion and Discussion
This research presents three different forecasting
methods: the Holt-Winters method with different
initial settings, the Box-Jenkins method, and LSTM
to model Thailand’s electrical appliance export
values. The results revealed that the Box-Jenkins
method gives the best forecasting model for
Thailand’s electrical appliance export values and
yields a MAPE of 8.0%. Therefore, the model
should be used to predict Thailand’s electrical
appliance export values.
The study confirms that Box-Jenkins is a
powerful method for time series forecasting. LSTM
usually gives the best result. However, this research
LSTM does not give the best result since the
training data may need to be larger. LSTM requires
many data for training and much time for tuning the
hyper-parameter of the networks to get a good result.
In case of time and data are limited, the Holt-
Winters method with initial settings from the
decomposition method and the Box-Jenkins method
are good choices for time series forecasting.
Acknowledgment:
This research was supported by King Mongkut’s
Institute of Technology Ladkrabang Research Fund,
School of Science, Grant number 2566-02-05-003.
References:
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Business and Industry Trends in Thailand
2021-2023: Electrical Appliance Industry,
pp.1-8
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Promotion, Department of International Trade
Promotion, 2021. February monthly report
2021, pp.1-2.
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Vercher E, Corberan-Vallet pp.517-533.
[4] Booranawong T. and Booranawong A.,
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Contribution of Individual Authors to the
Creation of a Scientific Article
Somsri Banditvilai and Yuwadee Klomwises
equally contributed to the present research, at all
stages from the formulation of the problem to the
final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
This research is supported by King Mongkut’s
Institute of Technology Ladkrabang.
Conflict of Interest
The authors have no conflict of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
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WSEAS TRANSACTIONS on SYSTEMS
DOI: 10.37394/23202.2023.22.47
Somsri Banditvilai, Yuwadee Klomwises
E-ISSN: 2224-2678
462
Volume 22, 2023
