Effects of the Covid-19 Pandemic on Turkish Natural Stone Industry: A Grey Forecasting Model

Abstract

When the indicators in recent years are examined in the developing and renewed economic environment in Turkey, it is seen that the momentum of the natural stone industry and its share in total mining exports have increased steadily. However, the Covid-19 pandemic in 2020, which affected the whole world, also affected the Turkish natural industry. Within the scope of this study, the export values of the Turkish natural stone industry on a monthly and yearly basis were evaluated both before the pandemic and during the pandemic. Export figures for 2020 and 2021 were tried to be estimated using the Gray Forecast model. With the effect of the Covid-19 pandemic, natural stone export figures for 2020 fell behind 2019 in February, March, April and May. With the normalization process in June, July and Months, normalization started in export figures and exceeded the export values of 2019 in September, October, November and December. In 2020, which was entered with great hopes, it was not possible to reach the targeted figures this year due to the pandemic. In addition, Also, export values for 2020 and 2021 were predicted using a GM (1,1) grey forecasting model, which is a method frequently used in uncertainty cases. 2020 and 2021 export values were estimated by using the GM (1,1) gray forecasting model, which is a method frequently used in uncertainty situations. It has been seen that the model can be used reliably to predict natural stone export figures. In the following years, some assessments and recommendations have been made that may make the Turkish natural stone industry stronger in the following years on issues such as health management of crises and adaptation to the current situation if such outbreaks are replicated in the global world economy.

Full text

Mühendislik Bilimleri ve Tasarım Dergisi
10(2), 520 – 531, 2022
e-ISSN: 1308-6693
Araştırma Makalesi
Journal of Engineering Sciences and Design
DOI: 10.21923/jesd.989253
Research Article
520
EFFECTS OF THE COVID-19 PANDEMIC ON TURKISH NATURAL STONE INDUSTRY: A
GREY FORECASTING MODEL
Gökhan EKİNCİOĞLU1, Deniz AKBAY2*, Erdal AYDEMİR3
1 Ahi Evran University, Kaman Vocational School, Department of Mining and Mineral Extraction, Kırşehir,
Türkiye
2 Çanakkale Onsekiz Mart University, Çan Vocational School, Department of Mining and Mineral Extraction,
Çanakkale, Türkiye
3 Süleyman Demirel University, Faculty of Engineering, Department of Industrial Engineering, Isparta, Türkiye
Keywords
Abstract
Turkish Natural Stone,
Export,
Covid-19 Pandemic,
Grey Forecast Model.
When the indicators in recent years are examined in the developing and renewed
economic environment in Turkey, it is seen that the momentum of the natural stone
industry and its share in total mining exports have increased steadily. However, the
Covid-19 pandemic in 2020, which affected the whole world, also affected the
Turkish natural industry. Within the scope of this study, the export values of the
Turkish natural stone industry on a monthly and yearly basis were evaluated both
before the pandemic and during the pandemic. Export figures for 2020 and 2021
were tried to be estimated using the Gray Forecast model. With the effect of the
Covid-19 pandemic, natural stone export figures for 2020 fell behind 2019 in
February, March, April and May. With the normalization process in June, July and
Months, normalization started in export figures and exceeded the export values of
2019 in September, October, November and December. In 2020, which was entered
with great hopes, it was not possible to reach the targeted figures this year due to
the pandemic. In addition, Also, export values for 2020 and 2021 were predicted
using a GM (1,1) grey forecasting model, which is a method frequently used in
uncertainty cases. 2020 and 2021 export values were estimated by using the GM
(1,1) gray forecasting model, which is a method frequently used in uncertainty
situations. It has been seen that the model can be used reliably to predict natural
stone export figures. In the following years, some assessments and
recommendations have been made that may make the Turkish natural stone
industry stronger in the following years on issues such as health management of
crises and adaptation to the current situation if such outbreaks are replicated in the
global world economy.
COVİD-19 PANDEMİSİNİN TÜRK DOĞAL TAŞ SEKTÖRÜNE ETKİLERİ: BİR GRİ
TAHMİN MODELİ
Anahtar Kelimeler
Öz
Türk Doğal Taşı,
İhracat,
Covid-19 Pandemisi,
Gri Tahmin Modeli.
Türkiye'de gelişen ve yenilenen ekonomik ortamda son yıllardaki göstergeler
incelendiğinde, doğal taş sektörünün ivmesinin ve toplam madencilik ihracatı
içindeki payının istikrarlı bir şekilde arttığı görülmektedir. Ancak 2020 yılında tüm
dünyayı etkisi altına alan Covid-19 salgını, Türkiye doğal taş endüstrisini de
etkilemiştir. Bu çalışma kapsamında hem pandemi öncesi hem de pandemi
döneminde Türkiye doğal taş sektörünün aylık ve yıllık olarak ihracat değerleri
değerlendirilmiştir. 2020 ve 2021 yılına ait ihracat rakamları Gri Tahmin modeli
kullanılarak tahmin edilmeye çalışılmıştır. Türkiye maden ihracatının %50’lik
kısmını Doğal Taş ihracatı oluşturmaktadır. Covid-19 pandemisinin etkisiyle 2020
yılı doğal taş ihracat rakamları Şubat, Mart, Nisan ve Mayıs aylarında 2019 yılının
gerisinde kalmıştır. Haziran, Temmuz ve Ağustos aylarında normalleşme süreci ile
birlikte ihracat rakamlarında normalleşme başlamış ve Eylül, Ekim, Kasım ve Aralık
*
İlgili yazar / Corresponding author: denizakbay@comu.edu.tr, +90-286-416-7705

EKİNCİOĞLU et al.
10.21923/jesd.989253
521
aylarında 2019 yılı ihracat değerlerinin aşmıştır. Büyük umutlarla girilen 2020
yılında pandemi nedeniyle bu yıl hedeflenen rakamlara ulaşmak mümkün
olmamıştır. Ayrıca belirsizlik durumlarında sıklıkla kullanılan bir yöntem olan GM
(1,1) gri tahmin modeli kullanılarak 2020 ve 2021 ihracat değerleri tahmin
edilmiştir. Modelin doğal taş ihracat rakamlarını tahminde güvenilir olarak
kullanılabileceği görülmüştür. İlerleyen yıllarda krizlerin sağlıklı yönetimi ve bu tür
salgınların küresel dünya ekonomisinde tekrarlanması halinde mevcut duruma
uyum gibi konularda önümüzdeki yıllarda Türkiye doğal taş sektörünü daha güçlü
kılabilecek bazı değerlendirmeler ve önerilerde bulunulmuştur.
Alıntı / Cite
Ekincioğlu, G., Akbay, D., Aydemir, E., (2022). Effects of the Covid-19 Pandemic on Turkish Natural Stone Industry:
A Grey Forecasting Model, Journal of Engineering Sciences and Design, 10(2), 520-531.
Yazar Kimliği / Author ID (ORCID Number)
Makale Süreci / Article Process
G. Ekincioğlu, 0000-0001-9377-6817
D. Akbay, 0000-0002-7794-5278
E. Aydemir, 0000-0003-4834-725X
Başvuru Tarihi / Submission Date
Revizyon Tarihi / Revision Date
Kabul Tarihi / Accepted Date
Yayım Tarihi / Published Date
01.09.2021
14.12.2021
20.12.2021
30.06.2022
1. Introduction
The effects of changes occurring in the world due to globalization are very rapid. The consequences of political
developments, economic crises, wars, and epidemics occurring at the national level as a result of globalization in
the world exceed the borders of the country and reach countries that are not bordering. Economically dependent,
economically dependent countries or foreign-dependent countries are adversely affected by such events due to
their fragile economies. Developing countries such as Turkey should be economically strong because they are
affected by developments on a global scale. The road to power in the global world is also through economic growth.
Developing countries, which consider economic growth as a goal, both enrich and develop by using their natural
resources (Başol et al., 2005; Ekincioğlu and Akbay, 2021).
The wide range of raw materials in the natural stone industry increases its competitiveness in global markets with
block and processed plate productions using modern production methods and contributes about $2 billion to the
country's economy every year.
As of 2019, the share of mining in Turkey's total exports was 2.60% ($4.3 billion) and the share of natural stone
exports in total mining exports was 43.74% ($1.86 billion) (TİM, 2020). When the data of recent years are
examined in the developing and renewed economic environment in Turkey, the momentum of the natural stone
industry is obvious. Therefore, to maintain the momentum and stability achieved, all scenarios should be prepared
and underlined what awaits the industry (Ekincioğlu and Akbay, 2021). However, this paper tries to answer the
following research questions:
 How can the extraordinary situations on natural stone industry be modelled?
 Today, Covid-19 pandemic also affected all industries on a global scale in 2020. So, can it be investigated
what effect the pandemic has had on the natural stone industry?
 Can a new model be developed under uncertainty with a time-series-based approach to achieve these
effects using Turkey export data until 2020 to 2021?
 Which method/s can be selected for clarifying the uncertainty?
Within the scope of this study, the development of the industry in recent years and the impact of the Covid-19
pandemic affecting the whole world on a global scale in 2020 were examined. In addition, 2020 and 2021 export
values were estimated with GM (1,1) grey forecasting model, which is a method frequently used in uncertainty
cases, and some evaluations and recommendations were made that could make Turkey's natural stone industry
stronger.
The rest of the paper is organized as follows. The analysis of the before Covid-19 pandemic Turkish natural stone
export is given with the global views in Section 2. Then, the effects of the Covid-19 pandemic on the natural stone
export values of Turkey are given with numerical analysis on the year 2020 in Section 3. The establishing the grey
forecasting models and their results are presented with error analysis on the year 2021 in Section 4. Finally, our
conclusions are presented by combining the actual and future analysis of the Covid-19 effects as a big crisis in the
last section.

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2. Before Covid-19 Pandemic Turkish Natural Stone Export
Natural stones are easy to process, resistant to environmental conditions and their aesthetic appearance has been
effective in their use throughout history. With the development of technology, the processing of hard rocks that
cannot be processed, the increasing ability of rocks to give plates, and the rapid increase of the needs of the
construction industry have made the natural stone industry the engine of mining in the world and our country
(Adıgüzel and Şengüler, 2019; Ekincioğlu and Akbay, 2021).
There are approximately 2500 licensed natural quarries in the industry and 1500 of them are actively working.
Approximately 200 large facilities and approximately 9000 medium and small enterprises and workshops operate
in the industry, including SME. Approximately 180000 workers and 5000 technical staff are employed in the
industry (TCKB, 2018). The natural stone industry has high added value compared to other industries. It is among
the industries that bring net foreign currency to the country as a result of its market. In other industries with high
added value, a ratio of 10% to 30% of the foreign currency revenue after exports remains in the country, while all
the foreign currency obtained from exports in the natural stone industry remains in the country (Kocaman, 2006;
Adıgüzel and Şengüler, 2019; Ekincioğlu and Akbay, 2021).
When the natural stone trade volume of our country between 2013 and 2019 is examined, it is seen that it varies
between 41% and 49%. In other words, nearly half of our country's mining exports, which are very rich in
underground resources, are natural stone exports (Table 1). Since 2013, Turkish natural stone exports have
ranged from 1.74-2.2 billion dollars and the lowest exports have been observed in 2015, 2016, and 2020 (Figure
1). During these years, there has been a decrease in both mining exports and natural stone exports. However, it is
seen that the decrease in natural stone exports is less than the decrease in total mining exports. The decrease in
2015 and 2016 was due to the fact that the People's Republic of China cut its incentives to the construction industry
during this period. The reason for the decrease in 2020 is the negative, diminutive, narrowing effect of the Covid-
19 pandemic on the country's economies and world trade (Ekincioğlu and Akbay, 2021).
Table 1. Turkish natural stone and mining exports values according to the years (IMIB, 2020)
Year
Mining Export
Natural Stone Export
Natural Stone Export/Mining Export
%
106 tonnes
109 $
106 tonnes
109 $
2013
22.31
5.03
8.44
2.22
44.14
2014
21.21
4.64
7.37
2.13
45.85
2015
20.14
3.90
6.52
1.91
48.94
2016
20.43
3.79
6.52
1.81
47.67
2017
24.70
4.69
7.94
2.05
43.69
2018
26.33
4.56
7.46
1.91
41.83
2019
27.15
4.31
7.14
1.86
43.24
2020
27.88
4.27
6.46
1.74
40.75
Figure 1. Turkish natural stone-mining export value and natural stone exports/mining exports ratio (NSE/ME, %)
(Ekincioğlu and Akbay, 2021)
2.22 2.13 1.91 1.81 2.05 1.91 1.86 1.74
5.03 4.64 3.90 3.79 4.69 4.56 4.31 4.27
44.14 45.85 48.94 47.67 43.69 41.83 43.24 40.75
0
10
20
30
40
50
60
0
1
2
3
4
5
6
2013 2014 2015 2016 2017 2018 2019 2020
Export Revenue (bilion ş)
NSE/M
E, %
Natural Stone Export Mining Export NSE/ME

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The decrease in export rates for 2015, 2016, and 2020 has been included in the table as an indication of how risky
it is for the industry to adhere to the single market. In terms of the following years, a possible economic or political
crisis in the People's Republic of China, where Turkey exports a very large part of its natural stone exports, or the
Chinese government restricting natural stone imports or stopping its imports completely, the Turkish natural
stone industry will be adversely affected. As a matter of fact, this scenario occurred in late 2019 with the Covid-19
pandemic that occurred in Wuhan, People's Republic of China, was effective all over the world in 2020. The largest
share of Turkey's total natural stone exports has remained unchanged in recent years to the People's Republic of
China (Table 2) (Ekincioğlu and Akbay, 2021).
Table 2. Export rates by countries (FOB) (%) (IMIB, 2020)
Countries
2013
2014
2015
2016
2017
2018
2019
2020
People's Republic of China
44.17
38.94
38.16
40.41
46.18
40.55
37.27
31.09
United States of America
13.41
15.22
17.03
15.96
14.37
15.69
15.34
18.72
Saudi Arabia
4.27
5.20
5.96
6.61
5.11
5.55
6.73
8.02
India
2.09
2.61
3.30
3.05
4.15
4.73
4.93
3.54
Israel
1.70
1.88
2.21
2.65
2.63
3.17
3.52
4.37
France
0.00
2.37
2.30
2.50
2.53
2.91
3.32
3.88
Iraq
5.17
5.28
4.26
3.95
3.11
3.27
3.43
3.61
Australia
1.12
1.50
1.64
1.72
1.75
2.09
2.13
2.43
United Arab Emirates
2.02
2.23
2.57
2.69
2.57
2.83
2.13
2.09
Other countries
26.05
24.77
22.57
20.46
17.6
19.21
21.2
22.25
The United States follows the People's Republic of China. Following these two countries, the total of natural stone
exports to Saudi Arabia, India, Israel, and other countries lags far behind natural stone exports to the People's
Republic of China. The People's Republic of China in block exports and the United States in processed product
exports are two important markets for the natural stone industry. When Figures 2 and 3 are examined, the first
place in the total export amount is the People's Republic of China (min. %47.36 – max. %59.15), but its share in
total natural stone exports is higher due to higher value-added processed plate exports to the United States. (min.
%13.41 - max. %17.13). These figures clearly prove the importance of high value-added product exports for the
Turkish economy (Ekincioğlu and Akbay, 2021).
Figure 2. Country shares (FOB) (%) in total natural stone export revenues (Ekincioğlu and Akbay, 2021)
44.17
38.94
38.16
40.41
46.18
40.55
37.27
31.29
13.41
15.22
17.03
15.96
14.37
15.69
15.34
18.47
42.42
45.84
44.81
43,63
39.45
43.76
47.39
49.99
0
10
20
30
40
50
60
2013 2014 2015 2016 2017 2018 2019 2020
FOB Export Rates %
CHN USA Other Countries

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Figure 3. Country shares in total natural stone exports (billion tonnes) (%) (Ekincioğlu and Akbay, 2021)
3. Turkish Natural Stone Export Impact of the Covid-19
How the figures for 2020 belonging to the People's Republic of China and the United States, the two largest markets
in the natural stone export market for Turkey, raw blocks and processed products, have changed is given in Table
3. The numbers given in red font in the table represent the decreases in export figures. When the data are
examined, it is seen that the natural stone export figures to the People's Republic of China, the center of the
pandemic that emerged in December 2019, decreased by around 50% from February 2020. According to the
People's Republic of China, natural stone export figures to the United States, where the pandemic reached later,
decreased slightly in February 2020, but the decrease in the amount of exports was not felt much on the revenue
side due to the rising dollar exchange rate. It is seen that the export figures to the United States have fallen
significantly in May 2020. When we look at the data for June 2020, it is seen that the sales amounts close to the
data of June 2019 last year were formed although the impact of the pandemic continues to accelerate in the
People's Republic of China and United States. This has been interpreted as a strong signal that natural stone
exports for Turkey begin the normalization process by June. However, the number of cases that started to increase
again in the Covid-19 pandemic, which took effect all over the world in July, has troubled shrinking economies.
This situation has led to a continued decline in exports to the People's Republic of China, which operates with high
stocks in the natural stone market, takes very drastic measures against the pandemic, and makes closures. Export
figures to the United States, whose economy has been severely shrinking, which has started to normalize early due
to the election period, and where the measures are not implemented very strictly according to the world as a
whole, continued to increase. Natural stone exports to the People's Republic of China decreased by 21% in total in
2020, while exports to the United States increased by 22% (Table 3) (Ekincioğlu and Akbay, 2021).
57.67
55.08
54.51
55.54
59.15
52.96
47.36
41.06
6.07
7.82
8.8
8.67
7.95
8.87
9.01
12.14
36.26
37.1
36.69
35.79
32.9
38.17
43.63
46.8
0
10
20
30
40
50
60
70
2013 2014 2015 2016 2017 2018 2019 2020
Export Rates by Quantity %
CHN USA Other Countries

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Table 3. People's Republic of China and United States export data for 2019-2020 (IMIB, 2020)
% Change
USA
FOB
%
2
5
18
-11
-43
54
18
22
29
35
33
25
14
Amount
%
-4
5
11
-9
-31
64
28
30
42
50
61
38
22
China
FOB
%
4
-48
-42
-27
-60
-13
-23
-28
-7
-18
0.5
-3
-11
Amount
%
1
-52
-44
-26
-58
-9
-21
-26
-5
-18
2
-1
-21
2020
USA
FOB
×106 $
44277
44398
44463
44306
44394
44373
32.1
44373
44439
35.0
34.2
31.9
325.2
Amount
×103
tonnes
48.7
49.6
57.4
49.5
46.6
67.3
79.6
63.2
77.4
83.0
87.5
75.9
785.7
China
FOB
×106 $
58.6
44211
44336
45.4
36.6
39.1
57.7
43.6
60.3
51.2
61.9
50.2
540.2
Amount
×103
tonnes
290.6
74.4
101.9
221.5
181.7
192.4
280.7
212.3
293.7
246.6
304.1
257.1
2657
2019
USA
FOB
×106 $
22.0
44367
44217
44461
31.2
44272
44254
44429
44371
44464
44433
44372
286
Amount
×103
tonnes
50.9
47.1
51.8
54.3
67.8
40.9
61.9
48.7
54.4
55.5
54.9
55.2
643.4
China
FOB
×106 $
56.1
44436
35.2
62.2
91.3
45.1
75.2
60.6
64.7
62.2
61.6
51.8
604.8
Amount
×103
tonnes
289.1
153.6
181.6
299.1
437.6
210.3
357.5
285.4
309.6
299.7
298.7
259.9
3382.1
Months
January
Februa
ry
March
April
May
June
July
August
Septem
ber
Octobe
r
Novem
ber
Decem
ber
Total
Figures 4 and 5 show total natural stone export figures monthly. When the last seven years are examined, it is seen
that the natural stone export figures reached their lowest level in February but reached their highest level during
the year, both with the opening of the quarries depending on the seasonal effect in May and with the effect of the
International İzmir Natural Stone and Technology fair held every year in March. However, with the pandemic effect
of 2020, it was seen that natural stone exports were at their lowest level during the year in May. When we look at
the data for June 2020, it is seen that the figures were above the sales amounts (tonnes) of June 2019 last year. It
is seen that this upward trend continues to spread throughout the year in direct proportion to the normalization
process all over the world. It is thought that the amount of exports expected to occur in May 2020 but could not be

EKİNCİOĞLU et al.
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526
realized due to the pandemic had a positive effect on the figures in the remaining six months of 2020 as "Hidden
May Export Amount" (Ekincioğlu and Akbay, 2021).
Table 4. Natural stone exports on a monthly basis by year (FOB million $) (IMIB, 2020)
Months
2013
2014
2015
2016
2017
2018
2019
2020
January
169.10
197.28
137.35
129.40
128.64
150.85
139.06
151.48
February
114.54
128.85
114.62
103.81
118.23
119.46
115.52
108.17
March
132.58
147.41
117.07
127.94
138.37
139.39
122.26
116.20
April
184.56
203.57
175.93
168.57
182.96
172.23
160.16
117.96
May
231.87
222.65
183.60
173.36
219.84
197.70
215.49
101.51
June
205.64
201.99
199.40
167.87
199.18
166.48
114.09
134.60
July
223.37
183.71
185.48
128.14
173.72
177.11
184.71
176.14
August
179.21
163.59
168.87
186.69
201.41
142.79
150.80
134.75
September
207.74
191.08
150.79
153.18
152.35
157.71
168.55
172.76
October
183.72
150.87
155.89
161.15
182.65
176.55
167.89
180.45
November
199.31
160.88
159.81
156.82
190.58
167.57
164.57
179.51
December
190.74
176.34
157.44
148.59
160.16
140.45
161.15
163.48
Total
2222.38
2128.22
1906.25
1805.52
2048.09
1908.29
1864.25
1737.01
Table 5. Natural stone exports of Turkey on a monthly basis by year (×103 tonnes) (IMIB, 2020)
Months
2013
2014
2015
2016
2017
2018
2019
2020
January
660
716
440
475
476
594
553
573
February
399
406
338
325
426
444
410
328
March
463
453
330
431
503
506
437
386
April
707
699
590
609
730
668
630
437
May
982
811
642
625
853
796
845
395
June
798
709
721
593
794
651
435
494
July
843
664
622
448
673
685
717
662
August
655
577
586
691
778
562
580
498
September
772
707
561
595
593
626
653
668
October
704
531
532
603
718
704
629
667
November
754
544
576
594
753
683
641
721
December
699
553
578
529
638
542
610
640
Total
8436
7370
6516
6518
7935
7461
7140
6469
4. Grey Prediction Model
Grey System Theory (GST) was proposed by Professor J. Deng in 1982 with titled as “Control Problems of Grey
Systems” that was the first study in this field. The GST applications were started to use for many real-life systems
such as social, economic, and technical systems since 1989 (Deng, 1989). On the other hand, the GST has many
research fields as clustering, incidence analysis, relational analysis, system modelling, decision making, input-
output analysis, control process etc. (Liu and Lin, 2006). According to progress of GST, it has applied as an effective
and powerful tool in many of the academic and industrial studies are scientific and technological, industrial,
mechanical, robotics, mechatronics, transportation, financial, military systems on transforming of cybernetics and,
also natural events and sources as meteorological, agricultural, ecological, hydrological, geological, biomedical,
mining etc. under grey uncertainties (Liu et al., 2016; Liu, Yang, Forrest, 2017).
Grey system modelling (GM) is a prediction tool using the historical data at least four. GM (1,1) denotes a one-
order one-variable grey difference prediction model. Then, the GM (1,1) model has more advantages over the
traditional prediction methods. It does not need to any distribution and statistical sample. In addition, it uses an
Accumulation Generation Operator (AGO) for smoothing the randomness on the primitive data and an Inverse
Accumulation Generation Operator (IAGO) for finding the predicted values (Liu, Yang, Forrest, 2017; Yang et al.,

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2018). In the recent scientific literature, grey prediction and forecasting methods are applied in many studies both
theoretical and practical modelling (Hsu and Chen, 2003; Ding et al., 2018; Akay and Atak; 2007; Kayacan et al.,
2010; Aydemir et al., 2013; Hamzaçebi and Es, 2014; Wei et al., 2019; Liu and Xie, 2019; Carmona-Benítez and
Nieto; 2020; Zhu et al., 2021).
4.1. The GM (1,1) Modelling
The modelling process of GM (1,1) is given as follows (Liu et al., 2017; Yang et al., 2018):
Step 1. Conduct the original time series data
󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜
[1]
where 󰇛󰇜󰇛󰇜 .
Step 2. Establish the 1-AGO (first-order accumulating generation operator) time series data
󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜
[2]
where 󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜

  .
Step 3. Obtain the 󰇛󰇜row data that is called mean sequence of 󰇛󰇜 generated by by consecutive neighbors
󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜
[3]
where 󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜 ,  in general as the even form of model GM (1,
1). The original form of grey prediction equation is given as a difference equation:
󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜
[4]
Then, after the Step 3, the original form of GM (1,1) is represented as the even form of GM (1,1) model that is given as follows:
󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜
[5]
where 󰇟󰇠parameter values are estimated using the least square method which satisfies

󰇛󰇜
[6]
where





󰇛󰇜󰇛󰇜
󰇛󰇜󰇛󰇜


󰇛󰇜󰇛󰇜




, 




󰇛󰇜󰇛󰇜
󰇛󰇜󰇛󰇜

󰇛󰇜󰇛󰇜




[7]
Step 4. Obtain the accumulating prediction equation as a time response function.
󰇛󰇜󰇛󰇜󰇛󰇛󰇜󰇛󰇜
󰇜󰇛󰇜
, .
[8]
Step 5. Obtain the prediction equation using 1-IAGO (first-order inverse accumulating generation operator).
󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇛󰇜󰇛󰇜
󰇜󰇛󰇜, .
[9]
4.2. Error Analysis
The prediction and/or forecasting studies need to be compared with the higher imprecision level. So, essential
accuracy measurement approaches which are the Mean Squared Error (MSE), the mean absolute error (MAE), and
the Mean Absolute Percentage Error (MAPE) are the most widely used. However, according to Chatfield (1988),
MSE and MAE can often be major variations in the scale of the observations between the different time series so
that a few series with large values can dominate the comparisons. At this phase, MAPE is mostly employed method
as needing the unit free measures. The forecasting error at time () can be defined as follows (Goodwin and
Lawton, 1999):

EKİNCİOĞLU et al.
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, 
[10]
where  is the actual observation value and  is also the forecasted/predicted value for period . Thus, the
Percentage Error (PE) and the Absolute Percentage Error (APE) can be calculated as respectively.


[11]


[12]
So, the MAPE calculation is given as follows in Equation 13.


󰇻
󰇻

 
[13]
In addition, Makridakis (1993) has presented some disadvantages of MAPE value, for a greater APE, the equal
errors above the actual observation than those below the actual value. So, the modified APE (Makridakis,1993)
and the smoothed APE (O’Connor et al., 1997) are developed respectively. However, in this study, besides using
MAPE, for residual correction, posterior error ratio () are also used to test the accuracy of GM (1, 1). The posterior
error ratio () can be calculated as (Yang et al., 2018):

[14]
where  is the residual standard deviation and  is the data standard deviation are given as follows:

 󰇛󰇛󰇜󰇜

 
[15]

 󰇛󰇛󰇜󰇜

 
[16]
Consequently, the adequacy levels of prediction accuracy for GM (1,1) are classified with four levels to MAPE and
C measures in Table 6 which is modified from Lewis (1982) and Yang et al. (2018).
Table 6. Adequacy levels of prediction accuracy for GM (1,1)
Prediction accuracy grades
MAPE
C
1 Excellent


2 Qualified


3 Barely Qualified


4 Unqualified


4.3. Computational Results
In this paper, the Covid-19 pandemic effects on the natural stone export values of Turkey from Table 1 in 2020
and grey forecasting model to 2021 are examined by showing model accuracy evaluations in Table 7. Two
forecasting models are developed which are titled as Grey Model 1 (GM1) and Grey Model 2 (GM2). GM1 model
has established by the years of 2013-2019 row data and then, for the year of 2020, the predict values are obtained
by monthly using Equation 17 with  MAPE value of the whole model.


[17]

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On the other hand, GM2 model has been established by the years 2013-2020 row data including pandemic year,
and then, for the year of 2021, the forecast values are obtained by monthly using Equation 18 with  MAPE
value of the whole model. The observed total value of export for the years 2013-2020 is obtained as 57845 ×103
tonnes and the predicted total value of export for the years 2013-2020 is also obtained as 55912.55×103 tonnes.


[18]
Table 7. Computational results on a monthly basis by year (×103 tonnes)
Grey Model 1
Grey Model 2
Months
Observed
2020
Predicted
2020
APE
(%)
Forecasted
2021
January
573
569.32
0.64
541.99
February
328
399.71
21.86
371.56
March
386
454.26
17.68
423.86
April
437
673.90
54.21
612.42
May
395
807.87
104.52
718.59
June
494
683.79
38.42
627.52
July
662
676.66
2.22
641.89
August
498
644.23
29.36
595.14
September
668
655.57
1.86
625.10
October
667
643.06
3.59
614.59
November
721
661.10
8.31
636.09
December
640
603.50
5.70
578.47
Total
6469
7472.97
288.38
6987.22
MAPE2020
24.03
MAPEMODEL1
7.88
MAPEMODEL2
3.34
C
0.23
According to Table 7, GM1 model has been included the pandemic effects. The months of Feb-Jun and Aug have a
very large deviation. So, the prediction results for the year of 2020 are obtain the 24.03 MAPE value against the
whole model which has 7.88 MAPE value for the years of 2013-2019. The GM1 results show that the pandemic
effects are very disruptive on the natural stone export values in grey highlighted cells. Then, GM2 model deals with
forecasting values that are given in Table 7 and Figure 4 for the year 2021.
Within the scope of the study, an export forecast was made for 2021 using data from 2013-2020 and given in Table
7. When the estimated export figures for 2020 are examined, it is seen that the impact of the pandemic, which
started in December 2019, began to affect the export figures expected to be as of February and started to fall below
the expected values for 2020. The difference was 72000 tonnes for February, 68000 tonnes in March, 237000
tonnes in April, and 413000 tonnes in May. Although there was a decrease in the difference between June and July
due to the effect of the normalization process in June, it was 146000 tonnes in August. With the export
normalization process that did not occur in the first eight months of 2020, export figures were formed above the
forecast values by spreading over the last four months.
0
200
400
600
800
1000
1200
1
5
9
13
17
21
25
29
33
37
41
45
49
53
57
61
65
69
73
77
81
85
89
93
97
101
105
2013 2014 2015 2016 2017 2018 2019 2020 2021
Forecasted
Observed
x 103tones
Natural Stone Export Volume
Years
Figure 4. The observed (2013-2020) and forecasted data (2021)

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The forecasted data has obtained from GM2 model using Equation 18 and for the year 2021, it is important to
continue the Covid-19 pandemic times and their effects on the industries. So, GM2 model has 3.34 MAPE value that
is excellent forecasting accuracy with 0.23 C value from Tables 6-7.
5. Discussion and Conclusion
As is known, the Covid 19 pandemic was first seen in the People's Republic of China and affected both the People's
Republic of China and all countries, especially our country, with which it has a trade relationship. The two
countries most affected by the pandemic in the world were the People's Republic of China and the United States.
The People's Republic of China, which covers 32% in exports, and the United States, which has a 15% share,
account for 52% of our natural stone exports. Turkish natural stone industry has been greatly affected by the fact
that the People's Republic of China and the United States, are the central two countries of the pandemic. When the
export figures for 2020 are analyzed, it is seen that the highest loss occurred in May. In this period, there was a
decrease of 52% in exports to the People's Republic of China and 31% in exports to the USA. In the rest of the year,
the figures that emerged with the normalization process were higher than the previous year.
When the Covid-19 pandemic process and the export figures for 2020 are examined, it is clear that a period of
memorization has been entered for the coming years. Turkey, which entered 2019 successfully, has negatively
affected the natural stone industry, as the industry has remained dependent on the two countries to date and these
countries are the countries most affected by the pandemic. Considering that the GM (1,1) forecasts for 2021 with
excellent accuracy are below 2019, it is thought that future planning should be made in managerial decisions.
It will be through institutionalization that Turkish natural stone companies can be more competitive both in the
country and in the world market. The way to have a stronger structure before the pandemics, political, etc. that
may occur after this will be through institutionalization. There are a few companies in the industry that make an
effort in this regard and try to gain brand value, and they have begun to get rewarded for their steps in this process.
It has been understood during the pandemic that it is no longer possible to catch up with the future with classical
commercial methods. Digital fairs and digital showcases will play an important role in achieving greater goals.
Companies should participate in such fairs and prepare the necessary technology infrastructure. The pandemic
process has shown that, as in other industries, new markets must be found, and alternatives must be created in
the natural stone industry. As observed in this difficult period, the industry is affected as much as the rate at which
your biggest buyer is affected by any crisis. Dividing the risk with alternative markets will strengthen the industry
economically.
It is thought that the Turkish natural stone industry will enter the coming years stronger with the review of the
issues that are tried to be emphasized in this study. Increasing the number of companies that have completed their
institutionalization and branding in the light of science and technology and reaching new markets with new
distance marketing techniques will make the industry less affected by any crisis. As a further research, the
roadmap of the sector should be updated every year by developing these forecasting models and making new
forecasts every year.
Conflict of Interest
No conflict of interest was declared by the authors.
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