Article citation information:
Borucka,
A., Kozłowski, E. Selected
polynomial identification techniques to evaluate maritime transport trends
around Covid-19. Scientific Journal of Silesian
University of Technology. Series Transport. 2023, 120, 51-68. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2023.120.4.
Anna BORUCKA[1], Edward KOZŁOWSKI[2]
SELECTED POLYNOMIAL IDENTIFICATION TECHNIQUES TO EVALUATE MARITIME
TRANSPORT TRENDS AROUND COVID-19
Summary. The Covid-19 pandemic has drastically affected the transport
sector, because of the restrictions introduced to limit the spread of the
threat. They concerned primarily passenger traffic, but trade in goods also
faced completely new challenges, related to increased consumption and the
dynamic development of e-commerce on the one hand and restrictions related to
the pandemic and sealing borders on the other. One of the most susceptible to
fluctuations in international trade is the maritime economy, which has been
analysed in this article. It was checked how the global threat affected sea
traffic in terms of gross weight of goods handled in main ports. The aim of the
study was to characterize the impact of the pandemic on sea transport depending
on the type of ship and to evaluate the current state of sea transport in the
context of the level shaped by forecasts based on observations from before the
coronavirus pandemic. The authors' assumption was to check whether the rail
transport market has already reached the level it could reach in the absence of
the virus threat. The use of a polynomial function was proposed for the study.
Time series containing observations up to the outbreak of the pandemic and
forecasts based on them, as well as time series containing additional
observations from the pandemic period were analysed. The study results obtained
allowed to conclude how the global crisis caused by the Covid-19
pandemic affected the cargo traffic in the sea transport, expressed by the mass
of goods transshipped in major ports, depending on
the individual types of ships.
Keywords: sea
transport, Covid-19 pandemic, cargo ships, polynomial
function
1.
INTRODUCTION
The Covid-19 pandemic has drastically affected the transport
sector. It was one of the first branches of the economy on which a number of
restrictions were imposed to limit the spread of the threat. Almost immediately
after its outbreak, restrictions were introduced on passenger transport, both
international and domestic [38, 25]. For air passenger transport, it was the
biggest crisis in history [3]. Moreover, of all industries, the aviation sector
turned out to be one of the most affected [34, 41]. The extraordinary drop in
passenger numbers, due to the bans on flights in individual countries, has led
to the suspension of most airlines. Operators had to stop their activities;
airports were closed, and all private and commercial flights were suspended
[40, 2]. Drops of several dozen percents were
recorded (the largest decrease compared to the same period of the previous year
was recorded in April and amounted to 87% [19]). According to IATA, the crisis
resulting from the pandemic has cost aviation more than $200 billion [15]
A
similar impact was recorded on the rail passenger transport market. Railway
carriers recorded a significant decrease in volumes resulting from the
introduced restrictions, but also a significant reduction in economic activity,
due to the introduction of remote work and the transfer of business meetings to
the network [5, 52, 53]. The global reduction in the
demand for rail passengers was about 80% - 95% [45], which was also largely due
to the change in the preferences of commuters, who began to choose individual
means of transport, such as a private car, cycling or walking, replacing public
transport in particular [16, 42]
In
Europe, in 2020, the number of travellers decreased in individual countries by
26 to 65% compared to the previous year [12, 43]. Transport restrictions in the
urban agglomeration, in turn, caused the number of visitors to public transport
locations to drop by as much as 80% [36] (March 2020), and the number of public
transport passengers worldwide fell by 50-90% [37]. Similarly, the pandemic has
reduced maritime passenger transport, reducing the number of sailings by almost
45% [32]. Human activities in the oceans have been radically altered,
especially in the context of passenger ferries and cruise ships. Cruise tourism
has been partially or completely suspended, and port activities in terminals
have been limited to a minimum to ensure the safety of the operating personnel
[29, 8].
Changes
in freight transport were not so significant. The pandemic became the reason
for increased consumption and a dynamic shift towards e-business, which is why
transport companies had to take action to maintain international mobility and
provide services at the highest level while complying with security procedures
[51, 23]. As a result, by the end of 2020, the global air cargo sector has
decreased by only 8% [18]. Similarly, rail transport, which in 2020 recorded a
decrease in transported weight by 5.6% (EU) [11]. Global road freight transport
experienced a significant drop in the first lockdown period in 2020, but on an
annualized basis, it fell by only 1% (EU) in terms of ton-kilometres (tkm) compared to 2019 [13].
One
of the most vulnerable to fluctuations in the international trade is the
maritime economy. Maritime transport is responsible for the transport of nearly
80% of the volume and 70% of the value of international trade in goods,
including goods of key importance to the economy, such as food or fuel. It is
responsible for 64% of the world's GDP [9, 1, 30].
Therefore, this article examines this branch of transport by checking how the
global threat affected sea traffic expressed in terms of the gross weight of
goods handled in main ports. Due to the fact that there are significant
differences depending on the transported goods, various types of ships were
analysed (ships intended for the transport of containers, for the transport of
dry and liquid bulk cargo, gaseous cargo, and also adapted for the transport of
rolling cargo and vehicles - Ro-Ro).
The
aim of the study was to characterize the impact of the pandemic on sea
transport depending on the type of ship and to evaluate the current state of
sea transport in the context of the level shaped by forecasts based on
observations from before the coronavirus pandemic. The authors' assumption was
to check whether the rail transport market has already reached the level it
could reach in the absence of the virus threat. It was proposed to use a
polynomial function for the study, because in the examined time series, the transport
weight did not meet the stationarity postulate. The degree of the polynomial
was selected using the difference method and by analysing quadratic variations
of differences, and then adding successive transformations of the time factor
and using linearity tests of the models.
A
time series containing observations up to the outbreak of the pandemic and a
time series containing additional observations from the period of the pandemic
were analysed. For each series, a trend was determined, which was described
using a polynomial, and forecasts were additionally set for the time series
until the outbreak of the pandemic. They were used to compare the current state
of sea transport with the forecast based on observations that do not take into
account the resulting threat. This allowed us to conclude to what extent the
global crisis caused by the Covid-19 pandemic has
already been overcome.
In
addition, by analysing the degree of the polynomial, it was possible to draw
conclusions on the significance of the impact of the pandemic on the freight
traffic of sea transport. If the trend in the series was identified using a
polynomial with a lower degree, it indicated in a certain way the resistance of
a given series to external factors, the higher the degree of the polynomial,
the more local extremes, and the lower the resistance to market fluctuations
[31, 55].
The
transport industry turned out to be one of the most vulnerable and affected
industries during the pandemic. The obtained results of the study allowed us to
conclude how the global crisis caused by the Covid-19
pandemic affected the cargo traffic in sea transport, expressed by the mass of
goods transshipped in major ports, depending on the
individual types of ships.
The
study presented was conducted using data from the European Statistical Office
EUROSTAT. They concerned the gross weight of goods transhipped in major ports,
first in general terms and then broken down by the type of cargo [10].
Individual types of ships, dedicated to transporting specific types of goods,
were analysed. They were:
Liquid
bulk goods, that are carried unpackaged and usually
transported in ships, which are commonly referred to as tankers. The
specificity of this transport concerns primarily the process of loading and
unloading, which is more complicated than in the case of other types of cargo.
Modern ships are loaded using discharge/articulated arm loading systems, which
are usually found in the off- and onshore loading and off-loading facilities,
while in offshore oil fields, crude oil can be refuelled directly from the
drilling rig. Liquid bulk cargoes are generally classified as edible, inedible,
hazardous and non-hazardous [26, 21]. Dangerous liquids include crude oil, LPG
(liquid petroleum gas), LNG (liquid natural gas) and chemicals (chemicals). The
liquids other than non-hazardous ones are, for example, vegetable oils, cooking
oils, milk, juices and other liquids that do not pose a potential threat to the
body and the environment [26, 21].
Dry
bulk goods, most
often uniform in composition, loaded directly into the cargo area of a ship,
mainly refer to unprocessed materials intended for use in the global production
process, most often those that must be kept dry throughout the transport
period. In particular, most agricultural products, such as cereals, seeds,
fodder, sugar, cocoa, and coffee, belong to this category, but there are also
products from the construction industry or the mining industry (metal ores,
cement, and coal). Such products account for about 38% of the total maritime
trade [14, 50].
Large containers can
house almost any types of goods; hence, we distinguish containers for the
transport of dry cargo, refrigerated, open, flat rack, tank, high cube, and
others, which are transported on the ships specially equipped with guides
intended for transporting this type of cargo units. In this case, a large part
of the cargo is carried on board. The growing level of trade in the world is
conducive to the popularity of container ships, and currently the largest of
them can transport over 20,000 TEUs [46, 47].
Ro-Ro ships
(short for Roll-on/roll-off) are adapted to carry rolling loads and wheeled
means of transport (passenger cars, trucks, and railway wagons) [20]. They are
distinguished by ramps used for loading and unloading, built in the bow or
stern of the ship (or placed on land), thanks to which manoeuvring operations
are much easier than when using a crane.
The time series of the gross weight of goods transhipped in ports for
each of the above-presented ships have been studied. For each of them, a trend
was identified in the time series
where
In the differential method, it is
assumed that the time intervals between successive readings in the time series
are constant, i.e.,
For a differential operator of order
where
If in the analysed time series
1. successively for
and squared variations of the differences:
2. based on the analysis and evaluation of elements
3. we identify the trend in the series
4. we use stepwise regression to determine the significant
predictors in the model (1).
The linearity of the model (1) was
checked using the Ramsey test [35, 24] of the following form:
where
At the significance level
and an alternative hypothesis
The Ramsey test [35, 49] consists of
adding to the set of independent variables (successive regressors)
in the form of powers, e.g., predicted values of an exogenous variable,
independent variables or principal components.
A restricted model (8) is
considered, in which, using the Least Squares Method [39, 48], estimators of
unknown parameters
Then the extended (unrestricted)
model is analysed
where the matrix
Using the Least Squares Method, the
estimators
and a sequence of residuals
The test statistic of the Ramsey
test [35] has the following form:
and holds a Fischer–Snedecor distribution with
1. for equation (1) we assume
2. for model (8) we use the Ramsey
test;
3. we estimate
4. if
5.
we identify the
trend in the series
6.
we use stepwise regression to determine the significant
predictors in the model (1).
First, the sea transport as a whole
was analysed, without division into specific types of ships. The volume of
goods in the analysed years is presented in Fig. 1. There is a clear (black
line) change in the development trend caused by the outbreak of the Covid-19 pandemic.
Fig. 1. Total sea transport in 2012-2022 (empirical data and model)
The identification was prepared based
on the observations until the outbreak of the pandemic according to the model,
which parameters are presented in Tab. 1 is marked in blue. The coefficient
of determination was 0.911. Additionally, Tab. 1 contains the values of the estimators
of the structural parameters of the model (1), standard deviations, values of
the
Tab. 1
Structural parameters for the trend matched to
the pre-pandemic period
– sea transport in total
|
|
Estimate |
Std. Error |
t value |
Pr(>|t|) |
|
|
785171.20 |
2954.932 |
265.716 |
0 |
|
|
95.69 |
5.208 |
18.375 |
0 |
The identification made on the basis
of observations during the entire analysed period is marked in red. The
difference between the proposed forecast and the actual level is significant.
Tab. 2 presents the structural parameters of the model for the entire period,
standard deviations,
Tab. 2
Structural parameters for the trend matched to
the entire period
– sea transport in total
|
|
Estimate |
Std. Error |
t value |
Pr(>|t|) |
|
|
793071.547 |
6346.245 |
124.967 |
0.000 |
|
|
-22.211 |
11.309 |
-1.964 |
0.056 |
|
|
2.776 |
0.947 |
2.932 |
0.005 |
|
|
-0.093 |
0.027 |
-3.504 |
0.001 |
|
|
0.001 |
0.000 |
3.848 |
0.000 |
In the next stage of the study, sea shipments
were analysed depending on the type of ship. This is justified by the varying
demand for goods during the pandemic. While the demand for necessities and
medical products increased sharply, the construction industry, for example, had
a significant stagnation, which justifies the analysis of ships dedicated to
individual goods.
Ships transporting liquid goods
present characteristics similar to those of the entire transport, which is
visible in Fig. 2.
Fig. 2. Sea transport of liquid goods
in 2012-2022 (empirical data and model)
The forecast prepared according to
the model for observations until the outbreak of the pandemic shows a similar
dynamic growth. The coefficient of determination of this model was 0.7105 and
the values of the estimators, standard deviations,
Tab. 3
Structural parameters for the trend matched to
the pre-pandemic period
– liquid bulk goods
|
|
Estimate |
Std. Error |
t value |
Pr(>|t|) |
|
|
296748.034 |
1608.377 |
184.502 |
0 |
|
|
25.506 |
2.835 |
8.998 |
0 |
The trend for the entire period was
identified using a polynomial of 5 degree, which shows a significant
sensitivity to external perturbations. The values of the structural parameter
estimators of this model, standard deviations,
Tab. 4
Structural parameters for the trend matched to
the entire period
– liquid bulk goods
|
|
Estimate |
Std. Error |
t value |
Pr(>|t|) |
|
|
304750.307 |
3460.161 |
88.074 |
0 |
|
|
-413.234 |
98.235 |
-4.207 |
0 |
|
|
42.933 |
8.528 |
5.035 |
0 |
|
|
-1.358 |
0.252 |
-5.388 |
0 |
|
|
0.014 |
0.002 |
5.491 |
0 |
The decrease in sea transport of
liquid goods visible in the chart results from the decrease in global demand,
which was recorded primarily in relation to all types of fuels, especially jet
aviation fuels, due to the almost complete stoppage of air traffic. Demand for
liquid petroleum gas (LPG) fell sharply and slightly less than the demand for
petrol [7].
The transport of bulk goods shows a
different dependency. Of course, the changes in this area too, caused by the
pandemic, were clear, and there was a sharp decrease (Fig. 3), but the growth
dynamics in this case and its forecast, determined based on the observations
until the outbreak of the pandemic, was not so significant and is linear.
Fig. 3. Sea transport of bulk
materials in 2012-2022 (empirical data and model)
The values of linear model
estimators, standard deviations
Tab. 5
Structural parameters for the trend matched to
the pre-pandemic period
– dry bulk goods
|
|
Estimate |
Std. Error |
t value |
Pr(>|t|) |
|
|
178073.393 |
2095.727 |
84.970 |
0 |
|
|
631.454 |
101.538 |
6.219 |
0 |
The determination coefficient of the linear
model was 0.5396. The value of the
Ramsey statistic is 1.1473, while the test probability
In this case, the recovery of the market after
the pandemic will take place faster, as shown by the model determined for the
entire period. The structural parameters of the model, standard deviations,
Tab. 6
Structural parameters for the trend matched to
the entire period
– dry bulk goods
|
|
Estimate |
Std. Error |
t value |
Pr(>|t|) |
|
|
174854.615 |
8055.985 |
21.705 |
0.000 |
|
|
4899.805 |
3331.416 |
1.471 |
0.149 |
|
|
-844.328 |
427.630 |
-1.974 |
0.055 |
|
|
57.105 |
22.788 |
2.506 |
0.016 |
|
|
-1.550 |
0.532 |
-2.912 |
0.006 |
|
|
0.014 |
0.005 |
3.191 |
0.003 |
This is due to the
fact that a significant part of bulk sea goods are
cereals, and the outbreak of the COVID-19 pandemic
slightly disrupted their production, as it is weather conditions that are an
important factor in this topic [54]. As a result of the pandemic, an increased
demand for cereals could be observed resulting from increased purchases by
states out of concern for food security. This was also facilitated by the fear
caused by the introduction of the lockdown, causing the society to accumulate
stocks, including food produced from cereals [54]. Hence, the rapid recovery of
this sector.
The COVID-19
pandemic also affected maritime container transport, which resulted mainly from
the destabilization of the container trade management caused by the stoppage of
some economies of the world (Fig. 4).
Fig. 4. Sea transport of container
ships in 2012 -2022 (empirical data and model)
The values of structural parameters of the
polynomial trend for the pre-pandemic period, standard deviations
Tab. 7
Structural parameters for the trend matched to
the pre-pandemic period
– large containers
|
|
Estimate |
Std. Error |
t value |
Pr(>|t|) |
|
|
170145.290 |
1458.753 |
116.637 |
0 |
|
|
41.091 |
2.571 |
15.984 |
0 |
However, Tab. 8 presents the values of
structural parameters for the trend determined for the entire period, standard
deviations of parameters
Tab. 8
Structural parameters for the trend matched to
the whole period
– large containers
|
|
Estimate |
Std. Error |
t value |
Pr(>|t|) |
|
|
166668.608 |
1864.480 |
89.391 |
0 |
|
|
88.765 |
8.600 |
10.322 |
0 |
|
|
-1.510 |
0.194 |
-7.781 |
0 |
In the case of container ships, in particular, the first months of the
pandemic brought a reduction in the volume of transport and cancellations of
cruises, but this was a short-term state [6]. Although in the most difficult
period (February 2020), port container turnover fell almost to the level from 8
years ago, these were temporary phenomena. There was a quick revival, and the
upward trend is still observed today [6]. This was due to the fact that the earlier
(before the pandemic) growth in the container industry was strong enough to
survive the effects of the crisis, and the reconstruction was supported by
ongoing containerization and the relocation of production to Asia [28, 44].
Temporary disruptions in the sea transport of transport
means resulted primarily from disruptions in the production of vehicles and the
closing of showrooms, hence the short-term decline, which was quickly rebuilt
(Fig. 5). This was also favoured by the growing popularity of ecological
vehicles.
Fig. 5. Ro-Ro ships sea transport in 2012-2022 (empirical
data and model)
Both the forecast according to the linear model for
observations before the pandemic and the trend determined according to the
linear model for the data from the entire period are very similar. The values
of structural parameters for the linear model before the pandemic and for the
model determined based on the data from the entire period, standard deviations
of parameters
Tab. 9
Structural parameters for the trend matched to pre-pandemic period
– Ro-Ro ships
|
|
Estimate |
Std. Error |
t value |
Pr(>|t|) |
|
|
82280.861 |
1366.906 |
60.195 |
0 |
|
|
434.539 |
66.227 |
6.561 |
0 |
Tab. 10
Structural parameters for the trend matched to the whole period
– Ro-Ro ships
|
|
Estimate |
Std. Error |
t value |
Pr(>|t|) |
|
|
82499.901 |
1305.034 |
63.217 |
0 |
|
|
408.406 |
48.351 |
8.447 |
0 |
The determination coefficient for the pre-pandemic model was 0.5661,
while for the entire period it was 0.6185. The value of the Ramsey statistic
for the pre-pandemic model is 2.6928, while for the model from the entire
period it is 1.6972. The test probability for the pre-pandemic model is
0.05054, while for the entire period it is 0.1697. Thus, at the significance
level
The restrictions related to the
pandemic had an impact on the transport of vehicles resulting from the closure
of production plants and points of sale, and the interruption of supply chains.
However, short-term shortages in supplies and the limited availability of new
cars affected the appetite of consumers, further intensified by their
resignation from public transport due to fears of being infected and switching
to private cars [33].
The transport industry, including
maritime transport, has been clearly affected by the pandemic. For a short
period of time, sea transport almost came to a standstill. However, the
situation began to normalize quite quickly. The demand for sea transport was so
great that - in parallel with the limited space on ships - it caused a rapid
and significant increase in freight rates. The dynamics of changes in the
freight price in the 3rd and 4th quarter of 2020 sometimes reached 10% - 15% of
the freight price from the previous week, which ultimately resulted in a change
of about 350% in the second half of 2020 compared to the levels from the
beginning of July [27].
As it is shown in this study, global
maritime freight traffic, expressed by the mass of goods transshipped
in major ports, has in most cases not yet recovered to the level predicted on
the basis of pre-pandemic data. However, the impact of the epidemiological
situation on particular types of ships was very heterogeneous. The greatest
fluctuations and low resistance of the series to external factors and market
fluctuations concerned ships carrying liquid and dry goods. The polynomials
determined were up to the fifth degree. This is due to the fact that especially
fuels, as well as food and construction products, are very sensitive to the
global economic situation. The transport of means transport turned out to be
less sensitive - here the relation in time is practically linear and the impact
of the pandemic on the trend line is negligible. Similarly, container ship
traffic is more resilient to change. The security here is the ability to change
the load, which can largely be adapted to the current needs of the market.
During the pandemic, these were, for example, mainly hygiene items such as
masks or disposable gloves.
The coronavirus has undoubtedly
upset the global balance. Lockdowns, forced restrictions in production and
transport were a huge challenge for the global economy. However, as the
conducted analysis shows, temporary downtimes were quickly averted, and the
biggest problem turned out to be not so much the functioning of sea transport
but rather rapid increases in sea freight price levels. The confirmation of the
high sensitivity of maritime transport allows us to conclude that this is an
area that could be more controlled, for example, in terms of statutory price
control. The analysis of sea freight price volatility is also an interesting
issue worth mathematical analysis and will be an element of further research by
the authors.
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Received 07.01.2023; accepted in
revised form 05.04.2023
Scientific Journal of Silesian University of Technology. Series
Transport is licensed under a Creative Commons Attribution 4.0
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[1] Faculty of Security, Logistics and Management, Military
University of Technology, Kaliskiego 2 Street, 00-908
Warsaw, Poland. Email: anna.borucka@wat.edu.pl.
ORCID: https://orcid.org/ 0000-0002-7892-9640
[2]
Faculty of Management, Lublin University of Technology, Nadbystrzycka
38, 20-618 Lublin, Poland. Email: e.kozlovski@pollub.pl.
ORCID:
https://orcid.org/0000-0002-7147-4903