An Anatomy of Cycles in Shipping Industry, 1946-2020

The paper provided a help to shipowners—we believe—by determining the duration of cycles, first historically, since 1741, and par excellence since 1945, to 2020, and then mathematically, using Chaos Theory. It was remarkable to find out that both approaches gave the same outcome: shipping cycles lasted 6 years (rounded). We have also explored the possibility to predict a shipping cycle with reference to previous repeated attempts to forecast freight markets, but in this paper, we wanted to see what to suggest to shipowners, when forecasting is impossible—as is! This is in line with most important Greek shipowners, like Mr. G Procopiou, who suggests to ignore forecasters. The paper, however, showed the important corollary that bad times are longer than good times, helping to avoid fatal mistakes as those committed by Sanko shipping of Japan in 1980s. We showed also the more important corollary for businessmen that technology brought shipping cycles closer! We have re-introduced the concept of Joker, rejecting the theory that shipping is a “poker game”. To predict the coming of a Joker has not been so far achieved, though we have predicted the start of the 2008 depression using Chaos theory… Ten at least Jokers have appeared since 1951, including the 2019 Pandemic.


Introduction
Shipping is an industry which suffers from frequent cycles approaching faster as time goes by. Table 1 below mentions 24 shipping cycles since 1741 and till How to cite this paper: Goulielmos, A. M. (2020). An Anatomy of Cycles in Shipping Industry, 1946-2020. Modern Economy, 11, 1671-1695. https://doi.org/10.4236/me.2020  World suffered also from 9 at least major wars, from which two global, since 1741! Wars are beneficial and harmful at the same time for world shipping: in wars ships are required to transport all kinds of means to those fighting, and for reconstruction afterwards, increasing thus seaborne demand; but also, ships are lost due to war causes.
Our prediction, however, is that local wars will continue… Now an Armenia-Azerbaijan war begun. In fact, our epoch (since 1945) is full of local wars (7 wars at least). Global wars, most probably, will be avoided, as no one will get out alive in a worldwide nuclear war… something well-known by global leaders.
World peace is maintained by the fear of nuclear death… Moreover, the duration of shipping cycles fell over 3 technological periods: from ~20 years to ~7 on average (Table 1). This suggests that technology-the factor which has changed, and no doubt, affected cycles, made the duration of recessions and depressions shorter…! Of course, it is useful to know that cycles now are coming sooner to get prepared and react properly (Goulielmos, 2020).
In future, a shipping cycle may be even shorter, as technology continuously im-proves… Shipowners have to learn to live with cycles as Greeks learned to live with earthquakes and… COVID-19! Our reference to technology is to that of building ships, including their mean of propulsion, speed, unloading/loading means, fuel etc., and how fast large and faster ships, or sophisticated ones, can be built! Can we blame shipbuilding for delivering ships to shipowners fast, even 1 say within 3 months? Or have we to blame shipowners for over-ordering ships and demanding to get delivery of them as soon as possible to get advantage of the rising market?
There are also involved "economies of scale"-a matter again of technology-by which supply can increase by leaps and bounds! To avoid a possible misunderstanding, economies of scale depend on the existence of an analogoussized demand, called "shipment" 1 or unit-load, which determines the maximum size of a vessel among other factors. Passenger ships are built marginally larger than the estimated demand per voyage to face a future increase.
To understand the magnitude of errors which can be committed by shipowners during a depression, we take the one between 1981 and 1987, where ~48 m dwt of tankers were ordered, ~221 m dwt were laid-up and ~93 m dwt were scrapped, out of an estimated fleet of 400 mdwt… A great waste of valuable resources, no doubt! This demonstrates sadly the failure of shipowners/and maritime economists to predict cycles!

Aim and Organization of the Paper
The purpose of this paper is to calculate the exact duration of shipping cycles, first historically, par excellence between 1945 and 2020, and then mathematical- 1 The maximum size of one shipment is a rather synthetic outcome depending mainly on the timing of individual demands grouped together, the storage facilities of the importers, delivery times to those ordered, common unload areas, capacity of storage facilities etc. ly. Also, we want to remind reader of the reasons that caused those cycles. Analysis here is based on cycle's definition provided by economic theory (i.e. from a good economic dictionary). We will refer also to a paper, which tried to forecast shipping cycles to see if this was possible before working on the assumption that forecasting is impossible in maritime economy… held also by the most powerful Greek shipowners.
In the shipping (game) 2 , we believe, that one at least… Joker is always in the pack of cards.
The paper is organized in 4 parts, after literature review: Part I, deals with the definition of business and shipping cycles; Part II, presents the 4 cycles in freight markets of tankers and dry cargoes, between 1947 and 2020, in an historical analysis; Part III, deals with the cycles in nonlinear Time Series; Part IV deals with the "impossibility theorem" of forecasting shipping cycles. Finally, we conclude.
Observers at old times came to the conclusion that crises formed part of a wave-like mechanism, acting on economy. They started then to call them "cycles" though a wave is not cyclical… but re-occurring. Cournot (1927)  theories of growth of GDP took its place as more important and also novel.
Modern economists were brought-up as we did with Keynes' General Theory in 1936, triggered by the 1929-1933 depression we believe, they were occupied or rather fascinated by the task to transforming Keynes "General theory" into a long run dynamic growth theory, (e.g. the "Harrod-Domar" growth model in 2 Martin Stopford (2009), by the way, was wrong to support the theory that shipping game is one resembling poker! Modern Economy 1940s was characteristic). Moreover, growth is something that all political parties agree, unlike "distribution of income". Stopford (2009; chapter 3) gave a detailed presentation of shipping cycles, and in addition, recorded the freight rates of dry cargo ships, and their cycles, since 1741 ( Figure 1).  Stopford (2009) argued that from 1945, and for 50 years, the mechanization of "bulk 5 " and "liner 6 " shipping, using also bigger 7 ships, and more efficient cargo-handling technology, produced a fall in real freight rates. This is quite true that efficiency came through economies of scale and better mechanization in ports and stronger unloading-loading means in both ships and ports. This is so because time everywhere is the secret factor in shipping to the extent that "economies of time" is a very important chapter.
Summarizing, the problem of cycles occupied economists very early, since 1600s. Schumpeter (and Stopford) were first to connect cycles with technology.
We, connected, cycle's duration with technology… To predict the coming of a Ships are used to transport cargoes in bulk like coal, grain, fertilizers, iron ore, oil etc. 6 Ships transporting products coming from manufacture and craft industry suitable for economic development. These ships are e.g. container-ships. 7 Shipowners and Onassis discovered that bigger ships attain a lower cost per ton of cargo. Many costs including building cost fall on average as they do not increase faster than the increase in carrying capacity (dwt).
DOI: 10.4236/me.2020.1110116 1676 Modern Economy cycle proved to be a hopeless endeavor for centuries. Its duration is also not pre-known. These are 2 points where forecasters have failed. Stopford (2009) described the above situation as the one where 30,000 shipowners play "poker"; we insist that the situation is not one of playing poker, but one of including a "Joker" in the pack of maritime cards. Joker manifests, after all, the "Free Will" of businessmen.
Greek shipowners realized the above situation and invented a win-win strategy (Goulielmos, 2020), that always works in their benefit, and ends to a higher competitive advantage. Surely, perfect timing in decision making is not accomplished by all humans… but Greeks achieved 86% accuracy in attempting it…

Definition of Business and Shipping Cycles
To give an idea of how shipping cycles are created, we present Demand depression, which started in 1979 for tankers, was due to the oil price increase, enforced by OPEC at that time.
As shown, it is clear that the fleet does not follow always trade, as in 1950-1964 and in 1975-1995. Shipowners over-ordered ships during peak periods, so that ships to be in numbers above of what was required (blue line above red one). A cycle, (called also business or trade), are 2.5 time periods of fluctuation (say in the level of economic activity, proxied e.g. by GDP), of a regular pattern with an expansion followed by a contraction, and again by an expansion… (a definition modified slightly by us from that found in Pearce, 1992).
The reason was that economists did not like to take them as dealing with random events 8 , like the weather. But are cycles random manifestations or are representations of deterministic chaotic time series?
The trade cycle, diagrammatically, is drafted as follows ( Figure 3).
As shown, a cycle has a peak: at B, and a trough: at D. Cycle's period is: either from A to E, or from B to F. A cycle starts from the trend line and returns to it (A-E). As shown, a cycle retards the uprising of GDP. This can be seen, as during the movement of GDP from A to E, had first to pass from C to E, before reaching E, and thus delaying. In other words, if GDP could avoid part CE, and the time required to pass it, then GDP could reach faster E, say in 1/2 time. The trend, however, may be downward as well! The cycle is not really a full one, but a sum of 2 halves… Cycle's amplitude is BG.
What is wrong, and dangerous, however, is to assume AC = CE (BD = DF).
In other words, expansion and contraction phases are not equal… In shipping we know very well that good times are much shorter than bad times!

The Shipping Cycle
As shown (Figure 4), the shipping cycle, CE, is drawn the same way as business Figure 3. The trade cycle. Source: modified from that in Pearce, 1992. 8 Economists convinced to deal with cycles when they saw them to return! They did not like to take them as dealing with "Winds and Waters"! cycle. Wrong is also here that: CG = GE! The dramatic implication of drafting a peak as equal to a trough, is mentioned below, in the case of "Sanko Shipping Company of Japan" in 1980s. The variable that interests par excellence maritime economists is freight rate and not so global GDP.
A shipping cycle, however, unlike business one, has clear causes: 1) a fall in the seaborne trade (demand) and/or 2) an increase in ship space (supply), cause a fall in freight rates, so that, for a short, or a long time, ships earn nothing above their cost… This leads ships to lay-up, (temporal removal from market), and eventually to scrapping (permanent removal from market), as the revenue from transporting a unit of cargo is less than her 9 cost.
As shown by Goulielmos (2020) demand and supply move independently one from the other! This disharmony causes the shipping cycles. Changes in demand seem to be the initiating factor, and supply follows. Small changes in demand (expressed in billion tons) cause great changes in supply (expressed in million tons-dwt), a par excellence nonlinear case… Crucial role play of course time and developments that may occur between "deciding to build a ship" and get deliver of her by her owners.

Recessions versus Depressions
We may distinguish recessions from depressions. A recession is a situation where 1) a fall in demand (seaborne trade), and/or 2) an increase in supply of ships, are small, so that the fall in freight rates that follows, is also limited and lasts a short time; i.e. "a low amplitude case"; this means a small % of ships in lay-up and also a more limited tonnage in scrapping. Figure 4. The shipping cycle. Source: modified from that in Stopford, 2009: p. 102. 9 In English a ship is a female. hand prices from £280,000 dropped to £5000! But these percentages etc. should not be taken as fixed 10 as these may not be repeated in future.
In a shipping depression, the variations naturally are greater, and its duration longer, vis-à-vis a recession: the 1929-1933 depression e.g. lasted 8 years (to 1936); the 1981-1987 dry cargo depression lasted 6 years, and the 2008-2013 lasted 5 years, or so, while the COVID-19 depression will last 1 year (presumably: 2020-2021). The time a good market lasts is not standard, and it depends on a number of factors; similarly, the time that a recession or a depression lasts is also unknown. We have to remember these facts.
Shipowners know (feel) when a recession/depression happens, and thus, they cut costs down, starting from crew costs (Niarchos), but they do not know how long a crisis is going to last, and they know nothing about the time when it will come… In shipping, there are, of course, mechanisms which are expected to "bring" equilibrium: when freight rates increase, owners order ships, but their delivery takes time, as mentioned, given the time for the "decision to order and for construction", securing finance etc.; when freight rates fall, shipowners create a provisional equilibrium (lay-up) and a permanent one (scrapping), if a recession becomes a depression.
But while a lay-up decision is relatively a fast one, a scrapping decision, as more serious and decisive, needs a number of years (3 -4 years) at a cost of course. Shipowners are optimistic persons, and they are always hoping. Hope dies last, they say…but it cannot avoid final death! Stopford (2009: p. 106) calculated the duration of shipping average peaks as equal to 3 years , and the duration of average troughs as equal to 5 years. Short booms mean that supply responded fast to a higher demand. It also means that long time charters should be preferred…

Peaks versus Troughs
To restore the truth in relation with the actual duration of the two half-circles of 1 shipping cycle, we have constructed the following ( Figure 5).
As shown, the time that 2 troughs last, are longer than the time1peak lasts.
Also, one trough may be deeper than another. This pattern is indeed real for shipping cycles. Stopford (2009: p. 107)  Our experience showed that there are no rules about shipping crises like: that only small ships are hit; or, only older ones; or, only tankers or only dry cargoes, and so on. Every ship has its own supply and demand, which determines her freight rate over her route given her size, age, flag etc. We saw cases where old ships prospered; also, smaller ones prospered… and vice versa. The increase in rates, due to lack of supply, and/or a rise in demand, given distances, induced a higher shipbuilding production, and upon its delivery, freight rates fell… Ships delivered in greater numbers than needed! Thus, the main causes were: "Korean war" and "1 st Suez Canal closure", which both created a greater demand, and an opportunity for economies of scale; while over-ordering caused a greater supply. These 3 events consisted also the 3 appearances of the Joker.
Let us remember the Jokers that have appeared during this period.
The Korean war did not last long. The more important event for shipping was the 1 st Suez Canal closure, but this was also short (6 months). Anyway, this closure induced different predictions by shipowners, where some believed that the Canal will not open soon (Onassis A, but not Gratsos C.), but it did. Moreover, economies of scale had naturally this period a great impact on supply.

Tanker Freight Rate Cycle, 1947-1963
The tanker freight rates (Figure 7) had also a cyclical pattern, between 1947 and

Dry Cargoes Freight Rates Cycles
The spot dry cargoes market during this period moved into a recession for 3 years (1970-1971-1972). The owners, who could predict, signed (long term) time charters ( Figure 8).
As shown (

Tanker Freight Rates Cycles, 1964-1972
In tankers, years 1967 and 1970 made the whole good difference (Figure 9). The

The Sanko Shipping Company of Japan
The 1981-1987 depression was serious, lasting 6 continuous years, and it was also deep. The depression "should" last 4 years, not 6, but "Sanko shipping company of Japan", comprehending shipping cycles wrong, embarked in an extensive shipbuilding program of several million dwt (Stopford, 2009: p. 126;Couper, 1999: p. 37).
Freight rates were depressed par excellence in 1983-1984. Certain owners, however, placed a large number of orders for bulk carriers. This was an act started by Sanko, which secretly ordered 120 dry cargoes ships of about 30,000 dwt each, or 3.6m dwt in total! This company lost money by investing massively and exclusively in 50 or so tankers certain years ago. Then it decided to turn to bulk carriers so that to obtain the profits required to make-up losses from tankers! The popular saying that: "do not put all your eggs in one basket" became true as Sanko was only a tanker owner. As secrets cannot be kept in shipping, Greeks, Norwegians and others rushed also to order ships after Sanko. This enormous and unexpected supply depressed dry cargo markets further 12 and for 2 more years and retarded its recovery till 2 nd half of 1987.
To the above outcome a number of other events contributed: 1) Shipowners had accumulated large cash reserves from the 1980 boom. 2) Banks had also large deposits of "petrodollars", as called, available to finance shipowners. 3) Ships were cheap due to overcapacity in shipyards. 4) Tankers were excluded 11 Like the appearance of a joker in a pack of cards, also a sudden, unexpected, appearance of an event in shipping markets, changes the normal pre-existing movement of freight rates either up or down. We tend to believe that the arrival of the joker is unpredictable… 12 Stopford mentions a similar case also in 1905-1906.  from orders due to their crisis. 5) New fuel-efficient ships emerged as a reaction to the substantial rise in oil prices after 1973. 6) The favorable yen/$ parity favored building ships in Japan.
But crucial for Sanko was its belief that a shipping cycle lasts definitely 4 or 6 years, as used to be in the near past; thus 1984 was going to be the next cyclical move up (1981-1982 or 1983 down; 1984-1985 or 1986 up), and thus they ordered in 1983 to get delivery in the considered uprising of the market in 1984-!
The above logic was right, but its basics were wrong. The basics were real cycles duration! Also, the high order of more than 3.6 m dwt by Sanko alone, increased supply of ships, so that the already depressed market to fall in an even lower level. The index (BFI-Baltic Freight Index) fell below 560 units.
The shipping cycle has no symmetry up or down! …This is the reason that we insisted to say above that peak times are shorter than trough times, and they have to check market every time. Moreover, a substantial rise in supply will definitely affect freight rate, given demand and distances. Sanko forgot the famous rule that supply and demand for ship services determine price…

Dry Cargoes Freight Rates, 1976-2007
Freight rates in dry cargo market for 1976-2007 are shown ( Figure 10). Three cycles can be singled-out (of 9, 6 and 9 years duration respectively).
As shown, the dry cargoes freight rates boomed, with peaks in 1980,1995,2004   This permits us to pre-tell that as soon as China recovers, and global trade recovers also, shipping will have many brighter days again. Surely, China will become soon the 1 st global maritime nation… One must take into account that a long prosperous period of extremely high freight rates, like the one after 2003, (to end 2008), made shipowners capable with abundant monetary means to seek opportunities, which everybody admitted by 2016. Crisis (like the one in 2009-2013) definitely brought greater opportunities for investing! As a corollary, we may say that shipping firms must create reserves from current profits to exploit opportunities, (only at rock-bottom prices), and overcome a depression… A strategic dividend policy has to be adopted and a correct depreciation policy. The higher the depreciation rate, the more savings are realized by the company for new investments. Shareholders can be satisfied to get a dividend for their share-capital above current deposit rates offered by banks, which any way are low, or even negative during and after 2008. So, shipping companies do not have to distribute their entire profits to shareholders, obtained in prosper times, to get prepared for the rainy days of recessions/depressions.
During COVID-19 ships in 2020 had problems to carry-out repairs in China, and other areas, where quarantines were in force; and also, they could not send or repatriate crews to/from quarantined ports… People working at home and avoiding to be were their colleagues were, as used to be, (tele-working or working from home), cut down consumption of fuel for private cars. All kinds of transportation hit, and par excellence air industry. Tourism halted; and the only trade was for specific medical supplies and… oranges supposed to beat virus. Many countries closed their borders or opened them with rules. COVID-19 is nothing but another Joker… No one pre-saw its coming… and no one knows its final departure after killing 1m humans by end Sept. 2020.

The Cyclical Period, 2008-2020 (13 Years)
The impact of the last depression starting at the end-2008-beginning 2009, is shown below (Figure 11) concerning its impact on the fleets of the 11 top-global maritime powers.
Greek  Notable, certain areas have grouped now in single markets like e.g. EU. Nowadays, shipping economists watch the seaborne trade of China 13 , and of EU, not USA, Japan and Germany, as we did in the past. USA in particular under present 2020 administration adopted a nationalistic policy protecting its own economy from Chinese imports. This was the policy adopted by nations soon after 2 nd world war, a policy of national autarky (self-sufficiency) 14 .
The fleets of the top 10 global nations are again shown below ( Figure 12).
As shown, 10 global fleets hold 69% of world carrying capacity, owning about 1.35b GT/DWT out of about 2b GT total, with 27,700 ships of average size: ~49,000 GT. Greece (as owner, including Greek flag) had the 1 st global position with about 18% share, and 53% in EU. It carries more than 1/5 of the trade from/to USA and EU.
Most important, however, is that Greece pursued economies of scale as argued all along in this paper with average size ~77,000 GT, followed by Japan ~59,000; while China had ~34,000, and Singapore ~45,000 (rounded to nearest thousand).
As shown, China had many small ships, unlike Hong-Kong having 60,258 GT average fleet size. Greece fixed its fleet with 32% in tankers, 23% in bulk carriers, 15% in LNGs and 15% in Chemicals (=85/%).
Above history has provided us with a lot of useful information. But is history repeated (Goulielmos, 2009)? Here we mentioned quite a number of Jokers. Can we predict the appearance of a Joker? Goulielmos (2009: p. 346) predicted that a cycle would start in 14 th October, 2008, (not known at that time)… and this was a unique forecasting… which came true.

Cycles in Nonlinear Time Series
Humans, in their inability to understand complex phenomena, tried to simplify economics by excluding a great part of reality ("reductionism"). Linearity is 14 Autarky is a situation where a country isolates itself from international trade by restrictions such as tariffs, in an attempt to be self-sufficient, usually for reasons of employment or politics.
closer to human brain, no doubt, when un-helped by artificial intelligence. This mentality fits exactly to the case of cycles.
For centuries, observers tried to make cycles regular, symmetric-up and -down (Peters, 1994: Chap. 6) and harmonic. Pioneers in this approach were Ancient Greeks-par excellence Euclid, Aristotle, Ptolemy-believing in a divine shape: the circle! They thought that Earth is and "follows" a perfect circle. Technology has been all along at their service. Non sentimental machines, will take all important decisions…?

Chaos Theory and Cycles
Chaos theory showed the existence of nonperiodic cycles and calculated their average duration ! Peters (1994: p. 37-38) distinguished cycles in: 1) periodic, and 2) non-periodic. In non-periodic cycles, Peters distinguished 2 of their sources: a) statistical and b) chaotic. The non-periodic cycles have no absolute frequency.
Statistical cycles are found in the "Hurst process", which is a "biased random walk", with no average length. The bias has direction and magnitude. The important issue is that this bias can change abruptly. This is what we meant by Joker-as an exogenous event, not-predictable, in the pack of cards. A random event! Jokers appear also in business life and in maritime economy. Mandelbrot (1972) studied cycles and argued that their duration is not only a matter of time series, meaning the time passed. Chaotic cycles e.g. can be produced by the "logistic equation", (a simple difference equation of 2 nd order), in the nonlinear dynamic systems; these systems are expressed by differential equations. But this logistic equation does not produce the economic or investment cycles (Peters, 1994), we know.
A method, called "Rescaled Range Analysis", can show an existing cycle and its duration (Figure 13).
As shown, the above equation-presents a smooth deterministic system with high H (=0.93 ≤ 1), and produces a cycle at n = 50 observations. Peters argued that stock and bond markets are non-periodic systems, (Granger, 1964;Peters, 1991;Cheng & Tong, 1992), unlike currencies. Peters (1994: p. 102) argued also that "Rescale Range Analysis" (Voss, 2013) is able to estimate the length of nonperiodic cycles, as mentioned.
This non-parametric statistical method is briefly presented in Appendix 1.
This is due to Hurst (1951) and is a generalization of the one of Einstein, where distance D is equal to the square root of time: { } D time 1 = , for a particle moving randomly in a stagnant liquid 15 (Einstein, 1905 This was a problem first encountered by Robert Brown in 1828, and remained unsolved till 1905. As a result, the case H = 0.50 = 1/2 = √ got the name "Brownian motion" or "white noise". 16 Range in a time series is the period that comes between maximum n and minimum n or mathematically: Range (adjusted) = Ra = max (Y 1 , ···, Y n ) -min (Y 1 , ···, Y n ) {3}, and so these are made nonnegative (Peters, 1994: p. 56). 17 Rescaled means divided by local standard deviation S. This genius idea of Hurst freed time series from the dimension of time in the sense that observations in centuries apart, can be compared without the need of time-scale adjustment.
H > 0.50 ≤ 1. In such a case this time series: 1) follow trends; 2) a rise in previous period is most probable to give an increase in next period; 3) they have a long memory/a long-term correlation between present and future, known as black noise (Peters, 1994: p. 310). Moreover, we distinguish time series in faster (1 ≤ H > 1/2) or slower (H < 1/2 or ≥0) than random ones (H = 0.5 = √).

Application of "Rescaled Range Analysis" to Shipping Market
We applied this method to Dry Cargo Market between 1741 and 2012 and we found H = 0.69 > 0.5 ≤ 1 (Figure 14) (we took the maximum H value of the series as this characterizes them, and for n ≥ 10).
As shown, shipping H exponent is 0.69 > 0.50 ≤ 1, and thus freight rate time series for dry cargoes are persistent. Using the same method, we found the duration of cycles, (Figure 15), in the 1sttechnological period, 1741-1852. The cycle duration is indicated at the time the log R/S curve flattens. Figure 14. H exponent -dry cargo market, 1741-2012-Yearly. Source: data from stopford; using MATLAB 7.9 v. Figure 15. Log R/S v. log n, 1741-1852, freight rates dry cargo cycle for sailing ships. Source: author with data from Stopford, 2009. This 1 st period, (112 years), shows a cycle at n = 7 years (log. 0.84 rounded), where R/S flattened. This is the maximum value after one cycle (Peters, 1994: p. 88;Mandelbrot & Wallis, 1969). As argued by Peters (1994: p. 92

) Rescaled
Range Analysis can reveal more clearly existing cycles if these are less than 4.
As shown (Figure 16), now (for 94 years), the cycle during the 2 nd technological period is shown at n = 6 years (log 0.78 rounded).
As shown (Figure 17), (for the last 71 years), the cycle is shown at n = 4 years (log. 0.60).
Cycle duration thus varies from period to period. From 1951 to 2004 we counted 7 cycles diagrammatically with an average duration of almost 7 years.
Chaos theory, however, gave an average cycle of 6 (rounded) years. The cycle duration fell since 1741 from 7 years to 4 years! Technology thus, albeit, became a curse and a blessing at the same time… Imagine a shipowner in the 1700s how happy was to scrap his/her vessel, when her technical life coincided with her economic life, at the moment when a shipping cycle begun!

Conclusion
Shipping time series-as shown beyond doubt-had an intense and frequent cyclicality, since 1741 to 2020. Their handling, however, was all along wrong, when this attempted by linear statistical methods like "Normal distribution 20 " and non-linear "GARCH" 21 .
Our main conclusions may be summarized in a Table 4.
The average historical duration of shipping cycles from 1951 to 2020 was 6 years (5.78). Chaos theory gave a cycle duration of 6 (5.67) years on average of a descending duration since 1945! It was a sad finding, however, to see that technology instead of improving business life made it worse… by bringing cycles nearer!
The theory of business cycle is indeed confusing: are the 2 semicircles equal?
Are bad times equal to good times, or are the former are longer? The facts revealed by the text should not be ignored, however, but shipowners have to be prepared to get advantage of them. We showed them how… Shipping crises (recessions; depressions) are not in the hands of shipowners exclusively, as many may believe, but shipbuilders help as well! Shipowners order ships, no doubt, and they bear the prime responsibility for it. Shipbuilders, however, offer finance and offer low prices, as the case may be, and faster delivery times. But, they cannot be blamed.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.