1

A COMPARISON OF MARITIME TECHNICAL ANALYSIS AND CHAOTIC

MODELING IN LONG TERM FORECASTING OF FREIGHT RATE INDICES

Alexandros M. GOULIELMOS (*),

former Professor of Marine Economics,

ag@unipi.gr,am.goulielmos@hotmail.com

Constantinos V. GIZIAKIS,

Professor of Maritime economics

Elias KAPOTHANASSIS,

PhD candidate

University of Piraeus, Department of Maritime Studies, 80 Karaoli and Dimitiou St.,

Piraeus 18534, Greece

(*) corresponding author,

ABSTRACT

The paper presents the main challenge facing the shipping industry, which is its inability

to produce reliable forecasts. As a result of poor forecasting, the shipping industry has

ordered 274 million dwt of dry cargo ships to be delivered by 2014. First, we examine

critically the available of tools developed in academia to predict stock prices and freight

rates. These have been developed in two main schools of market modeling: linear and

non-linear. Linear tools include such methods as the random walk/martingale, and the

latest flagship, GARCH/Co-integration analysis. Non-linear stochastic models include

non-linear deterministic/chaos theory models, developed since 1963 based on the work of

Mandelbrot. Of particular interest is Maritime Technical Analysis, which has its origins in

Hampton‟s 1990 monograph. This method supports the existence of short (3-4 years) and

long (16-24 years) shipping cycles, using a chartist approach. Twice since 1981, shipping

has experienced dramatic changes in the parameters governing the market, which

Mandelbrot has described as the “Joker in the pack”. These two violent discontinuities

were the energy crisis and the banking crisis. Running traditional and non-traditional

econometric tests, like BDS, on BPI daily and weekly rates 1999-2011, we have found

non-normality, long term correlation and chaotic characteristics (fractal and low chaos

dimensional one). The Hurst exponent is equal to 0.93, indicating black noise. The

Lyapunov exponent implies that forecasting beyond 6 weeks is impossible, but we found

a shortcut to long term chaotic forecasting by calculating cycle durations using data from

the previous 3 years, 4 to 6 years and 8 to 12 years using the Vn statistic. Maritime

technical analysis, however, provided us with valuable clues, not only for the short term

cycle, which will end in May 2011, but also the long term cycle, which will end by 2017.

KEYWORDS

Forecastin; freight rates; chaos; maritime technical analysis; BPI 1999-2011; Vn statistic;

H exponent; maritime chartists approach; testing for normality; independence; long term

memory

2

A COMPARISON OF MARITIME TECHNICAL ANALYSIS AND CHAOTIC

MODELING IN LONG TERM FORECASTING OF FREIGHT RATE INDICES

1. INTRODUCTION

(a) The great value of maritime forecasting

We believe that the more volatile markets are, the more forecasting is needed, especially

if markets suffer from abrupt falls or rises. Maritime markets are such markets (Figure 1).

Figure 1 gives the overall picture of the dry cargo index since 1741. Great spikes can be

seen in 1918 and in 2008. Stopford (2009) located 22 cycles, 8 of which occurred after

1947. The 1918 spike is due to heavy losses of ships due the First World War. The longer

cycles of 14 years and 15 years occurred in 1956 to 1969 and in 1988 to 2002. The last

cycle ended in end 2008 and lasted nine years.

Figure 1: Maritime Economics Freight index, 1741-2008.

Source: Stopford (2009)

In late 2008, one freight market fell by 94% from 11,793 units on 20th

May 2008 to 1,861

in August 2009. This great fall was not anticipated by ship-owners, academics or bankers.

Moreover, this is the great problem of maritime markets, which is that their future cannot

be seen.

(b) The uninterrupted ordering of new ships

The inability to foresee the future, we believe, results in orders being placed for new

ships, even in a crisis. Figure 2 shows the order for Capes.

0

200

400

600

800

1000

1200

0 50 100 150 200 250 300

Dry cargo index 1741=100.

YEARS

3

Figure 2: Contracts for shipbuilding placed each year for Capes,1996-2009, in Dwt

and in number of vessels.

Between 2006 and 2008 more than 160 million dwt of Capes were ordered. This abrupt

rise represents double the number of orders for the whole period between 1996 and 2005

(i.e. 10 years). After the 2007 all period high (88 million dwt), orders fell to half that level

in 2008 (48 million dwt) and to almost nothing (8 million dwt) in 2009. While ordering is

an action of optimism, delivery is now an action of real sorrow. In 2011, 132 million dwt

dry cargo ships will be delivered, in 2012 100 million, falling to 35 million in 2013 and 7

million in 2014 Clarkson‟s (2011). This pattern we have, elsewhere, Goulielmos et al.

(2010, p. 113 et seq.) attributed to the appearance of the „Joker‟ (see Analysis I below).

(a) Traditional methods to combat risk

All entrepreneurs face a common enemy in their business, namely risk. Figure 3 shows

ways of approaching risk. In financial markets they first used a simple method to combat

risk, called „Fundamental Analysis‟ Siriopoulos (1999).

Methods to study Risk in

Financial markets

Fundamental

Analysis

Technical

analysisModern finance

Heretic Finance

(where time series

has a long memory)

Figure 3: Methods of studying Risk in financial markets

0

100

200

300

400

500

600

0

10

20

30

40

50

60

70

80

90

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Number

D wt

Millions

Capesize Contracts Per Year DWT Number

4

Source: Inspired by Mandelbrot-Hudson, 2004, p. 7-13

Fundamental analysis (FA) is based on the idea that a result is always has a cause; if a

stock price is rising, the cause may be in the company, the industry or the economy. The

price of a stock, bond, derivative or currency, moves because of some event or fact,

which, more often than not, comes from outside the market. In a nutshell, if one knows

the cause, one can forecast, and manage risk. FA tries to apply economic theory directly

to the prediction of share prices, aided by mathematical/statistical and econometric

models. Moreover, FA aims to determine quantitatively the factors forming share prices

and estimate equilibrium price (or intrinsic value). FA argues that if the current price is

greater than its intrinsic value, the price must fall, and vice versa. The criticism taken

from Mandelbrot and Hudson (2004) is that a simple method like FA cannot deal with

complex reality. In real life, causes are obscure and critical information is unknown or

unknowable, and reasons are concealed or misrepresented. The connection between news

and prices is mysterious and inconsistent. A threat of war may cause the dollar to fall, or

to rise, for unknown reasons. Shortcomings in FA caused academics to develop technical

analysis (TA) (see Analysis IV).

2. PURPOSE OF THE PAPER

The purpose of this paper is to use maritime technical analysis (MTA), which developed

from Hampton (1990), and compare it with chaos theory, as a method for forecasting the

daily/weekly BPI on data for 1999-2011. The analysis will identify cycles. The Lyapunov

exponent1 indicates that only short term forecasting, of about 6 weeks outside the sample,

is possible. Using the cycle theory of chaos theory suggests that longer term forecasting is

possible. On the other hand, MTA allows predictions 20 years ahead. Anybody who

wishes to use MTA for this purpose, however, needs to be aware of its shortcomings.

3. STRUCTURE OF THE PAPER

Next follows a literature review on maritime forecasting. Then, Analysis I, deals with the

concepts of „poker‟ and „joker‟ in maritime business. Analysis II deals briefly with a

presentation of modern finance, from which we borrow the methodology and concepts.

Analysis III deals with the non-linear chaotic forecasting and cycle theory. Then,

Analysis IV deals with Maritime Technical Analysis and makes predictions with its help.

This is followed by the conclusion.

4. LITERATURE REVIEW

4.1 The efforts of general economists to predict (1933 onwards)

Economists working with stock prices assumed that the resulting price is the culmination

of purely random changes. Mills (1999) cited Working (1960) and Cowles and Cowles

and Jones (1933 to 1944 and 1960). Cowles in particular, sought to know whether market

1 This exponent due to Russian Lyapunov is used as a measure of the ability of a system to forecast.

5

analysts and financial analysts can predict future price changes. He found that there was

little evidence that they could.

Kendall (1953) argued Mandelbrot and Hudson (2004)2 that the weekly changes of many

financial prices could not be predicted from either past changes in the series themselves,

or from past changes in other price series. Equation [1] below Osborne (1959) is valid for

the logarithms of current prices with zero mean, constant variance and normal

distribution. Roberts (1959) argued that price changes are independent, while Osborne

argued that logarithmic price changes are normally distributed. This hypothesis came to

be termed a random walk3 (RW). It has also been agreed that prices are generated by a

Brownian motion (Brown 1828; Einstein 1905; Weiner 1923; Feder 1988; Peters 1994) 4

(BM). In rigorous terms RW is described as Pt=Pt-1+at [1], where Pt is the observed price

at q given time and at is the independent error term with zero mean. Let a price change

be: ΔPt = Pt-Pt-1 [2], which also has an independent error. Moreover: Pt= [3],

where i=1…t. Prices are so accumulations of purely random changes. Most of the works

using RW were collected by Cootner (1964) and developed in detail by Granger and

Morgenstern (1970). The RW model followed the doctoral thesis of Bachelier (1900) in

Paris entitled “The Mathematical Theory of Speculative Prices”. He developed many of

the mathematical properties of Brownian motion five years earlier than Einstein (1905),

who proved RW to be expressed as: distance= . The RW model can be tested

by the autocorrelation properties of the price changes Fama (1965), viewing equation [1]

above as a “model of an ARIMA Small (2005)5 process” Box and Jenkins (1976), i.e. a

one variable linear stochastic process. Of course there are also other approaches6 that use

linear stochastic models, like those determining the order of integration. Moreover,

relaxing, or rather, replacing, the RW hypothesis with that of a Martingale, (which rules

out the dependence of the conditional expectations of changes in future values on the

information available today‟), we can use ARCH7 models due to Engle (1982), as well as

other techniques. The modeling of integrated (financial) time series is very popular

2 British statistician, who took a long look at London shares, NY cotton and Chicago wheat, more than a

century of data, in search of conventional patterns upon which an investor could turn an easy buck. „On the

whole‟, he laconically concluded after pages of fruitless regression analysis, „I regard this experiment as a

failure…There is no hope of being able to predict movements on the exchange‟. 3 The term „Random Walk‟ appeared in a correspondence in Nature in 1905 between Pearson and Rayleigh

(*): (*) “The problem of the Random Walk, Nature 72, 294, 318, and 342”. 4 This motion is „the erratic movement of a small particle suspended in a fluid‟. This is due to water

molecules colliding with this particle. Einstein proved the relationship between Brownian motion and

random walk. Weiner modeled Brownian motion as a random walk with an underlying Gaussian statistical

structure. 5 ARIMA stands for ‟Autoregressive-integrated-moving average‟ process, i.e. a non-stationary stochastic

process related to ARMA. It becomes stationary if differenced d times, where d= integer. ARMA stands for

a stationary stochastic process mixed with AR and MA (moving average) processes. AR= a stationary

stochastic process, where the current value of time series is related to its past p values (p=an integer); if

p=1, we have AR(1) with infinite variance; if p=2, we have AR(2), related to previous 2 values. Small noted

that his data of financial time series exhibited deterministic components, which, however, are assumed by

ARIMA and GARCH to be stochastic. 6 One may distinguish between „integrated and non-integrated‟ time series. In maritime economy many

believe that one variable (say the freight rate) causes another variable (like the returns/profits or the supply

of ship services), and thus co-integration is a commonly tested hypothesis. 7 ARCH stands for the first-order „autoregressive conditional heteroskedastic‟ process. This is very popular

dealing with financial time series. However, it requires „conditional variance‟ ( to be always positive.

„Autoregressive conditional‟ means that the changes in variability are controlled by data‟s past behavior.

The variance is time-varying and conditional on past one. It exhibits frequency distributions with high

peaks at the mean and fat-tails.

6

among maritime economists. Tests for co-integration and estimation can be made with the

so called vector error correction model-VECM8.

4.2 Forecasting efforts by maritime economists

4.2.1 Linear regression models

Forecasting maritime markets, despite its high importance Stopford (2009), accounts for

few works, unlike maritime modeling. Tsolakis et al. (2003) presented a model to forecast

second hand ship prices from 1999 to 2001, using AR→ Xt+1=μ+ρXt+ , where μ is

the mean, η is a shock at t, ρ the autoregressive coefficient and X the second hand price.

They compared their (inside the sample) forecasts (not shown in their paper) with the

above equation with a structured error correction model, by calculating the mean squared,

absolute and percentage error. They found, strangely, that the two models shared success

among two different classes of ships: AR/VAR9 performed better in bulk carriers (handy,

Panamax and Cape; and handy tankers) and SEM performed better in larger tankers

(Panamax, Aframax, Suezmax and VLCC), but they gave no explanation why. They

argued that SEM is good to describe and forecast cycles and to evaluate policies, while

VAR is good for other jobs. Batchelor et al (2007) tested10

the performance of popular

time series models (meaning ARIMA and VECM), in predicting: (a) spot and (b) forward

freight rates.

The table below summarizes their results:

General VECM

model and

restricted one,

plus SURE, 10

and 20 steps

ahead.

Best in-sample fit

based on root

RMSE. Using

natural logs.

Stationarity exists

by ADF, Phillips-

Peron and KPSS

1992 tests.

Future rates

converge strongly

to spots. Futures

are more volatile

than spots and

harder to forecast.

Out of sample,

ECM fails to

predict future rates

but spots market

is efficient.

Out of sample,

all models

outperform

Random Walk.

Future rates do

help to forecast

spots.

Restricted

VECM

outperformed

RW.

VECM11

Unhelpful to

predict future rates.

Spots and future

rates co-integrate.

ARIMA or VAR

(Sims, 1980)

forecast better.

ARIMA less

accurate than RW

and VAR more

accurate than

VECM, S-

VECM perform

better than

VAR in spots,

but not in future

rates. S-VECM

outperforms

8 VARs containing integrated and co-integrated variables enable us to develop the VECM framework.

9 VAR=Vector AR.

10 Their results are questionable as they have reported: significant serial correlation and heteroskedasticity

and excess kurtosis in all series; excess skewness in most; Jarque-Bera departure from normality in all

routes for both spots and futures. 11

VECM forecasting implies dangers, if underlying market structure is evolving and…This is not robust to

structural change according to above authors.

7

ARIMA. RW.

4.2.2 Non-linear regression models

Forecasting freight rate markets using nonlinear regression methods, occurred after 1997

McConville and Rickaby (1995)12

, following the work of Li and Parsons. Li and Parsons

(1997) used a nonlinear regression model, i.e. an artificial neural network model.

Between 1986 and 1993, considerable attention has been paid to developing non-linear

regression mathematical models. Li and Parsons used the monthly tanker freight rates for

1980 to1995. Their results were mixed over the duration of forecasts: for one month

neural networks were either worse than or equivalent with ARMA; for five months

ARMA was worse; for 12 months ARMA was better and for 24 months ARMA was

equivalent. Lyridis et al (2004) tried to forecast the VLCC spot rates from 1979 to 2002

using neural networks, believing that those are more suitable for non-stationary non-linear

time series. Their forecasts, though better than those of Li and Parsons, showed deviations

from actual values, varying by between 30 and 60 world-scale units for one month to 12

months ahead.

4.2.3 Chaotic time series

Chaotic13

methods were first applied to maritime forecasting by (Goulielmos and Psifia

2009; Goulielmos 2009, 2010, 2011). These were followed by Thalassinos et al (2009).

Goulielmos and Psifia (2009) tried to forecast the one year weekly time charter of a

65,000 dwt bulk-carrier, from 1989 to 2008, using the non-linear methods of principal

components and kernel density estimation (KDE). Forecasts outside the sample, tested

with actual values after rates were published, varied from $28 per week to $623, i.e.

0.97% on a total of about $60,000. Moreover, Goulielmos (2009, p. 345) used 543 values

of the BPI to predict 6 weeks ahead using non-linear methods of OLS Farmer and

Sidorowich (1987) and KDE. The deviations inside the sample varied from 2.26% to

16.31% (i.e. $979) on about a $6000 weekly freight rate for August 26th, 2008 to

September 29, 2008. The prediction for September 29th

, 2008, was $2839 against an

actual value of $2376 indicating that the crisis was coming, compared with $4885 a week

previously. So, the methods captured the fall of the freight market. In addition,

Goulielmos (2010) used historic data of second hand ship prices to predict prices for the

next 12 months. Five non-linear methods were tested and three finally applied

simultaneously. He wanted to achieve deviations of less than 1% inside the sample, and

he did. Predicted prices varied from $64.5 million to $70.5 (2006-2007) and differed from

actual values (known afterwards when figures were published) by $64.4 to $ 70.82, which

is to say that they were very close. Thalassinos et al. (2009) tried to predict the Aframax

tanker rates (105,000 dwt double hull) on a 401 weekly charter rate index, using the False

Nearest Neighbors method for 30 steps ahead. Data were from the end of March 2000 to

12

found out of 1750 authors, 9 having studied forecasting demand between 1983 and 1993 and 12

forecasting „international trade‟, between 1971 and 1993, including M.Sc and Ph.D theses and studies by

organizations, like Drewry etc. It seems that none has used nonlinear techniques in these 21 studies. Among

the topics were: expectations (Wright: 1993), autoregressive modeling (1983), a PhD (1981) at the

University of Liverpool for forecasting charter rates and Hampton‟s 3rd

edition (1991). 13

It is the case when we have a stochastic behavior appearing in deterministic systems (Royal statistical

society, 1986 conference, UK). Chaos has the properties of sensitivity to starting conditions and the

existence of an attractor.

8

end of November 2007. The deviations achieved were from $4.2 to $1789.2 per week for

k=10, 20 time steps on about $33,000 and $1,737 for k=30 and relative error about 5.11%

maximum. Predictions on absolute amounts were almost twice as bad as those by

Goulielmos (2009). Moreover, the method used belongs to the so called geometrical

methods that serve the purpose of finding cycles, system dimensions and testing for

determinism. System dimensions must be calculated accurately first by other methods like

correlation dimensions, which are then confirmed by FNN.

5. ANALYSIS I: THE ‘POKER’ AND THE ‘JOKER’ EFFECT

5.1 The poker effect

Stopford (2009, p. 738-742) described four sets of shipping forecasting problems: (1)

dealing with behavioral variables, (2) applying wrong model specifications and

assumptions, (3) difficulty in monitoring results, and (4) difficulty escaping from the

present. He wrote (p. 700): “Shipping investors know very well that they are not dealing

with certainty. In fact they are in much the same position as a poker player making an

educated guess about his opponent‟s cards. The poker player knows he cannot identify the

hand exactly... But a professional uses every scrap of information to make an educated

guess about the range of possible hands. Although he will often be wrong, over a period

of time this information helps him to come out ahead. Shipping investors play the odds in

much the same way - they know they will not win every hand - but they also know that

the right information plays an essential part in narrowing the odds”. There are truths and

mistakes in the above statement. In effect Stopford (2009) recommends guessing based on

the best right information. We believe that maritime forecasting is possible, but it is not a

poker game. It is a “joker game”, although the arrival of the joker cannot be predicted,

while an opponent‟s cards can be.

5.2 The ‘Joker’ effect

To describe the joker effect, we will reproduce the process followed by Hurst (1951).

First, we simulate a random process using a deck of 52 cards containing numbers ±1, ±3,

±5, ±7 and ±9. The deck is repeatedly cut , and shuffled after each cut. The number of the

card appearing in each cut is written down, and a sequence of 1000 recorded. Hurst found

that they show an RW (calculated by a method called Rescaled Range Analysis Hurst

(1951)14‟- RRA). Hurst, however, was interested in a biased RW. To simulate that, he

shuffled the deck and cut it once, noting the number, which might be +3. He replaced this

card, reshuffled and created two decks of 26 cards (deck A and B). Then he took out the 3

highest cards from A and placed them into B, and also removed the three lowest cards

from B. By this method he created a bias of +3 in deck B. He also placed a joker in B and

reshuffled. Deck B now is a biased time series generator, and is used until the joker is cut,

whereupon the pack is re-biased. Hurst tried 1000 trials of 100 hands. The time series

then showed persistence/biased RW. The cuts of the deck were random, the generation of

time series was also random and the appearance of the joker was random, but still the

14

A method developed by Hurst to determine long-memory effects and fractional brownian motion.

9

series showed persistence15

. It seemed that a local randomness existed in a global

structure. In terms of forecasting, the trends of the time series persist until an economic

equivalent of the joker arises to change persistence/bias in magnitude or in direction or in

both. We subscribe to Hurst‟s theory and believe that the above paragraph describes our

industry more accurately, as the experience from the facts (of shipping cycles) has taught

us. This means that forecasting maritime markets will be of no special difficulty,

invalidating Stopford‟s argument that this is the case of a poker game; forecasting the

arrival of the joker, however, is impossible so far16

.

6. ANALYSIS II: THE MODERN FINANCE

What alternative methods have we to reduce risk? Besides those already described, we

have modern finance, which came after FA and TA, based on the mathematics of chance

and statistics, accepting that prices are not predictable, although their fluctuations can be

described by the mathematical laws of chance. Risk is measurable and manageable. The

work of this discipline started in 1900 with the work of French mathematician Louis

Bachelier, who studied financial markets in his doctoral thesis. It drew upon (Pascal

1623-1662; Fermat 1601,1654, 1665), who invented probability theory. Bachelier (1900)

passed over FA and established the RW model. It postulated that prices will go up or

down with equal probability, and their variation is measurable. Most changes fit a bell

shape histogram, i.e. 68% of moves are small, and within one standard deviation, or 1σ,

from the mean; 95% are within 2σ and 98% within 3σ. Extremely few of the changes are

very large. The numerous small changes cluster in the center of the bell; the rare big

changes are indicated by the edges or tails f the distribution. Mathematicians called this

bell curve „normal‟. The bell curve was first described by the German Gauss (1809). As

shown by Goulielmos et al (2010, p. 115), however, the dry cargo index of freight rates

between 1914 and 2008 exceeded changes of 3σ on many occasions, in 1914 4.57σ, in

1920 3.45σ, in 1960 3.08σ, in 1970 -3.28σ, in 1972 4.9σ, in 1973 -4.88σ and 7.04σ, in

1974 4σ and -3.55, in 2004 5.23σ, and in 2008 -9.56σ. These large changes are much

more common than are suggested by theory. 11 times maritime markets went out of the

bounds set by the normal distribution, where the probability for that is less than 2%. This

was totally unexpected. The joker has unpredictably appeared in 1973 in the form of the

energy crisis and in 2008 in the form of the banking crisis. Bachelier‟s 1900 doctoral

thesis was translated into English in 1964. A more general statement of Bachelier‟s

thinking goes by the name of the efficient market hypothesis (Fama, 1991). This means

that in an ideal market all relevant information is already priced into a security today.

Yesterday‟s change does not influence todays, nor today‟s tomorrows, and each price

change is independent from the last.

The critical assumptions of Bachelier‟s model were: (1) that price changes are statistically

independent, and (2) they are normally distributed. This, however, did not describe

15

This is the tendency of a time series to follow trends. A rise yesterday gives a probability for a rise next

day and vice versa. This is attributed to the memory existing in the series, which is also long and called

black noise. This memory is also called long term correlation, and is not taken into account in RW and AR

models. 16

This further means that we need a forecasting model that may start as a deterministic model with

persistence and cover many decades; next incorporating the forecasting of the joker, which is a random

phenomenon, and then continuing with the same deterministic model. In fact we need a model that forecasts

life, which has alternating events of determinism and events of randomness, we believe. This is for future

research, perhaps based on the late Prigogine‟s work in Physics.

10

reality, especially during the 1990s. As Mandelbrot and Hudson (2004) argued, many

financial price series have a memory and today does in fact influence tomorrow. Large

changes in prices today are likely to be followed by large changes next day, and the

reverse is also true. There is no well-behaved, predictable pattern in prices, nor a periodic

up-and-down procession from boom to bust in business cycles. There is a long term

memory and price time series have different degrees of memory. This makes the RW

model inapplicable.

7. ANALYSIS III: HERETIC FINANCE17

AND CHAOTIC TIME SERIES

7.1 Introduction

In this part will examine the tools that chaos theory can provide for solving the

forecasting problem of maritime indices, especially in the long run.

7.2 Financial versus maritime time series

7.2.1 Stationarity.

We will make here the assumption that maritime time series resembles financial time

series (Jing et al 2008; Chen et al 2010). As financial time series are non-stationary, we

assume that the same is the case for maritime time series, and for this reason we will

apply a filter to transform them into stationary series. Following the suggestion of Peters

(1994), we will use the first logarithmic differences. By so doing we have sacrificed one

observation.

7.2.2 Normality.

Moreover, financial time series are usually tested for normality as there is the probability

for mean and variance to be time-dependent. In effect if variance is time-varying, then

risk and management of it are different from the case where variance is constant. In our

case we calculated the Jarque-Bera test of normality18

. The JB was found to be equal to

866 (rounded) > 5.99 for a=5% for 2 degrees of freedom. The data, therefore, are not

normally distributed. This conclusion is in line19

with what we have described above

Goulielmos (2010).

7.2.3 BDS/IID test.

A further test is that of statistical independence, which indicates whether there are in the

data linear or non-linear dependencies. We skip this stage and go directly to test for „non-

linear independence‟, which will tell us whether our data can be described by a non-linear

model using the BDS Brock, Hsieh and Le Baron (1991) statistic (used for a diagnostic

17

We call heretic finance the school of finance invented by Mandelbrot since 1951 based on biased RW. 18

Kurtosis on non-stationary data for BPI for 2815 daily time charter rates is 1.670856 and skewness is

1.404267. JB= (2815/6)1.404267+ (2815/24) . 19

Almost all maritime economists in their models have found excess kurtosis and excess skewness but

provided no remedies for that.

11

test). This is a test for non-linear dependence in time series. It is a powerful test to find

out whether the iid hypothesis stands in a linear, chaotic or stochastic non-linear model.

Running this test with MATLAB program, we derived the four values of the BDS for

embedding dimensions/correlation dimensions 2, 3, 4, and 5 with e/σ=1.5 (which for low

dimensions), where σ is the standard deviation of a normally distributed sample, and

e=the dimensional distance. The values are: 10.0113, 11.8654, 13.1226 and 13.8816. For

a sample size n=500 (near our sample of n=573), the critical values with 99.5%

confidence level, are: 2.80, 2.86, 2.86 and 2.94 from the table due to Kanzler (1999).

Consequently our time series are not iid.

7.2.4 Efficient market hypothesis.

The hypothesis of the efficient market states that all available information is directly and

fully reflected in prices/time charters. Both (Samuelson 1965; Mandelbrot 1966) have

demonstrated that if the transaction cost is zero and if investors have easy access to the

quickly diffused information, then we may use an RW model. Fama (1965) classified

market efficiency in three levels: weak, strong and semi-strong. Moreover, Fama (1991),

and other financial analysts, argues that returns are characterized by short-term memory

or there is a short-term autocorrelation (not long-term dependence). Among the tests for

the existence of a memory, and its length, is Rescaled Range Analysis (RRA), first

described by Hurst, (Hurst 1951; Mandelbrot 1972; Greene and Fielitz 1977; Feder 1988;

Peters 1994).

7.2.4.1. A memory test.

Einstein (1905) proved that the RW model obeys the law20

: R=k [1], where R is the

distance covered, k is a constant and T is the time index. Hurst (1951) proposed a

generalization of Einstein‟s formula (Peters 1994; Steeb 2008), which then can be applied

to a broader class of time series, including the RW, as follows: R/S=k [2], where R/S is

the rescaled range Mandelbrot (1951-1977)21

, i.e. the range (maximum less minimum

value of time series) divided by (local) standard deviation, T is the index for the number

of observations, k is a constant of time series and H is the Hurst exponent or power law,

where 0≤H≤1. If H=1/2 then the series is independent and follows an RW or White noise

or BM.

Moreover, BM can be now generalized to fractal Brownian motion (FBM), using formula

[2]. In this paper H was found( Mandelbrot 1971; Peters 1994)22

to be equal to 0.93

(rounded) at n≥14 using 2815-1 daily time charter rates for BPI, 1999 to 2011. These and

other calculations were made using the computer program NLTSA V.2.0. H is found from

the regression: log(R/S) =log (k ) + H log (T) [3]. This is equation [2] after taking logs.

This H shows black noise23

in the series and a speed higher than that of the RW.

20

This law expresses the situation where the distance covered by a random particle undergoing random

collisions from all sides is directly related to the square root of time. 21

This is a dimensionless ratio that scales by H as time increases. Rescaling permits the comparison of

distant observations and it can be used for time series with no characteristic scale. It obeys fractal geometry. 22

Moreover, we have applied the Hurst process on first differences as suggested by Mandelbrot to avoid

taking values of H→1, we found no differences from the values obtained when we used first logarithmic

differences suggested by Peters . 23

The characteristics of a time series: (a) to follow trends, (b) to have memory and (c) to have observations

correlated no matter how distant is one from the other.

12

Moreover, there is a 93% probability that the series will increase in the next immediately

following period (2011+) (i.e. this is the „Joseph‟ effect) - invalidating the efficient

market hypothesis.

As shown in Figures 6 and 10, the series has the potential of sudden catastrophes (called

the Noah effect). This series is not distributed independently, but is biased. This bias is

due to the reactions of ship-owners in the current market conditions, using the

information about the current order book and delivery of ships released by shipping

statistical houses and shipyards.

7.2.4.2. Further information from H.

H can give us further information about the data of the BPI 1999 to 2011. The fractal

dimension of the probability space of BPI is FD=1/H= 1/0.93=1.075 (rounded) <2 (2 is

the value for an RW). Also, the fractal dimension of this time series equals FDTS=2-H=2-

0.93=1.07 which is <1.50. The rate of decay of the Fourier series is equal to

RDFS=2H+1=0.93*2+1=2.86. This is denoted by 1/ . The autocorrelation

function (measuring the covariance of a data series with itself) at some time lag τ, is

defined, for fractional Gaussian noise process H≠1/2 and large τ, as follows:

[4] or . A random walk requires C (τ) = 0 (except for τ=0). This indicates

long term memory effects and the correlations are positive for H>1/2 (=persistence).

Mandelbrot, Taqqu and Wallis (1979, 1969) showed the power of the nonparametric RRA

for determining the long run memory and dependence, even when time series are not

Gaussian and exhibit excess kurtosis and excess skewness, as is common in maritime

time series Jing et al. (2008). Moreover, there is a relationship between H and d

(integration coefficient) from ARFIMA models: d=H-1/2 and thus if 0<d<1/2 then the

ARFIMA process is stationary and possesses long term memory. Here d=0.93-0.50=0.43

<0.50 Siriopoulos (1998)24

. The mean orbital period25

is at 14 weeks (3.5 months) and

this indicates a non-periodic cycle.

7.3. Testing for the existence of chaotic dynamics

7.3.1. Introduction

We know that financial time series are good candidates for chaotic analysis and we

believe that the same is true for maritime time series. Even if a time series looks random

(e.g. Figures 6 and 10), it might still be deterministic Siriopoulos (1998). The new

element since 1985, and especially since 1987-89, however, is that chaotic signals must

be analyzed in the time domain state space of the system (phase space26

). Moreover,

simple non-linear models, though free of autocorrelation, can exhibit strong non-linear

dependence Granger and Andersen (1978). This is not new. Mandelbrot (1963) argued

that in uncorrelated returns large variations tend to be followed by large variations. This

24

In the General Index of the Athens Stock Exchange, d=0.30 25

A full orbital period is equal to a cycle. 26

A graph that allows all possible states of a system.

13

led (Engle 1982; Bollerslev 1986) to the ARCH and GARCH27

models respectively

(dealing with a time varying variance), but there are still certain anomalies.

7.3.2 Chaotic systems defined

A chaotic system (or a discrete chaotic time series) is a system exhibiting sensitivity to

initial (starting) conditions, which looks random or irregular. Depending on the dimension

of chaos, this system can be predicted. What we need to know is: (a) if there is sensitivity

on starting conditions, and (b) the dimension of the system. For the identification of a

chaotic time series, we have to construct first a pseudo-phase space using all possible

states of the system in the time delay method Packard, et al. (1980).

7.3.3. The system’s dimension28

Using one of the five methods available, i.e. the correlation dimension, we find system‟s

dimension. This method is due to Grasberger and Procaccia (1983). There is a number of

dimensions where the correlation dimension stabilizes at increasing embedding29

dimensions. This dimension applies also to the relevant attractor30

of the system. Here, as

shown in Figure 4, the correlation dimension - cd is equal 1.27 which is less than 2, and

fractal, at an embedding dimension of 18, calculated by the computer program NLTSA

(2000). White noise does not permit stabilization anywhere. This 1.27 also satisfies the

Eckman and Ruelle rule31

(1992) that cd≤2log2815=6.9. The time delay32

is set equal to

1, as suggested by Siriopoulos and Leontitsis (2000). So, the BPI 1999-2011 per day time

charter rate is chaotic of a dimension 2 which is less than 10 (i.e. a low dimensional

and predictable chaos).

Figure 4: System dimension by Correlation dimension versus embedding dimension

Source: Excel and NLTSA V.2.0 (2000)

27

GARCH stands for the Generalized, (meaning that it has been broadened to accommodate more

circumstances than ARCH in 1982), Autoregressive (AR), Conditional (meaning that the changes in the

variability are controlled by data‟s own past behavior), heteroskedasticity (meaning that data‟s variability

changes with time). This is a set of statistical tools to model data. 28

To analyze the problem of chaos in financial time series there are two methods: (1) the dimension

approach, used here and (2) the approach with artificial neural networks. 29

The idea is to embed time series in successive dimensions until we see (if dimensions are ≤4) a clear

picture of the object (the attractor) that is formed. This is done using as few equations as possible. 30

This is an object expressing the equilibrium level of the system. 31

Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems. 32

The system of time delay is a method to create another variable for each dimension, where

we have only one variable.

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 5 10 15 20 25

correlation dimension

embedding dimension

14

(a) The Lyapunov‟s exponent33

: the Lyapunov exponent can then be calculated. We

will use the method developed by Kantz (1994), which is considered robust and is not

influenced by the embedding dimension chosen. The attractor has a dimension of 1.27. It

has been argued Siriopoulos and Leontitsis (2000) that the Lyapunov exponent must be

twice that, 2.54 , while according to Takens34

(1981) it must be no

greater than 4: ≥2*1.27+1 4. NLTSA gives us the values of time evolution S(a)

and evolution a for the first 5 values of a, including 0. The maximum Lyapunov exponent

is given by the slope of the curve in Figure 4, which is determined by: S(a)= ,

where c is a constant.

Figure 5: Lyapunov exponent by the slope of S(a) = 1+c

Source: Excel and NLTSA

As shown in Figure 5, the Lyapunov exponent is equal to the slope of the curve, i.e.

0.1594, where the error35

, given by R² = 0.9902, is small in the area where a is in the

closed interval [0-5]. The exponent is positive, and allows us to forecast 1/0.1594 days

ahead =6.27→6 days, which is a very short period.

There are three further options for extending the prediction period: (1) to turn to MTA,

which we do in Analysis IV, (2) to transform the data into a shorter period, i.e. into weeks

and (3) to calculate cycles. Turning data into weeks, we obtain Figure 6. This has a self-

similarity property36

of time series, as can be seen by comparing Figure 6 with Figure 10.

The two figures are the same under scale.

33

A measure of the dynamics of an attractor. If positive, it measures a sensitive dependence on initial

conditions. 34

Detecting strange attractors in turbulence, Lecture notes in Mathematics 898, Springer-Verlang. 35

Where R² must be ≥98%. 36

Frequency distributions are self similar, if, after an adjustment for scale, they are much the same shape.

y = 0,1594x + 10,521R² = 0,9902

10,4

10,6

10,8

11

11,2

11,4

0 1 2 3 4 5 6

S(a) =time evolution

Evolution a

15

Figure 6: BPI per week, 1999-2011, 573 weeks

Source: Data and excel transforming 2815 days into weeks

Passing from days to weeks, the degree of persistence reduces from =0.93 to =0.735

for n=10 and for a total of n=573-1 weeks. The mean orbital period also reduced to 2.5

months. Following the same steps as above, we found the dimension equal to 1.22 at an

embedding dimension of 12. The dimension is again fractal, less than 2, and low. The

new Lyapunov exponent, 0.1709 at 97.3% = The prediction period is now

equal to 1/0.1709 = 5.85→6 weeks at a slightly higher error of +0.7%. This is an

improvement, giving predictability for 6 weeks rather than 6 days, but the prediction

period is still short. We turn now to the third option.

7.4. Non-periodic shipping cycles

To locate cycles we divide our weekly data of n=572 weeks into 14 groups so that N

times A equals n. We have chosen n=560 and we have found 14 integer dividers that

divide this exactly. We have plotted the log(R/S)n and log E(R/S)n against n to detect

cycles (Peters, 1994). The plot (not shown here) gave four non-periodic cycles: (1) at 16

weeks (4 months), (2) at 35 weeks (about 9 months), (3) at 80 weeks (20 months) and (4)

at 140 weeks (35 months).This 35 month cycle is very close to the cycle of 3-4 years

found by MTA (Analysis IV).

Peters (1994) suggested another more accurate method to calculate cycles. This is:

Vn=(R/S)n/ (Figure 7).

0,00

10000,00

20000,00

30000,00

40000,00

50000,00

60000,00

70000,00

80000,00

90000,00

100000,00

0 100 200 300 400 500 600 700

16

Figure 7: Vn versus log n for BPI 1999-2011 (weekly rates)

Source: Excel and NLTSA

The Vn statistic shows clearly 4 cycles in the period 1999-2011: (1) at 16 weeks (4

months), (2) a new at 35 weeks (about 9 months), (3) at 80 weeks (20 months) and (4) at

140 weeks (35 months). The criterion used for finding a cycle is that a cycle exists when

the Vn curve flattens out (called a break) Peters (1994, p. 92-93). The data used does not

allow us to identify37

any 20 years cycles, as the data collection period is shorter than that.

To overcome this difficulty, we examined 61 years from 1941 to 2007for the index and

found H3 = 0.64 at n=10, and three cycles Stopford (2009) 38

, this time of 6, 12 and 30

years. Moreover, for 259 years (1741-2008), H4 was higher and equal to 0.696 at n=10

and the cycles were 6 years and 129 years. These results indicate that shipping cycles

differ from period to period and from index to index, making prediction even more

difficult. The positive element from the above analysis is that certain cycle durations

appear again and again. This is unlikely to be mere chance.

8. ANALYSIS IV: MARITIME TECHNICAL ANALYSIS

8.1 Introduction

Technical analysis (TA) is used to recognize patterns, real or spurious, in studying large

quantities of data on prices, volumes, and indicator charts in search of clues to buy or sell.

TA expanded in the 1990s and appeared also on the internet, where stocks were traded.

All major forex (currency) houses use this analysis, and try to find support points and

trading ranges. Chartists for: (1) can at times be correct, and (2) their models may work at

times, but their theory is not a foundation on which to build a global risk-management

system Mandelbrot and Hudson (2004 ). Miner (1999) gives the objective of TA as: “To

identify those market conditions and the specific trading strategies that have a high

37

Mrs Psifia E-M found for the dry cargo charter index per trip on 1968-2003, 3 non-periodic cycles of 28,

60 and 105 months (2 years 4 months; 5 years and 8 years and 9 months). For dry cargo time charters 1971-

2003 there was one cycle of 2 years and 8 months. For dry cargo per trip charter 1971-2003 there were two

cycles of 48 and 96 months (4 years and 8 years). This means that each category has its own cycle(s), but

cycle duration is not very different from one index to another. 38

concluded that a cycle of 7 years is supported by statistics. The last 50 years, however, support a cycle of

8 years. This is also the mean value of the 12 cycles (i.e. 7.8 years). Six cycles lasted over 9 years. Nine

cycles appeared in bulk shipping since 1947. One thing is certain; cycles are non-periodic.

1

1,1

1,2

1,3

1,4

1,5

1 1,5 2 2,5 3

Vn=(R/S)n/sq. root of n

log n

17

probability of success”. The basic assumption of TA (Siriopolos 1999; Miner 1999) is

that the price level is determined by demand and supply. In addition, past price time series

shape the future levels of prices. There are two phases: an accumulation of shares, when

prices are low, and distribution, when prices are high. TA passed through three historical

developments: (a) the Dow Theory (1902, 1922 and 1932), (b) the Elliott theory of waves

(1930 onwards) and (c) the use of technical indices (1975 onwards). We will concentrate

on the second development that has influenced shipping especially the analysis due to

Frost and Prechter (1978). (Elliott 1930; Prechter 1980), argued that markets follow 8

(steady in number) full waves with a repeated (impulsive) formulation of 5 waves up, that

move according to a trend and 3 corrective waves down39

. These are followed by 34

medium waves and 144 small waves40

. All numbers obey the „Fibonacci‟ series. Here we

have also the „graphical TA‟ due to Gann41

(1878-1956), which we meet in stock

exchange index analysis in financial columns of newspapers referring to such concepts

like levels of support, resistance and retracement focusing on time and price (following

the „classical graphical TA‟). Gann used the geometric angles of the trend (mainly based

on the 45 degrees „equilibrium line‟ for the relation between price and time). As Peters

(1994) argued, charts are important tools for the day traders in all trading rooms and for

short-term investors. TA is based on the belief that there are regular market cycles, hidden

by noise or irregular perturbations that drive the market‟s underlying clockwork

mechanism. Spectral analysis finds only correlated noise, but nothing is certain. The

information used is related to the momentum of a particular variable and to market

dynamics and crowd behavior.

8.2 Maritime Technical Analysis (1990)

(Hampton 1990; Randers and Goluke42

2007), argue that it is possible to make accurate

long term forecasts of freight rates. They combine market psychology with cycles of

various durations. The techniques are based on a detailed analysis of over 40 years of

shipping statistics. In this historical analysis, there are long periods of low freight rates,

representing an 8 to 12 year correction phase of a long cycle, with a total duration of

about 20 years. Long cycle corrections are preceded by 8 to12 years of healthy freight

rates, when over-optimism caused a surplus of ships to be built (Figure 8).

39

Numbers 5 and 3 of Elliott are connected with the series of Arabic numbers introduced first in Italy by

Fibonacci (known as Leonardo of Pisa, 1180-1250) in his „book of abacus‟ in 1202. The Fibonacci series

1,1,2,3,5,8,13,21,34,55,89,144,233 are related with the „golden ratio or spiral logarithm‟ of Ancient Greeks;

this was known by Pythagoras, which is given by solving: This is called the

„golden mean or divine proportion‟. This number is present also in the works of Leonardo da Vinci and

Salvador Dali. This is the way to construct the so called „golden square‟. 40

The 5 waves up create 21 waves (5+3+5+3+5), while the 3 ones down create 13 waves (5+3+5). 41

„Successful stock selecting methods in Wall street‟, Institute of Economic finance (undated).

42 They argued that it is possible to explain much of the history of the world‟s shipping markets since 1950

as the interaction of two balancing feedback loops: a capacity adjustment loop which creates a roughly 20-

year wave, and a capacity utilization adjustment loop which generates a roughly 4-year cycle.

18

LONG CYCLE

(Idealized)

1

2

3

4

5 6

Resistance

Build-up Phase (8-12 Years) Correction Phase (8-12 Years)

Figure 8: Idealized Long-run shipping cycle of 16-24 Years due to Hampton

The long cycle of 16 to 24 years is a composite of 3+3 shorter cycles (Figure 9). In the

rising phase of the long cycle one finds 3 regular short cycles, each with peaks

approximately 3 to 4 years apart, consisting of 8 stages. This shorter idealized cycle of

Hampton consisting of 4 shorter cycles is shown in a historical picture (Figure 9) of the

1981-1987 crisis.

Figure 9: The 8 idealized stages of the short 3-4 years shipping Cycle, 1986-1990

Source: based on Hampton (1990)

8.3 Short-run MTA

Figure 10 shows several Hampton short cycles: (1) one between 2005 and 2008, (2) the

previous cycle, lasting from November 2002 to July 2005 (33 months from low to low;

this is shorter than the previous one of 2005-08 – 40.5 months), (3) a third cycle starting

on 16th

December 2008, predicted to terminate in April 2011.

Beginning 535.5

July 1986

535.5 July 1986

End (3 – 4 Years)

1648.

BFI

0

Stage 1

Support

Stage 2

Stage 3

Stage 4

η

Stage 5

Stage 6

Stage 7

Stage 8

BFI 800 (1990)

19

Figure 10: Panamax, 4 time charter routes of BPI $ per day, 01/11/99-25/01/11,

2815 days

Source: Excel and data for BPI

Figure 10 shows the picture from 01/11/1999 to 25/01/2011 per day for the BPI. The

cycles that can be read from the chart are 2½from one low to the next: one from day 760

to day1430, i.e. 22 months and 10 days, one from 1430 to 2240, i.e. 27 months and ½

from 2240 to 2815, i.e. 19 months and 5 days. This alternation of the cycles indicates that

cycles last longer as we move into the crisis and so the last half cycle - if symmetrical -

will last more than 39 months. The total will be 7 years and about 4 months for 3 short

cycles since 2002. The lowest value of the index occurred on 12/12/08 at $3537 (2286th

day) (and not on 13/10/2008 as predicted by MTA). Such deviations, however, are to be

expected. In order to get a clear picture of the charts representing cycles between 1985

and 2001, which are hidden in the above uniform Figure 10, we have worked out 2

Figures in the Appendix I separating period 1985-2001 from 2001-2010.

The starting level of the BPI cycle was at $1522 on 01/08/2005 (not shown). This can be

identified as point 0 in the Hampton cycle process (Figure 9). This must be equal of the

BPI at stage 8. What was the value of the index at stage 8 (end of cycle)? Actually, on

13th

Oct. 2008, it was $1584, which is close to $1522. This means that the end of 2008

shipping cycle had lasted 38.543

months from low to low. But in fact the cycle ended later,

on 15/12/08 (i.e. an additional 2 months), and thus the cycle lasted 40.5 months. Such

deviations are to be expected with MTA.

In more detail, the cycle started44

in fact on 23/01/06, rose (during stage 1) to 18/09/06

and $4160 and fell (during stage 2) to 23/10/06 and $3632. It then rose (during stage 3) to

14/05/07 and $6261 by gaining support from supply and demand equilibrium for ship

space. It then fell, (during stage 4), to 11/06/07 and $5472. Next, it reached its peak

(during stage 5) on 29/10/07 at $11524. Then, the fall started (during stage 6) to 28/01/08

and $5620, followed by an upward move (in stage 7) to 19/05/08 and $11056 (lower than

the peak). Finally there was a free fall to $1584 (during stage 8) on 13/10/08, which,

according to theory, should have been equal to that of stage 0, i.e. $ 1882. Figure 10

shows that a new cycle started on 12/12/08 at $3 537 (2286th day). This is expected to

43

Hampton‟s cycles in practice do not last exactly 36 or 48 months, as theory suggests, but they are shorter

or longer by up to 10% or 3.6-4.8 months. 44

It starts from a low stage 0, at 1882 units.

0,00

10,00

20,00

30,00

40,00

50,00

60,00

70,00

80,00

90,00

100,00

1

11

0

21

9

32

8

43

7

54

6

65

5

76

4

87

3

98

2

10

91

12

00

13

09

14

18

15

27

16

36

17

45

18

54

19

63

20

72

21

81

22

90

23

99

25

08

26

17

27

26

Tho

usa

nd

s $

DAYS

20

last 3 to 4 years, i.e. it will go into 2011-201245

. Our view is, however, that this ½ short

cycle will last 300 weeks or about 6 years, starting from early 2011. The correction phase

is the phase where excesses and mistakes in the build-up phase are corrected. According

to Hampton (1990) the freight market during this phase is not so regular and the first short

cycle 2008-11/12, as shown in Figures 5 and 10, is the shallowest (rates<$30000).

Ordering of new ships will cease, apart for speculation and during false dawn46

periods.

In addition, crisis has obviously cropped the upper high levels of daily time charters ($96

000). The 2008-2012 cycle is lower in level (<$30000 and = $3500)47

than the one before

it ($50000). This cycle comes in the middle and is followed by the all time grandiose

cycle. Today there is a crisis resembling that of 1981-87, with low rates, indicating poor

business. Survival will rest now, as then, on past reserves for crises. Companies have built

these reserves by not distributing all their profits to their shareholders. Crises create

opportunities for those with liquid assets. Figure 11 gives the latest available chart for the

short Hampton cycle, and show data (and forecast) up to the end of May 2011.

Figure 11: Hampton short cycle from 01/12/08 to May 2011

A synopsis of short term predictions Table 1 below summarizes the chartists‟ predictions.

45

This cycle shown here is only half, meaning that this cycle will go beyond Jan. 2011. 46

False dawn is a metaphor meaning that ship-owners proceed to get finance from their bankers on the

prospects of a deceptive dawn, i.e. an improvement of freight market, that proves to be temporary as the

dark returns and the real dawn comes after some time. A barometer of the market is the amount of laid up

tonnage that can enter and the market after deliveries have stopped. 47

The chart (Figure 7) shows 2 cycles from low to low; the non periodicity is evident.

Last 10 Years Average; $27,125

$0,00

$2,00

$4,00

$6,00

$8,00

$10,00

$12,00

$14,00

$16,00

$18,00

$20,00

$22,00

$24,00

$26,00

$28,00

$30,00

$32,00

$34,00

$36,00

$38,00

$40,00

01

-Dec

-08

16

-Dec

-08

31

-Dec

-08

15

-Jan

-09

30

-Jan

-09

14

-Feb

-09

01

-Mar

-09

16

-Mar

-09

31

-Mar

-09

15

-Ap

r-0

93

0-A

pr-

09

15

-May

-09

30

-May

-09

14

-Ju

n-0

92

9-J

un

-09

14

-Ju

l-0

92

9-J

ul-

09

13

-Au

g-0

92

8-A

ug-0

91

2-S

ep-0

92

7-S

ep-0

91

2-O

ct-0

92

7-O

ct-0

91

1-N

ov-0

92

6-N

ov-0

91

1-D

ec-0

92

6-D

ec-0

91

0-J

an-1

02

5-J

an-1

00

9-F

eb-1

02

4-F

eb-1

01

1-M

ar-1

02

6-M

ar-1

01

0-A

pr-

10

25

-Ap

r-1

01

0-M

ay-1

02

5-M

ay-1

00

9-J

un

-10

24

-Ju

n-1

00

9-J

ul-

10

24

-Ju

l-1

00

8-A

ug-1

02

3-A

ug-1

00

7-S

ep-1

02

2-S

ep-1

00

7-O

ct-1

02

2-O

ct-1

00

6-N

ov-1

02

1-N

ov-1

00

6-D

ec-1

02

1-D

ec-1

00

5-J

an-1

12

0-J

an-1

10

4-F

eb-1

11

9-F

eb-1

10

6-M

ar-1

12

1-M

ar-1

10

5-A

pr-

11

20

-Ap

r-1

10

5-M

ay-1

12

0-M

ay-1

1

T 4 T/C Routes for Baltic Panamax (Daily)

Stage 3

Stage 4

Stage 5

Stage 6

Stage 7

Stage 1

Stage 2

Stage 0

Stage 8

thousands

21

Table 1: Summary of 3-4 years predictions using Maritime Technical Analysis

2002-2011

Cycle duration Index Details

Nov. 2002- end July

2005,

44 months

BPI per week $1 500 start-$1 522 end

2005-2008,

40.5 months

BPI per week 01/08/05 start at $1 522

to end 13/10/08 at

$1 584really

ended 12/12/08 at $3

537

Detailed 2005-2008,

(about 35 months)

BPI average per week 23/01/06 $1 882 start,

end $1 584 13/10/08 ,

but really ended 12/12/08

$3 537

2008-2012,

28.5 months

BPI 4 routes time charter

per day

Start $4 500 on 01/12/08

to end Sept. 2010, but

really it will go on April-

May 2011

1999-2011- BPI 4 routes time charter

$ per day

12/12/08 at $3 537 to end

on middle 2011.

Chartists‟ predictions seem to be fairly consistent and as such can be used for forecasting.

According to theory this cycle is characterized by such decisions that involve the building

and scrapping of ships.

9. ANALYSIS IV: LONG-TERM SHIPPING CYCLES

With the aim of looking further into the future, we can look at a long term shipping cycles

of 16-24 years, starting in 2003. Figures 8 and 12, show the long shipping cycle of 16-24

years due to Hampton (1990). This consists of 2 phases and 3 shorter cycles within each

phase, totaling 6 cycles. This cycle started on 4th

August 2003 at $16 000; then freight

rates rose in three steps to $47 000, then to $51 000 and finally to $96 000. The fall

occurred on 5th

December 2008 giving a time charter of $ 4 058; it then rose to $36 000

and fell to $12 000 at the beginning of 2011. This cycle is known as Kuznets cycle.

During this cycle decisions concern the question of remaining in the industry or leaving,

due to a long correction phase of 8-12 years.

22

Figure 12: The 16-24 years cycle from 04/08/2003 to 2015

The build up phase consists of 3 regular cycles, each rising higher than the previous one.

As shown in Figure 12, to reach the final peak of $96 000 per day, there was an enormous

increase in the capacity to own, build and finance ships. Ship ordering dominates and

deliveries follow.

Behind the above picture, and during build-up phase, according to theory, new investors

will enter the market and existing ones expand their fleet with new-buildings or by

replacing older ships with newer and larger ones. This happened also 1981-87. The

owners are helped by shipyards and bankers. In the end, orders are placed because of the

optimism created by the very high freight rates of these 8-12 years, and then deliveries

take place creating an oversupply.

The build-up phase seems to have taken place between 2003 and December 2008 (65

months or 5 years and 5 months; shorter than the theoretical cycle of 8 years). Then the

correction phase started in December 2008 and is expected to last 8 years, or until 2016.

The first short cycle of three started in December 2008 and will go on until April 2011

(29 months). The correction phase is expected to be longer than the building up phase,

and it may last 8 years or more, given the high level of deliveries mentioned in the

introduction. The correction phase is much slower than the build-up phase. The scrapping

process is twice as slow as other adjustments, and thus it takes time to arrive at

equilibrium. Growth of the economies of China, India, Brazil, Russia, and Germany, and

their particular needs, may produce equilibrium faster.

10. CONCLUSIONS

This paper highlights the fact that the inability to forecast by shipping managers led them

to over-order. By 2014, 274 million dwt of dry cargo ships are expected to be delivered.

21-Jun-04,$18,126 29-Jul-05,

$10,727 05-Dec-08; $4,058

$0$4$8

$12$16$20$24$28$32$36$40$44$48$52$56$60$64$68$72$76$80$84$88$92$96

$100

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Χιλιάδες 4 T/C Routes for Baltic Panamax

BUILD UP PHASE

8-12 years

CORRECTION PHASE 8-12 years

Resistance

4th Aug. 2003

23

For the recovery, we have placed our hopes on the expected high growth of countries like

China and India for the years to come.

Are there any methods for predicting shipping markets? The answer was yes and no.

Chaos theory can provide predictions of weekly rates of BPI 6 weeks ahead, and by using

chaos cycle theory we can detect even a whole 20-year cycle. But we have been unable to

know in advance whether the next cycle will last 4 years or 20 years. For this we have

resorted to maritime technical analysis. The superiority of chaos theory over spectral

analysis, proved to be a defect here: the former method demonstrated the existence of

non-periodic cycles.

Moreover, this paper has shown that cycles not only vary from ship size to ship size and

from one period to the other, but also differ in according to the duration of the research

period used. Fortunately there is a general convergence to 3 cycle durations, as shown by

chaos theory: (1) around 3 years, (2) around 4-6 years and (3) around 8-12 years. The use

of exponent H has also given us the mean orbital period (=a cycle) of 10 years.

Surprisingly, this is in line with Stopford‟s (2009) calculations, who talked about cycles

of 7-8 years, but also of 9 years. This conclusion shows that our analysis is more accurate

than others, because we have shown that simple shipping cycles are not possible, and in

the past a belief in mechanical shipping cycles has proved dangerous. History has taught

us that demand and supply for the specific ship category, of size, flag, age etc.,

determines the ups and downs of her revenues. We have seen that the joker was finally

cut at the end of 2008, as it was 1981, totally unexpectedly.

Academics – in both maritime and general economics – have tried to provide models for

stochastic non-linearities. Various schools/analyses have emerged to manage risk based

on variance: Fundamental, Technical, Modern and Heretic Finance have been used to

forecast/analyze stock prices. Modern Finance was influenced by the doctoral thesis of

Bachelier (1900), who established the Finance Random Walk model. This model has

attracted the attention of many analysts, including Gauss, Brown, Einstein, Yule (1927),

Weiner, Fama, Box and Jenkins, Engle, Bollerslev and others. These have advanced the

well known models of stationary stochastic processes: AR ARMA ARIMA

GARCH. The characteristic of these models is the independence of one observation from

the other.

Reality, however, has confounded expectations based on these models‟ assumption of the

efficient market hypothesis. We have seen in the economy in general and in the maritime

economy in particular, quiet periods interspersed with bursts of turbulence. When we

allow non-linearity into our models, we see that markets violate not only the RW, but also

martingale models. For this reason, in this paper, we presented first a series of tests for

stationarity, normality, independence, long term memory and chaos. We kept at the back

of our mind the question of whether it is probable that shipping time series to have been

generated by non-linear deterministic laws of motion, like those found in the natural

sciences. There, time series behave in ways that look random by the traditional statistical

and econometric tests, but they are actually biased RW with long term dependence.

Finally, the human desire to know future led people to resort to (financial) astrology, or to

(Maritime) Technical Analysis. Even the mystery of the Arabic numbers and the

Fibonacci series, leading to the divine ratio known since the time of Pythagoras, have

been invoked to understand finance. Among Maritime economists, Hampton (1990)

advanced his theory of two idealized shipping cycles of 8 stages of 3-4 years combining

to give a total cycle of 16-24 years. In practice, all these cycles were shorter or longer

24

than predicted by at least ± 10%. The long-cycle showed two phases: build-up and

correction. Crises cropped the height of the freight rates to below $40000 per day. Two

and half short cycles can be seen between 2001 and 2011 as shown in Figure 10. The long

cycle, which started on 4th

August, 2003, is expected to end in 2018. Its correction phase

will last 10 years (2009-2018), whereas the build-up took 5.5 years. Phases, too, are

obviously uneven, as one might expect.

ACKNOWLEDGMENTS

Thanks go to my former PhD student M-E Psifia for preparing Figures 2, 11 and 12.

REFERENCES

Bachelier L, (1900), Theorie de la speculation, Annals de l‟ ecole normale superieure,

series 3, 17, 21-86.

Batchelor R-Alizadeh A and Visvikis I, (2007), Forecasting spot and forward prices in the

international freight market, International Journal of Forecasting 23, 101-114

www.sciencedirect.com

Bollerslev T, (1986), Generalized autoregressive conditional heteroskedasticity, Journal

of Econometrics, 31, pp. 307-327.

Box G E P and Jenkins G M, (1976), Time series analysis: forecasting and control,

revised edition, S. Francisco, Holden Day.

Brock W-Hsieh D and LeBaron B, (1991), Nonlinear Dynamics, Chaos and Instability:

statistical theory and Economic evidence, MIT Press, USA.

Carl Friedrich Gauss, in his book: „A Theory of the movements of celestial bodies‟, 1809

Chen S –Meersman H and Van de Voorde E, (2010), Dynamic interrelationships in

returns and volatilities between Capesize and Panamax markets, Maritime economics &

Logistics, Vol. 12, No 1, March, pp. 65-90.

Cootner P A (Ed.) (1964), The random character of stock market prices, Cambridge

Mass.: MIT Press.

Einstein A, (1905), Uber die von der molekularkinetischsen theorie der warme geforderte

bewegung von in ruhenden flussigkeiten suspendierten teilchen, Annals of Physics, 322.

Engle R, (1982), Autoregressive conditional heteroskedasticity with estimates of the

variance of UK inflations, Econometrica, to, pp. 987-1007.

Fama E F, (1965), The behavior of stock-market prices, Journal of Business, 38, 34-105.

Fama E, (1991), Efficient capital markets: II, Journal of Finance 46, 5, 1575-1617.

25

Farmer D J and Sidorowich J J, (1987), Predicting chaotic time series, Physical review

letters 59, p. 845-848.

Feder J, (1988), Fractals, NY, Plenum Press.

Frost A J and Prechter B, (1978), The Elliott Wave Principle, New Classics Library, NY,

USA.

Goulielmos A M and Psifia E-M, (2009), Forecasting weekly freight rates for one-year

time charter 65 000 dwt bulk carrier, 1989-2008, using nonlinear methods, Maritime

policy and Management, Vol. 36, No 5, Oct., 411-436.

Goulielmos A M, (2009), Is history repeated? Cycles and recessions in shipping markets,

1929 and 2008, Int. J. Shipping and Transport Logistics, Vol. 1, no 4, 329-360.

Goulielmos A M, (2010), Did the price of second-hand ships follow a predictable path

over the period 1976-2008? Int. J. Shipping and Transport Logistics, Vol. 2, no 4, 383-

410.

Goulielmos A M, (2011), Forecasting short-term freight rate cycles: Do we have a more

appropriate method than normal distribution?, Maritime policy and Management, Vol. 38.

Goulielmos A M-Lun Venus Y H-Ng Daniel C T and Cheng Edwin T C, (2010), The

Business of Shipping, Shipping and Transport Logistics Book series, Vol. 2.

Granger C W J and Andersen A P, (1978), An introduction to bilinear time series models,

Vandenhoek and Ruprechet.

Granger C W J and Morgenstern O, (1970), Predictability of stock market prices, Heath:

Lexington, USA.

Grassberger P and Procaccia I, (1983), Characterization of strange attractors, Physical

Review Letters A 50 (5), p. 346-349.

Greene M T and Fielitz B D, (1977), Long-Term Dependence in Common Stock Returns,

Journal of Financial Economics, 4, pp. 339-349.

Hampton M J, (1990), Long and Short Shipping cycles: the rhythms and psychology of

shipping markets, A Cambridge Academy of Transport Monograph, 2nd

edition, March.

Hurst H E, (1951), Long term storage capacity of reservoirs, Transactions of the

American society of Civil Engineers 116: 770-799, 800-808.

Jing L-Marlow P B and Hui W, (2008), An analysis of freight rate volatility in dry bulk

shipping markets, Maritime policy and Management, Vol. 35, 3, June, pp 237-251.

Kantz H, (1994), A robust method to estimate the maximal Lyapunov of a time series,

Physics Letters A 185, p77-87.

26

Kanzler L, (1999), Very fast and correctly sized estimation n of the BDS statistic, Depart.

Of Economics University of Oxford, http://users.ox.ac.uk/~econlrk

Kendall M J, (1953), The analysis of economic time series, Part I: Prices, Journal of the

Royal Statistical society, series A, 96, 11-25.

Li J and Parsons M G, (1997), Forecasting tanker freight rate using neural networks,

Maritime Policy and Management, Vol. 24, N1, 9-30.

Lyridis D V-Zacharioudakis P- Mitrou P and Mylonas A, (2004), Forecasting tanker

market using artificial neural networks, Maritime economics & logistics, Vol. 6, no 2, pp.

93-108.

Mandelbrot B B and Hudson R L, (2004), The (mis) Behavior of Markets, a fractal view

of risk, ruin, and reward, Basic books, NY, USA.

Mandelbrot B B, (1963), New methods in statistical economics, Journal of Political

Economy, 71, pp. 421-440.

Mandelbrot B B, (1966), Forecasts of future prices, Unbiased markets and martingale,

Journal of Business, 39, pp. 242-255.

Mandelbrot B B and Wallis J R, (1969), Some long run properties of Geophysical

records, Water resources research, 5, pp. 321-340.

Mandelbrot B B, (1972), Statistical methodology for nonperiodic cycles: from the

covariance to R/S Analysis, Annals of Economic and social measurement, 1(3), pp. 259-

290.

Mandelbrot B B and Taqqu M, (1979), Robust R/S Analysis of Long run serial

correlation, Bulletin of the International Statistical Institute, 48.

McConville J and Rickaby G, (1995), Shipping Business and Maritime Economics, An

annotated international bibliography, Mansell Publ. Co, UK, ISBN 0-7201-2180-9.

Mills T C, (1999), The econometric modeling of financial time series, 2nd

ed., Cambridge

University Press, ISBN 0-521-62492-4.

Miner R C, (1999), Dynamic Trading, Dynamic concepts in time, price and pattern

analysis with practical strategies for traders and investors, Dynamic Traders Group, Inc.,

Tucson, Arizona, USA. www.dynamictraders.com

NLTSA (2000), V.2.0 in Siriopoulos and Leontitsis (2000).

Osborne M M, (1959), Brownian motion in the stock market, Operations Research, 7,

145-173.

Packard N, Crutchfield J P, Farmer J D and Shaw R S, (1980), Geometry from a time

series, Physical Review Letters, 45, p. 712.

27

Peters E E, (1994), Fractal Market Analysis: applying chaos theory to investment and

economics, A Wiley Finance edition, NY, USA.

Prechter R, (1980), The major works of R N Elliott, NY, New classics library.

Randers J and Goluke U, (2007), Forecasting turning points in shipping freight rates:

lessons from 30 years of practical effort, System Dynamics Review, Vol. 23, No 2/3, 253-

284.

Roberts H V, (1959), Stock-market patterns and financial analysis: methodological

suggestions, Journal of Finance, 14, 1-10.

Samuelson P, (1965), Proof that properly anticipated prices fluctuate randomly, Industrial

Management Review, 6, pp. 41-49.

Sims C A, (1980), Macroeconomics and reality, Econometrica, 48, 1-48.

Siriopoulos C and Leontitsis A, (2000), Chaos: Analysis and prediction of time series,

Anikoula Editions, Salonika, Greece.

Siriopoulos C, (1998), Analysis and control of One-variable financial time series, 2nd

ed.,

Dardanos editions, Athens, Greece.

Siriopoulos C, (1999), Technical analysis: the „anathema‟ of the academics, whose

studies do not reject! (in Greek), Commercial Bank of Greece, Economic Review, pp 4-

16.

Small M, (2005), Applied Nonlinear Time series analysis: applications in physics,

physiology and finance, World Scientific, Series on nonlinear science, A, Vol. 52.

Steeb W-H, (2008), The Nonlinear Workbook, 4th

edition, World scientific, Singapore.

Stopford M, (2009), Maritime Economics, 3rd

edition, Routledge Publications, London,

UK.

Thalassinos E I-Hanias M P-Curtis P G and Thalassinos Y E, (2009), Chaos theory:

forecasting the freight rate of an oil tanker, Computational Economics and Econometric

Int. J., Vol. 1, No 1, 76-88.

Tsolakis S D-Cridland C & Haralambides H E, (2003), Econometric Modeling of Second

hand ship prices, Maritime Economics & Logistics, 5, 347-377.

Working H, (1960), Note on the correlation of 1st differences of averages in a random

chain, Econometrica, 28, 916-18.

Yule G U, (1927), On a method of investigating periodicities in disturbed series, with

special reference to Wolfer‟s sunspot numbers, Philosophical transanctions of the Royal

Society, 226, 267-298.

APPENDICES

28

Appendix I

0

2000

4000

6000

8000

10000

12000

0 50 100 150 200 250 300 350

BDI index, 1985 (end)-2010 (April) per month (304 obs.), 2 cycles shown.

Cycle duration: (1) 201-247 month 2001 Oct.-2005 July =46 monts total

(2) 248-287 2005 Aug.-2008 Oct.=39, total 85, 7 years and 1 month,

(3) 288-304....in process 16 m 2008-2010-11

BDI 1985-2001 Aug.

Cycles: (1) 19-54 months 1986 July-1989 July, 36 months

(2) 55-91 1989 Aug. -1992 Aug.=37 months

(3) 92-140 1992 Sept.-1996 Sept.=49 months

(4) 141-200 1996 Oct-2001 Sept. =60 months, of a total of 182 months,

15 years 2 months.