Maritime Economics & Logistics, 2004, 6, (93–108) r 2004 Palgrave Macmillan Ltd All rights reserved. 1479-2931/04 $30.00 www.palgrave-journals.com/mel

Forecasting Tanker Market Using Artificial Neural Networks D V LY R I D I S 1 , P Z A C H A R I O U D A K I S 1 , P M I T R O U 1 & A M Y L O N A S 1 1 School of Naval Architecture and Marine Engineering, National Te c h n i c a l U n i v e r s i t y o f A t h e n s , 9 , I r o o n P o l y t e c h n i o u S t . , 1 5 7 7 3 Athens, Greece. E-mail: [email protected]

Investing in the tanker market, especially in the VLCC sector constitutes a risky undertaking due to the volatility of tanker freight rates. This paper attempts to uncover the benefits of using Artificial Neural Networks (ANNs) in forecasting VLCC spot freight rates. This is achieved by analysing the period from October 1979 to December 2002, in order to detect possible causes of fluctuations, thus determine the independent variables of the analysis, and then use them to construct reliable ANNs. The aim is to reduce error and, most important, allow the model to maintain a stable error variance during high volatility periods. Among the findings are: ANNs can, with the appropriate architecture and training, constitute valuable decision-making tools especially when the tanker market is volatile; the use of variables in differential form enhances the ANN performance in high volatility periods while variables in normal form demonstrated better performance in median periods; ANN demonstrated mean errors comparable to the naı¨ve model for 1-month forecasts but significantly outperformed it in the 3-, 6-, 9- and 12-month cases; finally, the use of informative variables such as the arbitrage between types of crude oil as well as Capesize rates can improve ANN performance. Maritime Economics & Logistics (2004) 6, 93–108. doi:10.1057/palgrave.mel.9100097

Keywords: Artificial neural networks; tanker market; forecasting.

INTRODUCTION Perhaps the most alluring feature of the freight market, a feature that historically attracted prominent financial researchers like Koopmans (1939)

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and Tinbergen (1931), has been its cyclical nature. As far as research on bulk cargo market is concerned, two are the leading studies that were completed at the same time. The first is the one undertaken by Koopmans (1939), while the second is that of Zannetos (1966). Both studies focus on the tanker market. Paradoxically, following the study of Zannetos (1966), there has been no other attempt to provide a complete financial description of the bulk cargo market. Koopmans (1939) and Zannetos (1966) used as a starting point the financial theory which they then tried to implement in the freight market. According to Veenstra (1999), the handicap of this research strategy is that it ignores certain traits unique to the freight market, such as its structure and its cyclical nature. A third research, undertaken by Svendsen (1958), adopted a different strategic analysis of the market. Starting from tangible elements of shipping, such as ports, ships and costs, it then moved to an analysis of the freight markets. Li and Parsons (1997) were the first who attempted to implement the ANN technology in forecasting the freight rates of the crude oil tankers in the Mediterranean (Med-Med). In their study, they used data from 1980 to 1995 and three variables, namely the same freight rate time series, the Drewry’s tanker demand index and the total capacity of the active tankers. In order to forecast the freight rates time series, they developed two models of ANN. The first used information only from the self-correlation of freight rates, while the second used information from all three variables. The main objective of this paper consists of setting up artificial neural networks that can predict the VLCC spot freight rates of the route Ras Tanura – Rotterdam after 1-, 3-, 6-, 9- and 12-month periods (Shimojo, 1979; Pindyck and Rubenfeld, 1997; Beenstock and Vergottis, 1993). As emphasis was placed mainly on revealing significant changes to the trend of the tanker market (and predicting fluctuations), this was used as a criterion for the validation of the results rather than the mean absolute error. This paper is structured as follows. It starts with a brief history and analysis of the tanker market since 1979. The methodology to be used, the criteria for selecting the input variables and other parameters of the ANN are given subsequently. Following this, the ANN methodology is implemented and the results obtained are discussed, while, finally, the general conclusions of the paper are presented.

B R I E F H I S T O R Y A N D A N A LY S I S O F T H E TA N K E R M A R K E T Seaborne oil trading began in the late 19th century with major origin source producer being North America (USA), major destination consumer the European countries and a small portion heading to the Far East. Many things Maritime Economics & Logistics

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have changed since the first shipment in 1861, but the tanker market and generally charter shipping markets were the pioneers of the era of globalised economy. The two World Wars created a great shortage in the shipping markets, increasing demand for fuel and average distance, and decreasing size and productivity of the tanker fleet. A major long-term impact of World Wars on shipping markets was that the postwar time period had a rapidly increasing fleet supply, a significant surplus, laid up and slow streaming, and subsequently a saturated market with low freight rates. A crucial turning-point in the tanker market was the OPEC foundation. In 1973, OPEC decided to use oil as a weapon against USA and as a result the oil price quadrupled and the tanker market collapsed. In a very short time period, VLCC prices fell by more than 20 million US$. The market situation inverted positively in 1979, after the Iranian crisis, and a VLCC valued at $11 million in 1978, reached the price of $30 million in 1979. In 1980, the war between Iran and Iraq led to the war of tankers in 1984. In all, 11 VLCC were sunk and in total 71 vessels were seriously damaged. As a result, there was a significant decrease of surplus capacity. In 1989, the Exxon Valdez accident changed totally the face of the global tanker market. New regulations emerged after the accident – for example, OPA90 – putting new constraints on tanker routing. In 1990, Iraq invaded Kuwait and the tanker market warmed up for a short period of time. In 1999, another major accident (Erica) resulted in modifying the EU maritime policy for tankers and in increasing the freight rate difference between old and newly built tankers. The tanker market is dependent on the global socioeconomic environment, and the state of the market is established under numerous excitations. One can say that it would be very difficult to reveal all qualitative and quantitative excitations and the corresponding impact on freight rate determination. Tanker freight rates depend on supply and demand for sea transport which, in their turn, are functions of numerous other parameters. Oil and petroleum product movements, from their limited sources of origin to their innumerable destinations, form a dynamic system with continuous fluctuations and change of characteristics. These fluctuations have a stochastic nature caused by stochastic excitations such as wars, accidents, oil shocks, new regulations, canal or pipelines closures, etc. As a result, freight rates have also an apparently unpredictable if rather circular nature through time. These events cause volatility to the parameters that form supply and demand equilibrium and consequently to tanker freight rates. Our current research effort focuses on the interactions between the major tanker market parameters and the formation mechanism of freight rates. The interactions between tanker market parameters and freight rates have a variety of proportions on volume and time lag and lead. For example, a simple statistical analysis using cross- correlation techniques shows that freight rate Maritime Economics & Logistics

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time series are positively correlated – with 2–6 months time lead – with the newbuildings orderbook but, in the long run, freight rates are negatively correlated – with 1–2 years time lag – with the orderbook. The aforementioned interactions between freight rates and various market parameters are not always explainable and certainly not obvious in many cases. It is also crucial to recognise hidden correlations in the market variable set and thus to avoid multicollinearity problems. Therefore, it is necessary to perform a sedulous research over tanker market variables, combining expert judgement, statistical methods and data-mining techniques in order to form an explanatory multidimensional model and an efficient logical analysis framework for tanker market fluctuations. METHODOLOGY Artificial Neural Networks (ANN) may be viewed as an advanced pattern recognition technique with application in time-series forecasting. Forecasting is based on the fact that time-series past values may influence future values and that explanatory variables transfer information for the target variable. ANNs are more suitable for the analysis of non-stationary non-linear time series, such as those found in the tanker market, than linearly based autoregressive models. The ANNs used in this paper are typical MultiLayer Perception networks – MLPs. MLP is a supervised ANN in the sense that data used for training and testing the network is paired with the target data. Knowledge of target data provides a starting point for iteratively modifying the network weight variables in the direction of minimising the error by comparing the network response with the target data. Therefore, the ANN is trained in an adaptive manner over many iterations in order to extract patterns in the input – in sample set – and to provide a forecast for the selected time series. ANN ability to generalise is tested with the test set of vectors – out of sample set. Training input data are formed in vectors, a collection of discrete values of selected input variables. Input variables can be classified in informative variables, that is, those that have low correlation with the independent variable, and in descriptive variables, that is, those that have causality and high correlation with the independent variable. Based on the above, the following variables were considered to be the most important factors in this study:





demand for oil transportation (measured in ton-miles); active fleet; crude oil production; crude oil price;

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surplus as a percentage of active fleet; time charter rates; newbuilding prices; secondhand prices; bunker prices; scrap prices; oil stock building.

The first step is then to select the appropriate random variables to be introduced in the model; to do this, the criteria for their selection should be described. The main criteria used in selecting the appropriate variables were the following: 1. 2. 3.

The correlation between the independent and dependent variables, measured by the correlation coefficient; The low multicollinearity between the independent variables; Expert judgment.

Let X, Y be two random variables. The correlation factor of the two is calculated by the equation: n P ðxi  mx Þ  ðyi  my Þ COV ðX; Y Þ i¼1 R¼ ¼ ð1Þ sx  sy sx sy where: mX is the mean of random variable X, mY is the mean of random variable Y, sX is the standard deviation of random variable X, sY is the standard deviation of random variable Y. The autocorrelation coefficient of the dependent variable was also calculated to establish whether it could be used as an input variable. Crosscorrelation coefficients of all variables were calculated too, thus introducing the phenomenon of time delay which is often observed in the tanker market. Multicollinearity disorients the ANN’s and leads to poor performance by providing a piece of information many times over. Multicollinearity can be measured either by calculating correlation coefficients between the independent variables, or by calculating the Variance Inflation Factor. For a set of k variables, the Variance Inflation Factor is given by VIF ¼

1 1  R2

ð2Þ

where R2 is the coefficient of determination between an independent variable and the k1 residual variables. Maritime Economics & Logistics

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Expert judgement is an asset when dealing with the shipping market and it is the result of a thorough knowledge and analysis of the events that influenced the tanker market during the last 23 years. The next step is to process the input variables. Initially, all the values of the time series were normalised [0,1] in order to ease the processing of calculations of the ANNs. Normalisation was made according to the equation: x0j ¼

xj  m Mm

ð3Þ

where: M is the maximum value of the time series, m is the minimum, x is the non-normalized value, x0 is the corresponding normalised value. The use of exponential moving averages as well as common moving averages yielded significant benefits in the subsequent effort to denoise time series with high volatility. More specifically, exponential moving average deletes irregular noise and takes into account the most recent values of the time series. The exponential moving average is calculated by the equation: n P

EMA ¼

on  Xkn

i¼0 n P

ð4Þ on

i¼0

where: X is the variable, o is a parameter selected by the researcher. Use of variables in differential form such as Value of month j-Value of month j-1 (first derivative of the variable) provides the ANN with extra ability of generalisation. This ability enables it to converge to values ‘first seen’ and additionally strengthens the performance of the ANN in periods with high variances. On the contrary, use of variables in differential form did not produce satisfactory results in more regular periods. An input set consisting of variables in differential form, as well as of variables in normal form was proven to be the optimum solution. All ANNs tested were based on the Feed Forward Back Error Propagation algorithm which comprises the most effective training algorithm for econometric models. An iteration of the algorithm can be expressed as follows: Xkþ1 ¼ Xk  ak k

ð5Þ

where: x is the weight vector, a is the training rate, g is the gradient. In order to improve the ability of the network to generalise, the use of Bayesian regularisation was considered appropriate. This was done by inserting a training function. According to the aforementioned approach, the weights are Maritime Economics & Logistics

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assumed to be random variables with determined distributions. In this way the network selects which of the weights play a significant role and which do not. All the attempts that were carried out used either one or two hidden layers. This was due to the fact that, as established, two hidden layers are adequate in providing reliable forecasting results. The number of nodes of each hidden layer was determined by trial and error. Results show that when a single layer is used, the number of nodes of this layer must be at least equal to the number of the input variables. The performance function determines when the training of the ANN should stop. In the Feed Forward Back Error Propagation algorithm the most applicable performance function is the mean sum of the square errors. This is given by the following equation: F ¼ mse ¼

N 1 X ðti  ai Þ2 N i¼1

ð6Þ

where: t is the target value, a is the output value. Potential increase of the performance function is a sign of overtraining. Then, the training process must be stopped. At times, an alternative performance function may be used. The benefits from the application of the latter are a smoother response of the network and a smaller probability of overtraining. This function is described by the following equation: msereg ¼ g  mse þ ð1  gÞ  msw

ð7Þ

where: msereg is the performance function, g is the performance ratio, msw is mean of sum of squared weights defined as msw ¼

n 1 X  w2 n j¼1 j

ð8Þ

where: n is the number of weights, w is the individual weight. In all the attempts that were made, the logistic sigmoid (LOGSIG) was used as the transfer function. One of the main concerns in the course of the study was to ensure that the resulting ANNs would be applicable on a wide range of cases and that they would take into account the significant fluctuation tendencies of the freight rate. Furthermore, the ANNs should present the least possible margin of error during forecasting, while they should also be trained-set to take into account the widest range of entry variables possible. This was achieved through the employment of the effective number of parameters (ENP). The ENP expresses the number of Maritime Economics & Logistics

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weights taken into account during the convergence of an ANN. The ENP to the total sum of weights of the ANN ratio constitutes the ANN’s performance ratio. The performance ratio expresses the extent to which the entry variables are demonstrably useful to the convergence of an ANN. Should an ANN present a minimum margin of performance ratio between 0.5 and 0.7, then the entry variables account sufficiently for the dependent variable. If the performance ratio is above 0.7, then entry variable selection can be considered as very good. It was also noted that the ANNs developed and trained during the course of the study featured a good performance ratio, creating legitimate expectations for the ultimately correct selection of entry variables. Finally, it has to be added that in the initial stages of the study, experimentations with dummy variables took place. More specifically, two dummy variables were inserted: one being assigned a value of 1, when an unforeseeable event took place resulting in an increase of freight rates (eg the outbreak of a war), while the other variable was assigned a value of 2, when an unforeseeable event led to the reduction of freight rates (eg economic depression). The elements required for the creation of the dummy variables were derived from the first part of the study, the historic account. The objective of this effort was the deduction of bounded forecasting, that is, predicting freight rates as a result of the impact of a conjectural unexpected event. The effort to produce a bounded forecast did not yield the intended results since the ANNs trained in accordance to this methodology tended to underestimate the course of the freight rate market in periods of tranquility, while tending to overestimate it in periods of crisis. (Crooks, 1992; Demuth and Beale, 1996; Frees, 1996; Jang et al, 1997; Azoff, 1994; Trippi and Turban, 1996).

I M P L E M E N TAT I O N O F M E T H O D O L O G Y, D ATA , A N D R E S U LT S The amount of data may prove deciding in the effort to forecast a time series using ANNs. In our paper, data in monthly time series was used and distinct efforts were made to increase the sample. In time series concerning shipping data, sources were Lloyds Shipping Economist and Drewry’s Shippping Statistics. For time series concerning tanker market the source was the Monthly Energy Review. In our subsequent forecasts, training data for all variables ranged from February 1981 to September 2001, and test data ranged from December 2000 to December 2003. During the course of the study, more than 100 ANNs were trained. Experimentations were carried out with almost all potential combinations of variables and different architectures. Furthermore, each type of network was Maritime Economics & Logistics

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101 Table 1: Number of input variables for each forecast interval Forecast interval (months) Number of variables

1 6

3 12

6 13

9 13

12 13

Table 2: Performance of ANNs in a 1-month forecast and number of nodes per layer Number of nodes 6 12 16 18

Mean error on a WS basis 16,53 15,74 14,56 15,75

trained numerous times in order to extract the optimum number of repetitions and parameters. It was observed that use of a smaller number of variables is recommended for forecasting on a short-term scale. On the contrary, a larger sum of variables is more beneficial on a time scale longer than 3 months. The number of variables used for the best forecasts is presented in Table 1. Turning to the architecture of the ANNs vis-a`-vis the attempted forecasts, the following is noted. In all successful forecasts, a hidden layer was used, containing as many nodes as the entry variables, the only exception being the 1-month forecast, where the use of a large number of variables appeared to confuse the ANN. In that case, more nodes were used in the hidden layer as the variables were few and the generalisation potential limited. In Table 2, the performance of this particular ANN (1-month forecast) in relation to the nodes of the layer is reproduced. In the following section, the specific results for each forecast interval are discussed. 1-Month forecast In the case of the 1-month forecast, the results of the study are not encouraging. The error is comparable to that of the naı¨ve model, where the value forecasted is assumed to be the same as the most recent one. Additionally, the ANN forecast appears to converge with the course of the time series with a 1-month time delay. Naturally, this tendency hinders the potential for decision making, as this time delay equals the time frame where the forecast takes place. Nevertheless, it has to be added that this time delay is characteristic of the ANNs and has been observed in similar efforts in the past (Veenstra, 1999). Turning to the ANN training, it has to be noted that, for the particular time scale, the best methodology is the use of a limited number of important variables and of a more complex architecture. On the basis of this methodology, Maritime Economics & Logistics

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20.00

12

10 20

02 -

08 20

02 -

06 20

02 -

04 20

02 -

02 20

02 -

12 20

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01 -

08 20

01 -

06 20

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01 -

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00 -

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0.00

Figure 1: 1-Month forecast for the 12-2000 to 1-2003 time frame

a longer period of training is required (320 repetitions) while the performance ratio appears reduced, marginally above 0.5. The results are given in Figure 1. 3-Month forecast In the case of forecasting for the next 3-months, the results produced were much more encouraging in comparison to those of the 1-month forecast. The error of the resulting forecast appeared reduced by 33% in relation to the naı¨ve model. More variables (12) were used while the ANN was simplified. A number of nodes in the hidden layer equal to the entry variables was selected, the repetitions required were 130, while the performance ratio fluctuated close to 0.7. This reinforces the importance of information concerning the entry variables. As far as the forecasting analysis is concerned, the following observations can be made:







During the recession of the first semester of 2001, the ANN forecast evinces a relative instability. It is however observed that when the ANN misses the movement of 1 month, the resulting forecast shows high accuracy. The ANN foresees the change of tendency both in the end of 2000 and the end of 2002. When attempting to predict a fluctuation of more than 30 units in the WS scale, the forecast is accurate in 75% of the cases. There is no case where an erroneous important change of tendency repeats itself, immediately following the forecasting point. The results for the 3-month forecast are given in Figure 2.

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20.00

2003-3

2003-2

2003-1

2002-12

2002-11

2002-10

2002-09

2002-08

2002-07

2002-06

2002-05

2002-04

2002-03

2002-02

2002-01

2001-12

2001-11

2001-10

2001-09

2001-08

2001-07

2001-06

2001-05

2001-04

2001-03

2001-02

0.00

Figure 2: 3-Month forcasting in the 02-2001 to 03-2003 time period

6-Month forecast Forecasting 6 months ahead demonstrated the highest absolute error in relation to all the attempted forecasts. Nevertheless, the error appeared greatly reduced (35%) in relation to that of the naive model. In all, 13 variables were used for the forecast, and this was the maximum set of variables used in any of the cases (forecast intervals). In the initial stage, the forecast period was extended by 2 months in order to obtain a more complete picture of the behaviour of the ANN during the recession of the beginning of 2001. Overall, 13 nodes were used in the hidden layer, along with an equal number of variables. In total, 200 repetitions were required during training while the performance ratio was 0.73. In relation to the analysis outcome, the following can be observed:






The ANN evinces a high degree of accuracy both in the freight rate and in the classification forecast until the first 3 months of 2002. After the first 3 months of 2002, the ANN demonstrates significant instability, the highest being that of forecasting freight rates for February 2003. Nevertheless, as it was also observed in the 3-month forecast, the ANN appears to be improving its forecasting accuracy the immediately following month. In general, the ANN demonstrates better behaviour during market recession than during market prosperity. The results for the 6-month forecast are given in Figure 3.

9-Month forecast 9-month forecast might just constitute the most encouraging case out of all those examined. The error was lower in comparison to that of the 6-month Maritime Economics & Logistics

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140.00 120.00

OUTPUT TARGET

100.00 80.00 60.00 40.00 20.00

20

01 2 0 -03 01 2 0 -05 01 2 0 07 01 2 0 -09 01 2 0 -11 02 2 0 01 02 2 0 -03 02 2 0 -05 02 2 0 07 02 2 0 -09 02 -1 20 1 03 2 0 -1 03 2 0 -3 03 -5

0.00

Figure 3: 6-Month forecast for the period 03-2001 to 06-2003

forecast and almost half of that of the naı¨ve model. In order to produce this forecast, 13 entry variables were used, with 13 nodes in the hidden layer, as in the 6-month forecast. Totally, 300 repetitions were required, a number that constitutes the highest that was used in any of the cases. The performance ratio appeared improved, reaching 0.85. The analysis of the results demonstrated the following:






Out of the 26 months for which forecasts were made, the error surpassed 20 WS units in seven of the cases. It surpassed 40 WS units only in two cases, one of which concerned September of 2001. Classification forecasting appeared improved. In fact, when it failed, it usually preceded the freight rate time series. The ANN did not present significant instability in relation to the other forecast cases. The results of the 9-month forecast are given in Figure 4.

12-Month forecast The yearly forecast that was produced presented the lowest mean absolute error, following the 3 months and 1-month forecasts. In relation to the naı¨ve model, the forecast appeared to be improved and its error fluctuated around 44% of the naı¨ve model’s error. In order to materialise the forecast, 13 variables were once again used, with 13 nodes in the hidden layer, as in the 3- and 6-month forecasts. Totally, 280 repetitions were required, while the performance ratio was 0.84. Maritime Economics & Logistics

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01 2 0 08 01 -1 20 0 01 2 0 12 02 -0 20 2 02 2 0 04 02 -0 20 6 02 2 0 08 02 -1 20 0 02 -1 20 2 03 -2 20 03 -4 20 03 20 6 03 -8

0.00

Figure 4: 9-Month forecast for the 06-2001 to 09-2003 time frame

In relation to forecasting performance, the following need to be observed:









In this forecast, the ANN presented median behaviour, namely it underestimated the booms and busts. Such a trait is negative when significant changes of tendency have to be forecasted. For the first time in the forecasts produced, the ANN did not rectify an erroneous significant change of tendency in the immediately following forecast. This happens in August–September 2002. It has, however, to be stressed that this appears to be an isolated case. It can be observed that the ANN presents a tendency to delay in the busts while it acts prematurely on the booms. For the last part of this forecast, predicting the boom of September 2003 with a time lag of 1 month is very encouraging.

The results for the 12-month forecast are given in Figure 5. In closing this section, we summarise, in Table 3, the training parameters of the optimum ANN in every forecast case. Furthermore, Figure 1, compares the mean square error of the naı¨ve model to the one of the ANN. CONCLUSIONS In this paper, we initially analysed the tanker market since 1979 in order to establish the most important factors affecting it. Then we tried to predict its behaviour using these factors as input variables to Artificial Neural Networks. Having real historical data for the route Ras Tanura –Rotterdam, we attempted to predict the market after 1-, 3-, 6-, 9- and 12-month periods and tested our methodology against the most recent data. Maritime Economics & Logistics

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OUTPUT TARGET

80.00 60.00 40.00 20.00

20 01 -1 20 1 02 -0 20 1 02 -0 20 3 02 -0 20 5 02 -0 20 7 02 -0 20 9 02 -1 1 20 03 -1 20 03 -3 20 03 -5 20 03 -7 20 03 20 9 03 -1 1

0.00

Figure 5: 1-Year forecast for the 11-2001 to 12-2003 time frame

Table 3: Training parameters for all forecasts

Forecast (months) Number of weights Number of effective variables Repetitions Performance ratio Mean error (WS)

ANN 1B

ANN 3D1

ANN 6G1

ANN 9G1

ANN 12G1

1 112.00 59 320 0.53 14.56

3 156.00 107 130 0.69 17.72

6 182.00 133 200 0.73 24.46

9 182.00 155 300 0.85 23.62

12 182.00 152 280 0.84 22.2

From our work, the following main conclusions can be drawn:












ANNs that fail to increase quickly the number of effective parameters usually do not yield useful results. The number of effective parameters (ENP) should increase gradually. Sudden error decreases or ENP increases foreclose an inadequate or excessive ANN training. The joint introduction of variables in the form of differences and of absolute values leads to the optimum results for the particular type of time series. When only the first type of variables is used then the ANN presents instability while when the second type of variables is used, its convergence with the excessive lack of continuity of the time series is inadequate. The introduction of the entire past freight rate time series as an independent variable seems to further confuse instead of helping train the ANN. The presence of informational variables such as the petrol price or arbitrage can be especially useful. In attempts made in the absence of such variables, the error appeared to increase. Concerning the representation of the demand for transportation services, it appears that the representation of the total demand is preferable to that referring only to the particular type of tanker.

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Figure 6: Comparison of the mean error of the neural network with the one of the naı¨ve model







It was generally observed that the more the time delay (according to which the forecasting is made) increases, the more difficult the training becomes and the greater the number of repetitions required for training the ANN. More specifically, during the forecast of a 9- or 12-month period, ANNs appear to be exceptionally unstable and the problem of under- or overtraining becomes more pronounced. With regard to the mean absolute error, it is observed that it increases up to the forecast for the 6-month period while it decreases immediately after that. In all cases, ANNs tend to follow close enough the freight rate time series, despite its irregular behaviour, with the possible exception in the 12month forecast (Figure 6).

In general it can be said that Artificial Neural Networks represent one very promising tool in forecasting freight rate time series, but, as also in other cases, a combination of various forecasting methods may eventually prove consistently more accurate.

Acknowledgements The authors would like to particularly thank Mr Dimitrios Mitrou, credit analyst in the Agean Balt Bank, who contributed substantially in the research for the macroeconomic analysis of the tanker market. REFERENCES Azoff, M. 1994: Neural Network Time Series Forecasting of Financial Markets. Wiley: New York. Beenstock, M and Vergottis, A. 1993: Econometric Modelling of World Shipping. Chapman & Hall: London. Crooks, T. 1992: Care and Feeding of Neural Networks. AI Expert 7(7): 36–41. Maritime Economics & Logistics

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108 Demuth, H and Beale, M. 1996: Neural Network Toolbox for use with MATLAB. The Math Works Inc.: Natick, MA. The Drewry Monthly. Drewry Shipping Consultants Ltd. (ed). Frees, E. 1996: Data Analysis Using Regression Models. Prentice-Hall: Englewood Cliffs, NJ. Jang, JSR, Sun, CT and Mizutani, E. 1997: Neuro-Fuzzy and Soft Computing. Prentice-Hall: Englewood Cliffs, NJ. Koopmans, TC. 1939: Tanker Freight Rates and Tankship Building. Report Nr. 27. Netherlands Economic Institute: Haarlem, The Netherlands. Li, J and Parsons, MG. 1997: Forecasting tanker freight rate using neural networks. Maritime Policy and Management 24: 9–30. Monthly Energy Review. Energy Information Administration (ed). U.S. Department of Energy (http://www.eia.doe.gov/). Pindyck, R and Rubenfeld, D. 1997: Econometric Models and Economic Forecasts. McGraw-Hill: New York. Shimojo, T. 1979: Economic Analysis of Shipping Freights. Kobe University. Shipping Economist. Lloyd’s (ed). Clare Longley. Svendsen, AS. 1958: Sea Transport and Shipping Economics. Weltwirtschaftliches Archiv. Republication for the Institute for Shipping and Logistics: Bremen. Tinbergen, J. 1931: Ein Schiffbauzyclus? Weltwirtschaftliches Archiv 34: 152–164. Trippi, RR and Turban, E. 1996: Neural Networks in Finance and Investing. Irwin. Veenstra, AW. 1999: Quantitative Analysis of Shipping Markets. Delft University Press Postbus. Zannetos, Z. 1966: The Theory of Oil Tankship Rates. MIT Press: Boston.

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