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Maritime Policy & Management
The flagship journal of international shipping and port research
Volume 38, 2011 - Issue 6
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Original Articles

Forecasting short-term freight rate cycles: do we have a more appropriate method than a normal distribution?

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Pages 645-672 | Received 11 Jun 2010, Accepted 17 Jan 2011, Published online: 07 Oct 2011

References and notes

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  • Goulielmos and Kaselimi [43] reviews four to five works that tried to forecast port traffic. This paper will appear in the International Journal of Shipping and Transport Logistics, Vol. 3
  • Goulielmos, A. M. and Kaselimi, V., 2011, A non-linear forecasting of container traffic: the case-study of the Port of Piraeus, 1973–2008. International Journal of Shipping and Transport Logistics, 3(1), 72–99
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  • Kavussanos and Alizadeh [46] criticized her for not taking into account the stochastic properties of her variables and for not taking 20 years data, at least, to examine a full shipping cycle. These authors assume a single 20 years cycle, which has ignored short-term cycles for 4 years or even long waves of 54 years (Kondratieff waves)
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  • He was criticized too by [46] for short data and for ignoring stochasticity
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  • He also did not take into account the stochastic properties of his variables (as argued by [46])
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  • This means information available for historical prices only
  • The time was rather short (<20 years). Their formulation was inappropriate to test EMH, as co-integration (due to Engle and Granger [55]) is not a sufficient, but a necessary, condition, as argued by [46]
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  • They came to mixed results, due to same mistakes found also in Hale and Vanags, as mentioned by [46]
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  • These terms and acronyms are defined below
  • A computer-based simulation, considered as imitating the human nervous system that can learn from experience
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  • The model started as a business game in 2005 between Antwerp and Delft Technical University and was presented at the 2005 IAME conference
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  • Goulielmos , AM and Psifia. , M-E . 2006 . Variations in charter rates for a time series between 1971 & 2002: can we model them as an effective tool in shipping finance? . International Journal of Transport Economics , XXXIII ( 2 ) : 257 – 278 .
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  • GARCH is not appropriate if time series have a memory
  • Exponential GARCH
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  • The bias is created by investors in capital markets as they react in the current economic conditions until new information comes in and modifies the previous bias
  • This can be used to reveal periodic cycles by plotting log R/S to log n [82] (pp. 91–92). Vn , however, provides an easier way and gives a better estimate of the cycle length and is also more precise, even when noise is present. Hurst [80] used Vn to test the stability [82] (p. 92)
  • This means to divide the adjusted range by the local standard deviation. This was considered a master stroke [82] (p. 57). In simple language, rescaled range (R/S) is a name short for “range (R) divided by standard deviation (S)” [18] (p. 202). Dividing by standard deviation is described as normalizing, i.e., “volatility is normalized.” This gives another name of this method—the normalized volatility method
  • Between (R/S) n and there is a linear relationship of the classical form: Y = a + bX
  • Adjusted to a mean of zero and this is always non-negative
  • n is treated as a distance index or time index of time series
  • If , then observations are not identically and independently distributed. In the case of non-independent and non-identical observations, the present influences the future. Mathematically, this last relationship is expressed by: (*), where C is a correlation measure. If the system follows a random walk, then the correlation (C ) between present and future is zero, as there is no dependence between observations and the system is random. The method helps to see if an apparently random time series can be characterized by long-term memory. In fact, it is based on the range, which is rescaled by removing any trend (i.e., it is de-trended). (*) This measure is a correlation of the increments; it has been defined by [82] (pp. 184–185). It expresses the correlation of the changes in position of a process over time t with all increments of time t that precede and follow it
  • If the time series was increasing in the previous time period, it will keep increasing in the present and vice versa
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  • It is called an object in which the parts are in some way related to the whole, or the whole has self-similar components. If objects are solid and continuous, as in Euclidean plane geometry, they have integer dimension. A probability density function that is statistically self-similar is a fractal distribution. This means that in different increments of time, the statistical characteristics remain the same. The fractal market hypothesis is valid when many investors have different investment horizons and the information set, important to each investment horizon, is different. The market becomes unstable if all investors have the same information set [82] (p. 309)
  • It is such a system if it has a fractal dimension and exhibits sensitive dependence on initial conditions
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  • It shows the probability that two points are within a certain distance from one another
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  • (1) AR 1927, autoregressive process, a stationary stochastic process where the current value of a time series is related to the past p values (p = any integer). An AR (1) process has an infinite memory. (2) ARMA, autoregressive moving average process, a stationary stochastic process that can be a mixed model of AR and MA. MA, a stationary stochastic process in which the observed time series is the result of the MA of an unobserved random time series. (3) ARIMA, autoregressive integrated moving average process, a non-stationary stochastic process related to ARMA. (4) ARCH 1982, an AR with conditional heteroskedasticity, a non-linear stochastic process where the variance is time varying and conditional upon the past variance, with high peaks at the mean and fat tails. These are models for the analysis of the predictability of variance introduced by Engle, Bollerslev, Nelson, and others. (5) The GARCH 1986, as mentioned, means the generalized ARCH. It refers to a set of statistical tools to model data whose variability changes with time. The changes in variability are controlled by the data’s own past behavior and it has been generalized toaccommodate more circumstances as a further development of initial ARCH. (6) EGARCH 1991, exponential GARCH
  • This initially means that the error terms are not normal and independently distributed with expected mean 0 and variance equal to σ 2. We may symbolize this by: This is called “normality assumption” in the classical regression model [100] (p. 23). A second variant is This means that errors are not only iid, including the assumptions of (7), but also cover the further assumption that all characteristics of the error distributions are identical, including all moments (and not only Mean and Variance as in (7)). Random variables by satisfying (7) satisfy also (8). Independence here means zero covariance, but the reverse is not true, unless there is a multivariate normality. Two random variables with zero covariance are uncorrelated
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  • Details of the concepts of kurtosis and skewness are in the Appendix
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  • Indicates the amount by which a stock reacts to the market. Beta = 1 means the stock moves in lockstep with the market overall and so it does not magnify market risk
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  • Normal distribution or Gaussian distribution is a continuous probability one that describes data clustering around the mean
  • Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable. The coefficient of excess skewness is: (=0 for symmetry), where μ 3 is the third moment and μ 2 the second moment. If γ 1 > 0, the long tail is on the right of the distribution (positive skew), as here, like χ 2 distribution. First moment is the mean, second the variance, third skewness and fourth kurtosis
  • Kurtosis is a measure of the “peakedness” of the probability distribution of a real-valued random variable. The coefficient of excess kurtosis is: γ 2 = μ 4/ − 3 where μ’s are the second and fourth moment. If γ 2 ≤ 0 the distribution is platykurtic with fat in the center and being thinner in the tails than normal and if γ 2 ≥ 0 means leptokurtosis, i.e., thinner in the center and fatter tails, as in many occasions in shipping. Two kinds of excess kurtosis are shown (Appendix)
  • Standard and Poor’s 500 had a kurtosis of 43.36, 1970–2001; Nasdaq Index 5.78; French CAC-40 4.63, all > 3 [18] (p. 96)
  • A higher probability than a normally distributed variable with values near the mean
  • This is a new method. An investor decides first the level of certainty he/she wishes, say 95% probability for losses to be below the risk point [18]
  • Range = 89 842.5. Minimum = 6655. Maximum 96 497.5. Standard deviation = 16 552
  • At this point, we would like to note that when analyzing time series, it is necessary for the researcher to subtract the trend, and transform the series into a stationary, non-linear system. A stationary non-linear system is the one that is not subject to temporal dependence based on some outside influence. This process is produced by using “filters” that convert the time-series linearly. The method of first logarithmic difference is used here rather than other filters
  • Jarque, C. M. and Bera, A. K., 1980, Efficient tests for normality, homoscedasticity and serial independence of regression residuals. Economics Letters, 6(3), 255–259
  • Brock, W., Dechert, D., Scheinkman, J. and LeBaron, B., 1996, A test for Independence based on the correlation dimension. Econometric Reviews, 15(3), 197–235
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  • As in our sample
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  • This is the dimension of a system found by embedding as used in dynamic systems
  • If the process was anti-persistent ( ), the ratio would be decreasing as n values increase and the V-statistic plot will have a negative slope. Finally, if the system followed random walk (H = 0.5), and thus no correlation between observations existed, the ratio would be steadily increasing at the square root of time and its plot would be a horizontal line (time = number of observations, n)
  • Hampton, M. J., 1990, published in 1989, ‘Analysis and shipping cycles I and II’, Seatrade Journal, 19–23. Long and Short Shipping Cycles: The Rhythms and Psychology of Shipping Markets, Monograph, 2nd ed. (Cambridge: Cambridge Academy of Transport), March, p. 66
  • Goulielmos , AM . 2010 . What can we learn from 259 years of shipping cycles? . International Journal of Shipping and Transport Logistics , 2 ( 2 ) : 125 – 150 .

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