Shipping finance: time to follow a new track?

References and notes

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• The amount by which the stock reacts to the market
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• The measure of the peakedness of the probability density function (normality means alpha = 2)
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• This can be defined as equal to X(t) if X(t) is such that R/S∞d H . Mandelbrot (1983, p. 249) called this Hurst noise. Shown by Mandelbrot, B. B., 1983, The Fractal Geometry of Nature (New York: Freeman & Co.) that 0 ≤ H ≤ 1
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• This formula comes from Peters (ibid. 19, pp. 184–185). It expresses the correlation of changes at t with all increments of time t that precede and follow it
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• Hurst, instead of applying the statistical tool, called range directly (difference between the highest and lowest values) he adjusted the data to remove the trend for time intervals of varying length and the starting point. After that he computed the range, which should increase at square root of time (interval), but this strangely grew faster. Mandelbrot and Hudson (ibid. 12, p. 179) took that as a symptom of scaling → fractality. Then Mandelbrot placed this concept in the long dependence and extended it to the financial prices (Mandelbrot, B. B., 2002, Gaussian self-affinity and fractals: globality, the earth, 1/f Noise & R/S (New York: Springer Verlag). Fractal is a pattern or object whose parts echo the whole, only scaled down (Mandelbrot and Hudson, ibid. 12, p. 208
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• This is required for most econometric models function on the assumption that the generating process of time series is stationary
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• Some of the most commonly used ‘filters’ are the first differences of observations, their first logarithmic differences, their AR(1) residuals and a combination of them
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• Ibid. 19
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• Always the last value of the accumulated departures has to be equal to zero (0)
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• This called by Peters (ibid. 19) as a Master Stroke, making the time-series timeless and comparable along decades and centuries. This was one of his problems with the River Nile having 900 years of data
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• This is presented in Peters (ibid. 19, Chapter 5 and p. 71)
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• This equation however, due to Anis, A. A. and Lloyd, E. H., 1976, The expected value of the adjusted rescaled range of independent normal summands. BIOMETRIKA, 63, 111–116, had been rejected by Peters (ibid. 19, p. 69) who declared that this way of calculating the expected (R/S) n values cannot be used for large n values as the Γ factor values become too large
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• Anis and Lloyd (ibid. 68)
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• Siriopoulos and Leonditsis (ibid. 70, p. 15)
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• This reflects the volatilities of the market in comparison with time charter. But future research will be extended to time charter also
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• It must have a fractal dimension and must exhibit sensitive dependence on initial conditions. It is a deterministic nonlinear dynamic system that can produce random-looking results
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