Forecasting weekly freight rates for one-year time charter 65 000 dwt bulk carrier, 1989–2008, using nonlinear methods

Abstract

This paper forecast/predicted the one-year time charter weekly freight rates earned by a 65 000 dwt bulk carrier using 996 weeks of data from 1989 to 2008. First, the need and the importance, but also the futility, of forecasting is discussed in shipping. This is a volatile industry that can be easily likened to the roulette. The introduction is followed by a literature review that has examined the principal recent works in this area and presented a critique of earlier works. Most of the research studied dealt with the shipping industry per se. Since the methods used are considered as a departure from the classical Random Walk, a comprehensive section of the paper is devoted to the methodology of nonlinear, chaotic and deterministic methods. The relevant time series have been transformed into stationary ones, as this is the proper practice (using first logarithmic differences). The time series were tested for randomness (identically and independently distributed) and for long-term correlation using BDS statistic. The methods used were: Rescaled Range Analysis and the related Hurst Exponent; Power Spectrum Analysis; V-statistic and BDS Statistic (using software MATLAB 5.3 and NLTSA V.2.0/2000). The analysis of the data was presented in three separate sections. The relevant ‘attractor’ of the system has been graphically shown. System's dimension has been calculated, which was found to be non-integer, fractal and equal to 3.95. This finding permitted us to proceed to forecasting, as this is a case of a low dimensional chaos (3.95 < 10 dimensions). In order for the predictions to be robust, the prediction horizon allowed was found equal to 8.24 weeks, as indicated by the positive maximum Lyapunov exponent (0.12 rounded). Then NLTSA software was used to make prediction inside- and forecasting outside- the sample, using by selection nonlinear Principal Components and Kernel Density Estimation methods.