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

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.

[1]  Alexander M. Goulielmos.  Risk analysis of the Aframax freight market and of its new building and second hand prices, 1976-2008 and 1984-2008 , 2009 .

[2]  Chi K. Tse,et al.  Reconstruction of Chaotic Signals with Applications to Chaos-Based Communications , 2008 .

[3]  A. Goulielmos,et al.  Do Nonlinear Tools Make a Difference in Handling Shipping Derivatives , 2008 .

[4]  Alexandros M. Goulielmos,et al.  A study of trip and time charter freight rate indices: 1968–2003 , 2007 .

[5]  C. Peretti.  Long Memory and Hysteresis , 2007 .

[6]  Alexandros M. Goulielmos,et al.  Shipping finance: time to follow a new track? , 2006 .

[7]  Alexander M. Goulielmos,et al.  Determining the Duration of Cycles in the Market of Second-Hand Tanker Ships, 1976-2001: is Prediction Possible? , 2006, Int. J. Bifurc. Chaos.

[8]  Alexandros M. Goulielmos,et al.  Variations in Charter Rates for a Time Series Between 1971 and 2002: Can We Model Them as an Effective Tool in Shipping Finance? , 2006 .

[9]  Steve Engelen,et al.  Using system dynamics in maritime economics: an endogenous decision model for shipowners in the dry bulk sector , 2006 .

[10]  R. Cont.  Volatility Clustering in Financial Markets: Empirical Facts and Agent-Based Models. , 2005 .

[11]  M. Small.  Applied Nonlinear Time Series Analysis: Applications in Physics, Physiology and Finance , 2005 .

[12]  A. Einstein.  Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen [AdP 17, 549 (1905)] , 2005, Annalen der Physik.

[13]  P. Campbell.  The (mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward/Fractals and Scaling in Finance: Discontinuity, Concentration, Risk/Yale Alumni Magazine , 2005 .

[14]  Richard L. Hudson,et al.  The Misbehavior of Markets: A Fractal View of Risk, Ruin, and Reward , 2004 .

[15]  Alexandros M. Goulielmos.  A treatise of randomness tested also in marine accidents , 2004 .

[16]  Dimitrios V. Lyridis,et al.  Forecasting Tanker Market Using Artificial Neural Networks , 2004 .

[17]  Steffen Bayer,et al.  Business dynamics: Systems thinking and modeling for a complex world , 2004 .

[18]  William H. Press,et al.  Numerical recipes in C , 2002 .

[19]  John D. Sterman,et al.  System Dynamics: Systems Thinking and Modeling for a Complex World , 2002 .

[20]  Willi-Hans Steeb,et al.  The Nonlinear Workbook , 2005 .

[21]  Ludwig Kanzler,et al.  Very Fast and Correctly Sized Estimation of the Bds Statistic , 1999 .

[22]  O. Lingjærde,et al.  Regularized local linear prediction of chaotic time series , 1998 .

[23]  R. Shanmugam.  Introduction to Time Series and Forecasting , 1997 .

[24]  Walter C. Labys,et al.  Fractional dynamics in international commodity prices , 1997 .

[25]  Michael G. Parsons,et al.  Forecasting tanker freight rate using neural networks , 1997 .

[26]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[27]  Richard A. Davis,et al.  Introduction to time series and forecasting , 1998 .

[28]  Richard T. Baillie,et al.  Long memory processes and fractional integration in econometrics , 1996 .

[29]  Dimitris Kugiumtzis,et al.  Chaotic time series. Part II. System Identification and Prediction , 1994, chao-dyn/9401003.

[30]  N. Christophersen,et al.  Chaotic time series , 1995 .

[31]  Edgar E. Peters.  Fractal Market Analysis: Applying Chaos Theory to Investment and Economics , 1994 .

[32]  L. Tsimring,et al.  The analysis of observed chaotic data in physical systems , 1993 .

[33]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[34]  George Sugihara,et al.  Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series , 1990, Nature.

[35]  H. Abarbanel,et al.  Prediction in chaotic nonlinear systems: Methods for time series with broadband Fourier spectra. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[36]  A. Lo.  Long-Term Memory in Stock Market Prices , 1989 .

[37]  Farmer,et al.  Predicting chaotic time series. , 1987, Physical review letters.

[38]  G. P. King,et al.  Extracting qualitative dynamics from experimental data , 1986 .

[39]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[40]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[41]  C. Jarque,et al.  An efficient large-sample test for normality of observations and regression residuals , 1981 .

[42]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[43]  C. Granger,et al.  AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING , 1980 .

[44]  W. Fuller,et al.  Distribution of the Estimators for Autoregressive Time Series with a Unit Root , 1979 .

[45]  G. Box,et al.  On a measure of lack of fit in time series models , 1978 .

[46]  M. T. Greene,et al.  Long-term dependence in common stock returns , 1977 .

[47]  B. Mandelbrot.  Statistical Methodology for Nonperiodic Cycles: From the Covariance To R/S Analysis , 1972 .

[48]  G. Box,et al.  Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models , 1970 .

[49]  J. R. Wallis,et al.  Some long‐run properties of geophysical records , 1969 .

[50]  S. Smale.  Diffeomorphisms with Many Periodic Points , 1965 .

[51]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[52]  H. E. Hurst,et al.  Long-Term Storage Capacity of Reservoirs , 1951 .

[53]  G. Yule.  On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers , 1927 .