Abstract
The modeling of the dynamic relationship between the changes of the wind and the waveheight has been an important topic from various standpoints such as oceanography, technology and navigation safety. Generally, when we apply the standard statistical models for the waveheight prediction, the observation of wind direction has been treated as the ordinary time series data, not reflecting unique properties as directional data. In this article, we develop a time series model with linear and angular–linear variables, by extending the angular–linear regression model considered by Johnson and Wehrly. Our prediction test based on extrapolation suggested the possibility that the angular–linear time series structure gave positive effect on improving the prediction accuracy of the time series model, in which the original wind direction is included as a linear variable.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Athanassoulis G.A., Stefanakos C.N. (1995) A nonstationary stochastic model for long-term time series of significant wave height. Journal of Geophysical Research 100(C8): 16149–16162
Box, G. E. P., Jenkins, G. M. (1976). Time series analysis, forecasting and control (revised edition). San Francisco: Holden-Day
Brockwell P.J., Davis R.A. (1991) Time series: theory and methods. Springer, New York
Brockwell P.J., Davis R.A. (1996) Introduction to time series and forecasting. Springer, New York
Brown B.G., Katz R.W., Murphy A.H. (1984) Time series models to simulate and forecast wind speed and wind power. Journal of Climate and Applied Meteorology 23: 1184–1195
Cunha C., Guedes S.C. (1999) On the choice of data transformation for modelling time series of significant waveheight. Ocean Engineering 26: 489–506
Dahlhaus R. (1997) Fitting time series models to nonstationary process. Annals of Statistics 25(1): 1–37
Dahlhaus R., Giraitis L. (1998) On the optimal segment length for parameter estimates for locally stationary time series. Journal of Time Series Analysis 19(6): 629–655
Daniel A.R., Chen A.A. (1991) Stochastic simulation and forecasting of hourly average wind speed sequences in Jamaica. Sol Energy 46(1): 1–11
Fisher N.I. (1993) Statistical analysis of circular data. Cambridge University Press, Cambridge
Fisher N.I., Lee A.J. (1992) Regression models for an angular response. Biometrics 48: 665–677
Hokimoto T., Kimura N., Iwamori T., Amagai K., Huzii M. (2003) The effects of wind forcing on the dynamic spectrum in wave development: A statistical approach using a parametric model. Journal of Geophysical Research 108(C10): 5–1512
Jammalamadaka S.R., Lund U.J. (2006) The effect of wind direction on ozone levels: A case study. Environmental and Ecological Statistics 13: 287–298
Jammalamadaka S.R., SenGupta A. (2001) Topics in circular statistics. World Scientific, Singapore
Johnson R.A., Wehrly T.E. (1978) Some angular–linear distributions and related regression models. Journal of the American Statistical Association 73: 602–606
Kitagawa G., Gersch W. (1985) A smoothness priors time-varying AR coefficient modeling of nonstationary covariance time series. IEEE Transactions on Automatic Control 30: 48–56
Makridakis S., Andserson A., Carbobe R., Fildes R., Hibon M., Lewandowski R., Newton J., Parzen E., Winkler R. (1984) The forecasting accuracy of major time series methods. Wiley, New York
Mardia K.V., Jupp P.E. (2000) Directional statistics. Wiley, New York
SenGupta A. (2004) On the constructions of probability distributions for directional data. Bulletin of the Calcutta Mathematical Society. 96(2): 139–154
SenGupta A., Ugwuowo F.I. (2006) Asymmetric circular–linear mutilvariate regression models with application to environmental data. Environmental and Ecological Statistics. 13: 299–309
Stefanakos, C. N., Athanassoulis, G. A., Barstow, S. F. (2002). Mutivariate time series modelling of significant wave height. Proceedings of International Society of Offshore and Polar Engineers Conference, III, (pp 66–73).
Toll R.S.J. (1997) Autoregressive conditional heteroscedasticity in daily wind speed measurements. Theoretical and Applied Climatology. 56: 113–122
Walton, T. L., Borgman, L.E. (1990). Simulation of non-stationary, non-gaussian water levels on the great lakes. Journal of the ASCE, Waterway Port, Coastal, and Ocean Engineering Division. 116(6), 664–685
Yim, J.Z., Chou, C., Ho, P. (2002) A study on simulating the time series of siginificant wave height near the keelung harbor, Proceedings of International Society of Offshore and Polar Engineers Conference, III, pp. (92–96).
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Hokimoto, T., Shimizu, K. An angular–linear time series model for waveheight prediction. Ann Inst Stat Math 60, 781–800 (2008). https://doi.org/10.1007/s10463-008-0207-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10463-008-0207-z