Advertisement

Markov-Switching Linked Autoregressive Model for Non-continuous Wind Direction Data

  • Xiaoping Zhan
  • Tiefeng Ma
  • Shuangzhe Liu
  • Kunio Shimizu
Article
  • 29 Downloads

Abstract

In this paper, a Markov-switching linked autoregressive model is proposed to describe and forecast non-continuous wind direction data. Due to the influence factors of geography and atmosphere, the distribution of wind direction is disjunct and multi-modal. Moreover, for a number of practical situations, wind direction is a time series and its dependence on time provides very important information for modeling. Our model takes these two points into account to give an accurate prediction of this kind of wind direction. A simulation study shows that our model has a significantly higher prediction accuracy and a smaller mean circular prediction error than three existing models and it is illustrated to be effective by analyzing real data. Supplementary materials accompanying this paper appear online.

Keywords

Circular regressive model Mean circular prediction error Non-continuous wind direction Prediction accuracy 

Notes

Acknowledgements

We would like to thank the Editors and Reviewers very much for their many valuable comments and advice which led to a significantly improved presentation of the manuscript. The research by the first two authors was supported by 111 Project (Grant No. B18062) and the National Natural Science Foundation of China (Nos. 11471264, 11401148, 11571282) and Fundamental Research Funds for the Central Universities (Nos. JBK120509, JBK140507).

Supplementary material

13253_2018_331_MOESM1_ESM.r (2 kb)
Supplementary material 1 (R 2 KB)
13253_2018_331_MOESM2_ESM.xlsx (2.4 mb)
Supplementary material 2 (xlsx 2467 KB)

References

  1. Abe, T., Ogata, H., Shiohama, T., Taniai, H., (2017). Circular autocorrelation of stationary circular Markov processes. Statistical Inference for Stochastic Processes 20(3): 275–290.MathSciNetCrossRefMATHGoogle Scholar
  2. Ailliot, P., Bessac, J., Monbet, V., Pène, F., (2015). Journal of Statistical Planning & Inference. Journal of Statistical Planning & Inference 160(1): 75–88.MathSciNetCrossRefMATHGoogle Scholar
  3. Ailliot, P., Monbet, V., (2012). Markov-switching autoregressive models for wind time series. Environmental Modelling & Software 30: 92–101.CrossRefGoogle Scholar
  4. Alizadeh, S.H., Rezakhah, S., (2014). Hidden Markov mixture autoregressive model: stability and moments. Communications in Statistics - Theory and Methods 42: 1087–1104.MathSciNetCrossRefMATHGoogle Scholar
  5. Artes, R., Toloi, C.M.C., (2010). An autoregressive model for time series of circular data. Communications in Statistics - Theory and Methods 39: 186–194.MathSciNetCrossRefMATHGoogle Scholar
  6. Augustyniak, M., (2014). Maximum likelihood estimation of the Markov-switching GARCH model. Computational Statistics & Data Analysis 76: 61–75.MathSciNetCrossRefGoogle Scholar
  7. Bauwens, L., Dufays, A., Rombouts, J.V.K., (2014). Marginal likelihood for Markov-switching and change-point GARCH models. Journal of Econometrics 178: 508–522.MathSciNetCrossRefMATHGoogle Scholar
  8. Bhattachary, S., SenGupta, A., (2009). Bayesian analysis of semiparametric linear-circular models. Journal of Agricultural, Biological, and Environmental Statistics 14(1): 33–65MathSciNetCrossRefMATHGoogle Scholar
  9. Breckling, J., (1989). Analysis of Directional Time Series: Application to Wind Speed and Direction. Lecture Notes in Statistics 61. Springer-Verlag, Berlin.Google Scholar
  10. Brunetti, C., Scotti, C., Mariano, R.S., Tan, A.H.H., (2008). Markov switching GARCH models of currency turmoil in Southeast Asia. Emerging Markets Review 9: 104–128.CrossRefGoogle Scholar
  11. Craig, P.S., (1988). Time Series Analysis for Directional Data. Thesis. Trinity College Dublin.Google Scholar
  12. Erdem, E., Shi, J., (2011). ARMA based on approaches for forecasting the tuple of wind speed and direction. Applied Energy 88: 1405–1414.CrossRefGoogle Scholar
  13. Finzi, G., Fronza, G., Rinaldi, S., (1978). Stochastic modelling and forecast of the dosage area product. Atmospheric Environment 12(4): 831–838.CrossRefGoogle Scholar
  14. Fisher, N.I., (1993). Statistical Analysis of Circular Data. Cambridge University Press: Cambridge.CrossRefMATHGoogle Scholar
  15. Fisher, N.I., Lee, A.J., (1994). Time series analysis of circular data. Journal of the Royal Statistical Society, Series B 56: 327–639.MathSciNetMATHGoogle Scholar
  16. Goldfeld, S.M., Quandt, R.E., (1970). A Markov model for switching regressions. Journal of Econometrics 1: 3–16.CrossRefMATHGoogle Scholar
  17. Hamilton, J.D., (1989). A new approach to the economic analysis of nonstationary time series and business cycle. Econometrica 57(2): 357–384.MathSciNetCrossRefMATHGoogle Scholar
  18. Hokimoto, T., Shimizu, K., (2014). A nonhomogeneous hidden Markov model for predicting the distribution of sea surface elevation, Journal of Applied Statistics 41(2): 294–319.MathSciNetCrossRefGoogle Scholar
  19. Holzmann, H., Munk, A., Suster, M., Zuccnini, W., (2006). Hidden Markov models for circular and linear-circular time series. Environmental and Ecological Statistics 13: 325–347.MathSciNetCrossRefGoogle Scholar
  20. Jammalamadaka, S.R., SenGupta, A., (2001). Topics in Circular Statistics. World Scientific: Singapore.CrossRefGoogle Scholar
  21. Ji, L., Tan, H.W., Wang, L., (2012). Wind direction modeling using Markov chain. Journal of Central South University Science and Technology 43(8): 3274–3279.Google Scholar
  22. Kato, S., (2010). A Markov process for circular data. Journal of the Royal Statistical Society, Series B 72: 655–672.MathSciNetCrossRefGoogle Scholar
  23. Kazor, K., Hering, A.S., (2015). Assessing the performance of model-based clustering methods in multivariate time series with application to identifying regional wind regimes.Journal of Agricultural, Biological, and Environmental Statistics 20(2): 192–217.MathSciNetCrossRefMATHGoogle Scholar
  24. Kim, S., SenGupta, A., (2013). A three-parameter generalized von Mises distribution. Statistical Papers 54(3): 685-693.MathSciNetCrossRefMATHGoogle Scholar
  25. Lagona, F., Picone, M., Maruotti, A., (2015). A hidden Markov model for the analysis of cylindrical time series. Environmetrics 26: 534–544.MathSciNetCrossRefGoogle Scholar
  26. Lee, A.J. (2010). Circular data. Wiley Interdisciplinary Reviews: Computational Statistics 2: 477–486.CrossRefGoogle Scholar
  27. Ley, C., Verdebout, T. (2017). Modern Directional Statistics. Chapman and Hall/CRC.Google Scholar
  28. Liu, S., Ma, T., SenGupta, A., Shimizu, K., Wang, M.Z., (2017). Influence diagnostics in possibly asymmetric circular-linear multivariate regression models, Sankhyā B: Indian Journal of Statistics. 79(1): 76–93.MathSciNetCrossRefMATHGoogle Scholar
  29. Mardia K.V., Jupp P.E., (2000). Directional Statistics. Wiley: Chichester, UK.MATHGoogle Scholar
  30. Maruotti, A., (2016). Analyzing longitudinal circular data by projected normal models, a semi-parametric approach based on finite mixture models. Environmental and Ecological Statistics 23(2): 257–277.MathSciNetCrossRefGoogle Scholar
  31. McMillan, N., Bortnick, S.M., Irwin, M.E., Berliner, L.M., (2005). A hierarchical Bayesian model to estimate and forecast ozone through space and time. Atmospheric Environment 39(8): 1373–1382.CrossRefGoogle Scholar
  32. Pewsey, A., Neuhäuser, M., Ruxton, G. D., (2013). Circular Statistics in R. Oxford: Oxford University Press.MATHGoogle Scholar
  33. Stephens, M. A., (1969). Techniques for directinal data. Technical Report, Department of Statistics, Stanford University, Stanford.Google Scholar
  34. Wehrly, T.E., Johnson, R.A., (1980). Bivariate models for dependence of angular observations and a related Markov process. Biometrika 67(1): 255–256.MathSciNetCrossRefMATHGoogle Scholar
  35. Zhan, X., Ma, T., Liu, S., Shimizu, K., (2017). On circular correlation for data on the torus. Statistical Papers,  https://doi.org/10.1007/s00362-017-0897-5.
  36. Zhang, J., Pu, J., (2002). A Bayesian approach for short-term transmission line thermal overload risk assessment. IEEE Transactions on Power Delivery 17: 770–778.CrossRefGoogle Scholar

Copyright information

© International Biometric Society 2018

Authors and Affiliations

  • Xiaoping Zhan
    • 1
  • Tiefeng Ma
    • 2
  • Shuangzhe Liu
    • 3
  • Kunio Shimizu
    • 4
  1. 1.Law SchoolSichuan UniversityChengduChina
  2. 2.Center of Statistical Research, School of StatisticsSouthwestern University of Finance and EconomicsChengduChina
  3. 3.Faculty of Education, Science, Technology and MathematicsUniversity of CanberraCanberraAustralia
  4. 4.School of Statistical ThinkingThe Institute of Statistical MathematicsTokyoJapan

Personalised recommendations