Advertisement

Gaussian Process Kernels for Noisy Time Series: Application to Housing Price Prediction

  • Juntao Wang
  • Wun Kwan Yam
  • Kin Long Fong
  • Siew Ann Cheong
  • K. Y. Michael Wong
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11306)

Abstract

We study the prediction of time series using Gaussian processes as applied to realistic time series such as housing prices in Hong Kong. Since the performance of Gaussian processes prediction is strongly dependent on the functional form of the adopted kernel, we propose to determine the kernel based on the useful information extracted from the training data. However, the essential features of the time series are concealed by the presence of noises in the training data. By applying rolling linear regression, smooth and denoised time series of change rates of the data are obtained. Surprisingly, a periodic pattern emerges, enabling us to formulate an empirical kernel. We show that the empirical kernel performs better in predictions on quasi-periodic time series, compared to popular kernels such as spectral mixture, squared exponential, and rational quadratic kernels. We further justify the potential of the empirical kernel by applying it to predicting the yearly mean total sunspot number.

Keywords

Gaussian processes Time series prediction Housing price prediction Empirical kernels 

Notes

Acknowledgements

We thank Prof. Chihiro Shimizu for forwarding the data to us. This work is supported by the Research Grants Council of Hong Kong (grant numbers 16322616 and 16306817).

References

  1. 1.
    Rasmussen, C.E., Williams, C.K.: Gaussian Process for Machine Learning. MIT Press, Cambridge (2006)zbMATHGoogle Scholar
  2. 2.
    Wilson, A.G., Adams, R.P.: Gaussian process kernels for pattern discovery and extrapolation. In: Dasgupta, S., McAllester, D. (eds.) Proceedings of the 30th International Conference on Machine Learning. Proceedings of Machine Learning Research, vol. 28, pp. 1067–1075. PMLR, Atlanta (2013)Google Scholar
  3. 3.
    Brahim-Belhouari, S., Bermak, A.: Gaussian process for nonstationary time series prediction. Comput. Stat. Data Anal. 47(4), 705–712 (2004)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Lee, C.H.L., Liu, A., Chen, W.S.: Pattern discovery of fuzzy time series for financial prediction. IEEE Trans. Knowl. Data Eng. 18(5), 613–625 (2006)CrossRefGoogle Scholar
  5. 5.
    Kim, K.J.: Financial time series forecasting using support vector machines. Neurocomputing 55(1–2), 307–319 (2003)CrossRefGoogle Scholar
  6. 6.
    Cao, L.J., Tay, F.E.H.: Support vector machine with adaptive parameters in financial time series forecasting. IEEE Trans. Neural Netw. 14(6), 1506–1518 (2003)CrossRefGoogle Scholar
  7. 7.
    Kim, T.Y., Oh, K.J., Kim, C., Do, J.D.: Artificial neural networks for non-stationary time series. Neurocomputing 61, 439–447 (2004)CrossRefGoogle Scholar
  8. 8.
    Hamada, K., Kashyap, A.K., Weinstein, D.E.: Japan’s Bubble, Deflation, and Long-Term Stagnation. MIT Press, Cambridge (2011)Google Scholar
  9. 9.
    Tsay, R.S.: Analysis of Financial Time Series, vol. 543. Wiley, Hoboken (2005)CrossRefGoogle Scholar
  10. 10.
    Hui, E.C., Yue, S.: Housing price bubbles in Hong Kong, Beijing and Shanghai: a comparative study. J. Real Estate Finance Econ. 33(4), 299–327 (2006)CrossRefGoogle Scholar
  11. 11.
    Phillips, P.C., Shi, S., Yu, J.: Testing for multiple bubbles: historical episodes of exuberance and collapse in the S&P 500. Int. Econ. Rev. 56(4), 1043–1078 (2015)CrossRefGoogle Scholar
  12. 12.
    Yiu, M.S., Yu, J., Jin, L.: Detecting bubbles in Hong Kong residential property market. J. Asian Econ. 28, 115–124 (2013)CrossRefGoogle Scholar
  13. 13.
    Fletcher, R.: Practical Methods of Optimization. Wiley (2013)Google Scholar
  14. 14.
    MATLAB: Statistics and Machine Learning Toolbox Release 2017b. The MathWorks Inc., Natick (2017)Google Scholar
  15. 15.
    Hyndman, R.J.: Measuring forecast accuracy. In: Gilliland, M., Sglavo, U., Tashman, L. (eds.) Business Forecasting: Practical Problems and Solutions, pp. 177–184. Wiley (2015)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.The Hong Kong University of Science and TechnologyHong KongChina
  2. 2.Nanyang Technological UniversitySingaporeSingapore

Personalised recommendations