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

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


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.


Gaussian processes Time series prediction Housing price prediction Empirical kernels 



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).


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

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

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