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

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.