2019/02/09 by Nick James, James, Nick, Román Marchant +5
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #Applications (stat.AP) #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #FOS: Economics and business #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Finance (q-fin.ST) #Stock Market Forecasting Methods #Time Series Analysis and Forecasting
paper · pdf · doi:10.48550/arxiv.1902.03350
openalex publication_date 2019/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and dependency of financial time series in a non-parametric fashion assuming that the time series consists of a finite, but unknown number, of locally stationary processes, the locations of which are also unknown. The model allows a non-parametric estimate of the dependency structure by modelling the auto-covariance function in the spectral domain. All our estimates are made within a Bayesian framework where we use aReversible Jump Markov Chain Monte Carlo algorithm for inference. We study the frequentist properties of our estimates via a simulation study, and present a novel way of generating time series data from a nonparametric spectrum. Results indicate that our techniques perform well across a range of data generating processes. We apply our method to a number of real examples and our results indicate that several financial time series exhibit both long-range dependency and non-stationarity.