Bayesian Nonparametric Adaptive Spectral Density Estimation for Financial Time Series

Nick James; Roman Marchant; Richard Gerlach; Sally Cripps

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arXiv · 1902.03350

Bayesian Nonparametric Adaptive Spectral Density Estimation for Financial Time Series

Nick James·Roman Marchant·Richard Gerlach·Sally Cripps

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Abstract

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.

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q-fin.ST cs.LG stat.AP stat.ML

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BibTeX RIS

Nick James, Roman Marchant, Richard Gerlach, Sally Cripps. 2019-02-09. Bayesian Nonparametric Adaptive Spectral Density Estimation for Financial Time Series. https://arxiv.org/abs/1902.03350

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