Bayesian Nonparametric Adaptive Spectral Density Estimation for Financial Time Series
This addresses a long-standing issue in financial time series modeling for economists and analysts, but it is incremental as it builds on existing spectral and Bayesian techniques.
The paper tackled the problem of distinguishing non-stationarity and long-range dependency in financial time series by developing a Bayesian nonparametric adaptive spectral density estimation method, which performed well in simulations and identified both features in real financial data.
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.