DeepAI AI Chat
Log In Sign Up

Bayesian Nonparametric Adaptive Spectral Density Estimation for Financial Time Series

by   Nick James, et al.

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.


page 5

page 7


Optimally adaptive Bayesian spectral density estimation

This paper studies spectral density estimates obtained assuming a Gaussi...

Bayesian nonparametric spectral density estimation using B-spline priors

We present a new Bayesian nonparametric approach to estimating the spect...

Bayesian estimation of the autocovariance of a model error in time series

Autocovariance of the error term in a time series model plays a key role...

A general modelling framework for open wildlife populations based on the Polya Tree prior

Wildlife monitoring for open populations can be performed using a number...

Nonparametric Value-at-Risk via Sieve Estimation

Artificial Neural Networks (ANN) have been employed for a range of model...

Bayesian Characterizations of Properties of Stochastic Processes with Applications

In this article, we primarily propose a novel Bayesian characterization ...