preprints.org > social sciences > econometrics & statistics > doi: 10.20944/preprints201607.0004.v1

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 4 July 2016 / Approved: 4 July 2016 / Online: 4 July 2016 (09:57:31 CEST)

Using recent developments in econometrics and computational statistics we consider the estimation of the instantaneous rate of asset return process when the underlying Data Generating Mechanism (DGM) is an Ornstein-Uhlenbeck process, driven by fractional noise, and sampled at fixed intervals of length h. To address the problem we adopt throughout the paper an exact discretization approach. This enable us to exploit the fact that a flow sampling scheme arises naturally when observing the DGM. For, while the instantaneous rate of return process is unobservable at points in time, its time integral over successive observations is observable since it equals the increment of log-prices. Exact discretization delivers an ARIMA(1,1,1) model for log-prices with a fractional driving noise. Building on the resulting exact discretization formulae and covariance function, a new Markov Chain Monte Carlo (MCMC) scheme is proposed and we examine the properties of both the time and frequency domain likelihoods / posteriors through Monte Carlo. For the exact discrete model we adopt a general sampling interval of length h. This allow us to determine the optimal choice of h independent of the sample size. An empirical application using high frequency stock price data is presented showing the relevance of aggregation over time issues in modelling asset prices.

Bayesian modeling, long memory/anti-persistence; continuous time modeling; MCMC