ARFIMA modeling of financial assets volatility.

摘要

In the dissertation we investigate how asset volatility can be modeled with the stationary ARFIMA model. The investigation is done using volatility estimates of S&P500 index and futures returns. Our analysis reveals presence of long memory in the return volatility, which provides ground for modeling volatility with the ARFIMA model. Model selection, model estimation, convergence measure and model checking are discussed. We find that ARFIMA(1,d,1) model successfully captures the correlation structure of the volatility data.; In the dissertation we also develop computational techniques and statistical procedures that can be applied while modeling with ARFIMA. In particular, we consider two problems: estimation of the ARFIMA model and unit root testing procedures.; Our Bayesian estimation procedure for the ARFIMA model is based on an approximation to the likelihood function. Bayesian analysis of the likelihood is performed with Monte Carlo Markov Chain sampling. The procedure allows simultaneous parameter estimation and can be applied to large time series.; The second econometric issue we consider in the thesis is unit root testing procedures. Using the maximal invariant principle, we derive two ratio tests: a locally best invariant test and a point optimal test. The point optimal test is characterized as being the most powerful invariant for a sharp stationary alternative. Monte Carlo study shows that the test achieves higher power than the Dickey-Fuller test.