Date of Award


Degree Name

Doctor of Philosophy


Computational Science


Maria C. Mariani


This work is devoted to the study of modeling high frequency time series including extreme fluctuations. As the high frequency data are collected at extremely fine scales, the fluctuations can capture the dynamics of data that evolve over time. A class of volatility models with time-varying parameters is used to forecast the volatility in a stationary condition at different lags. The modeling of stationary time series with consistent properties facilitates prediction with much certainty.

A large set of high frequency financial returns, closing prices of stock markets, high magnitudes of seismograms generated by the natural earthquakes, and the mining explosions is studied. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH), Asymmetric Power Autoregressive Conditional Heteroscedasticity (APARCH), and Stochastic Volatility (SV) models are used to predict the data volatility. The data involving statistical noise and inaccuracies are continuously changing over time. Thus a filtering technique is performed to estimate the time-varying parameters by minimizing their variance. It is shown that the stochastic volatility (SV) is a better forecasting tool than GARCH (1, 1) and APARCH models, since it is less conditioned by autoregressive past information. We forecast one-step-ahead log volatility that is able to detect the extreme fluctuations of high frequency data.

A new approach is proposed to simulate the special case of high frequency data that do not fit always with the SV model. As the data reflect stochastic nature of most measurements over time, a stochastic differential equation with Ornstein-Uhlenbeck process has been applied in this case. This analysis helps to achieve the higher accuracy and fidelity for estimating the time-varying parameters of data volatility via Maximum Likelihood Estimation.




Received from ProQuest

File Size

76 pages

File Format


Rights Holder

Md Al Masum Bhuiyan