Long Memory Time Series Modelling: Computational and Statistical Efficiency, Nonstationarity/Noninvertibility and Goodness of Fit

Texas A&M Research Foundation, College Station TX

Investigators

Abstract

In view of the rapid expansion of the application of long memory models and growing interest in high frequency data, the research plan of this project stresses both statistical and computational efficiency in modern long memory modelling. The goal is to develop statistically sound and computationally efficient methods for long memory time series in estimation and goodness-of-fit testing. To reach this goal, the investigator focuses on the three lines of research. The first line of research concerns the semiparametric estimation of memory parameter of nonstationary time series. Nonstationarity is a very common feature in economics, finance and network traffic data. Our goal is to develop estimators that allow nonstationarity in series and retain the same efficiency as the stationary case without compromising the computational efficiency. The second line of research focuses the estimation of a full parametric long memory model, namely ARFIMA which is potentially noninvertible. In practice, time series are often differenced one or more times to induce stationarity. Sometimes overdifferencing may occur. The investigator considers both frequency and time domains MLE and derives the asymptotic properties for them. The investigator also provides an efficient algorithm to evaluate the likelihood function so that the exact MLE can be applied on a large data set. The availability of high-frequency data on returns of financial assets has intrigued a great amount of research in volatility modelling. In the last line of research, the investigator extends a few statistical procedures which were previously developed for the linear processes to stochastic volatility models. The investigator proposes a class of goodness-of-fit tests for stochastic volatility models. These tests are periodogram-based statistics that not only circumvent the computation of fitted residuals but also can be evaluated via the fast Fourier transform algorithm. Furthermore, they are asymptotically normal under the null and consistent against a wide class of alternatives. Lastly, the investigator studies the relation between two or more long memory stochastic volatility series, a relationship called fractional cointegration. The investigator proposes an estimator for the cointegration parameter and derives its consistency. The investigator studies the finite sample properties of the proposed procedures through simulation studies. This research is motivated by the emerging trend to analyze high frequency time series including economic and financial data. The proposed methods not only provide practitioners feasible statistical procedures in modelling time dependent data across a number of disciplines, but also lead a direction of future research in time series toward computational efficiency. The up-to-date developments in the research plan will be modified and transform into the applied time series course for the new coming online graduate program which will be launched in year 2006 by the Department of Statistics for serving the higher education needs of professionals who work in industrial statistics, biostatistics and statistical teaching, including minorities, women and older students with families and full-time jobs. The programs can help students, especially those who might otherwise not be able to do so, achieve their goals of personal enrichment and career advancement.