Mathematical Sciences: New Directions in Time Series

Three research projects that explore some recent and innovative methodologies of active interest in time series analysis are investigated. The first focuses on the problem of obtaining robust recursive estimates for ARMA models, and will initially address a number of important issues that arise when redescending robust criteria are employed in the recursive procedure. In the second project, applications and finite sample properties associated with the spectral envelope methodology for analyzing categorical time series are investigated. The extension of this methodology to real-valued time series is also explored. The development and integration of exploratory time series analysis methods within the dynamic graphical environment is considered in the final project, and provides an effective means to perform the research involved in each project concurrently. The development of new procedures for analyzing time series data is an important and active area of research across a variety of disciplines. Typically, time series analysis is equated with data that is observed sequentially over time (eg. stock market prices, temperature), but in other disciplines 'time' may simply be a positional index that defines, for example, the order of the base-pair codings (a,t,g,c) in DNA sequences. In this project, three innovative approaches to time series analysis are investigated. The first concerns the problem of retaining the ability to obtain useful information about a time series process when aberrant observations may be present. The second approach deals with the concept of a 'spectral envelope' which provides an objective criterion for assessing periodic patterns in qualitative series such as DNA sequences. A large component of the research involved in both these approaches will be incorporated into the last project where the development of highly interactive exploratory graphical methods for time series analysis is pursued.