Time Series Analysis and Applications

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The focus of this research is on a number of topics relating to applications of time series analysis. The motivation for the first project is the analysis of DNA sequences. One important task is to translate the information stored in the protein-coding sequences (CDS) of the DNA. A common problem in analyzing long DNA sequence data is in identifying CDS that are dispersed throughout the sequence and separated by regions of noncoding. It is well known that DNA sequences are heterogeneous, and even within short subsequences of DNA, one encounters local behavior. In this proposal, the interest is in extending the spectral envelope methodology to capture the local behavior of such sequences. To address this problem of local behavior in categorical-valued time series, local spectral envelope with estimation via mixtures of smoothing splines will be explored. It is the hope that this methodology will help emphasize any periodic feature that exists in a categorical sequence of virtually any length in a quick and automated fashion. Projects such as the human genome project have produced large amounts of data. It is believed the methods will prove to be useful in the analysis of the vast quantities of data being produced by various genome projects. Another primary objective of this proposal is to explore spatio-temporal modeling by developing models similar to the STARMAX model. The goal is to develop a general methodology, but the research will be governed by obtaining solutions to difficult problems in biosurveillance, such as monitoring bioterrorism, and in medicine, such as the analysis of concurrent EEG-fMRI recordings. Although data is being collected in real-time by various organizations such as the CDC, data analytic tools that support both temporal and spatial data analysis and visualization are sorely lacking. At the present time, most analysis is accomplished by dropping (either by ignoring or by aggregating) either time or space. EEG has been a key tool in the study of the brain for decades. However, despite its multiple clinical and research uses, such as in epilepsy, little is yet known about the underlying generators of EEG activity in humans. Functional MRI (fMRI) recorded in concert with EEG may provide a method for localizing and identifying these sources. By using the EEG signal as a reference for fMRI maps, concurrent EEG-fMRI opens a new avenue for investigating specific brain function. The focus of this research is on a number of topics relating to applications of data collected in time, in space, or in sequence. The motivation for the first project is the analysis of DNA sequences. One important task is to translate the information stored in the protein-coding sequences of the DNA. Projects such as the human genome project have produced large amounts of data. It is believed the methods will prove to be useful in the analysis of the vast quantities of data being produced by various genome projects. Another primary objective of this proposal is to explore spatio-temporal modeling by developing new statistical models. The goal is to develop a general methodology, but the research will be governed by obtaining solutions to difficult problems in biosurveillance, such as monitoring bioterrorism, and in medicine, such as the analysis of concurrent EEG-fMRI recordings. Although data is being collected in real-time by various organizations such as the CDC, data analytic tools that support both temporal and spatial data analysis and visualization are sorely lacking. At the present time, most analysis is accomplished by dropping (either by ignoring or by aggregating) either time or space. EEG has been a key tool in the study of the brain for decades. However, despite its multiple clinical and research uses, such as in epilepsy, little is yet known about the underlying generators of EEG activity in humans. Functional MRI (fMRI) recorded in concert with EEG may provide a method for localizing and identifying these sources. By using the EEG signal as a reference for fMRI maps, concurrent EEG-fMRI opens a new avenue for investigating specific brain function.