| The availability of large data sets and powerful computing resources has made data analysis an increasingly viable approach to understanding random processes. Of particular interest are exploratory techniques which provide insight into the local path behavior of highly positively correlated processes. We focus on actual and simulated teletraffic data in the form of time series. Our foremost objective is to develop a methodology of identifying and classifying shape features which are essentially unrecognizable with standard statistical descriptors.;Using basic aspects of human vision as a heuristic guide, we have developed an algorithm which "sketches" data sequences. Our approach to summarizing path behavior is based on exploiting the simple structure of a sketch. We have developed a procedure whereby all the "shapes" of a sketch are summarized in a visually comprehensible manner. We do so by placing the shapes in classes, then displaying, for each class, both a representative shape and the number of shapes in the class. These "shape histograms" can provide substantial insight into the behavior of sample paths.;We have also used sketches to help model data sequences. The idea here is that a model based on a sketch of a data sequence may provide a better fit under some circumstances than a model based directly on the data. By considering various sketches, one could, for example, develop a Markov chain model whose autocorrelation function approximates that of the original data. We have generalized this use of sketches so that a data sequence can be modeled as the superposition of several sketches, each capturing a different level of detail.;Because the concept of path shape is highly visual, it is important that our techniques exploit the strengths of and accommodate for the weaknesses of human vision. We have addressed this by using computer graphics in a variety of novel ways. |
