Time Series Analysis: A New Look at Some Old Problems

This dissertation gives a comprehensive report of my doctoral research in time series analysis from summer 2006 to spring 2009. It is comprised of two main efforts: interval estimation for an autoregressive parameter and arc length tests for equivalent ARIMA dynamics. Such problems are traditional in statistics, but three new theorems and several simulations are presented here that help elucidate new ways to handle them

Using Arc Length to Cluster Financial Time Series According to Risk

This article investigates how arc length can be used to partition financial time series according to variability (risk). This technique is predicated on the idea that arc length is an index of volatility, and thus the end result is that safer stocks can be sorted from more risky ones. Performance of arc length is compared with squared returns and absolute returns, two commonly used measures for quantifying the variability of prices. An application involving 30 popular stocks is presented using Maharaj, k-means ++, and correlation-based clustering techniques