Time Series Analysis: Financial Engineering

Abstract: Time-series analysis is a statistical method of analyzing data from repeated observations on a single unit or individual at regular intervals over a large number of observations. Time-series analysis can be viewed as the exemplar of longitudinal designs. The most widely employed approach is based on the class of models known as Autoregressive Integrated Moving Average (ARIMA) models. ARIMA models can address several major classes of research questions, including an analysis of basic processes, intervention analysis, and analysis of the pattern of treatment effects over time. Technical aspects of ARIMA models are described, including definitions of important terms, statistical estimation of parameters, and the model identification process. Examples are employed to clarify the technical discussion. Recent extensions of ARIMA modeling techniques include multiunit time-series designs, multivariate time-series analysis, the inclusion of covariates, and the analysis of patterns of intra-individual differences across time.

Keywords: ARIMA models; autocorrelation; longitudinal designs; single-subject research; time-series analysis; within-subject research