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Topics in univariate time series analysis with business applications
Recent technological advances in sensor and computer technology allow the observation of business and industrial processes at fairly high frequencies. For example, data used for monitoring critical parameters of industrial furnaces, conveyor belts or chemical processes may be sampled every minute or second. A high sampling rate is also possible in business related processes such as mail order distribution, fast food restaurant operations, and electronic commerce. Data obtained from frequently monitored business processes are likely to be autocorrelated time series that may or may not be stationary. If left alone, processes will typically not be stable, and hence they will usually not posses a fixed mean, thus exhibiting homogeneous non-stationarity. For monitoring, control, and forecasting purposes of such potentially non-stationary processes it is often important to develop an understanding of the dynamic properties of processes. However, it is sometimes difficult if not impossible to conduct deliberate experiments on full scale industrial plants or business processes to gain the necessary insight of their dynamic properties. Fortunately, intentional or inadvertent process changes that occur in the course of normal operation sometimes offer an opportunity to identify and estimate aspects of the dynamic behavior. To determine if a time series is stationary, the standard exploratory data analytic approach is to check that the sample autocorrelation function (ACF) fades out relatively quickly. An alternative, and at times a sounder approach is to use the variogram – a data exploratory tool widely used in spatial (geo) statistics for the investigation of spatial correlation of data. The first objective of this dissertation is to derive the basic properties of the variogram and to provide the literature on confidence intervals for the variogram. We then show how to use the multivariate Delta method to derive asymptotic confidence intervals for the variogram that are both practical and computationally appealing. The second objective of this dissertation is to review the theory of dynamic process modeling based on time series intervention analysis and to show how this theory can be used for an assessment of the dynamic properties of business and industrial processes. This is accompanied by a detailed example of the study of a large scale ceramic plant that was exposed to an intentional but unplanned structural change (a quasi experiment). The third objective of this dissertation concerns the analysis of multiple interventions. Multiple interventions occur either as a result of multiple changes made to the same process or because of a single change having non-homogeneous effects on time series. For evaluating the effects of undertaken structural changes, it is important to assess and compare the effects, such as gains or losses, of multiple interventions. A statistical hypothesis test for comparing the effects among multiple interventions on process dynamics is developed. Further, we investigate the statistical power of the suggested test and elucidate the results with examples.
Khachatryan, Davit, "Topics in univariate time series analysis with business applications" (2010). Doctoral Dissertations Available from Proquest. AAI3427545.