Supervised Aggregative Feature Extraction for Big Data Time Series Regression

In many applications, and especially those where batch processes are involved, a target scalar output of interest is often dependent on one or more time series of data. With the exponential growth in data logging in modern industries such time series are increasingly available for statistical modeling in soft sensing applications. In order to exploit time series data for predictive modelling, it is necessary to summarise the information they contain as a set of features to use as model regressors. Typically this is done in an unsupervised fashion using simple techniques such as computing statistical moments, principal components or wavelet decompositions, often leading to significant information loss and hence suboptimal predictive models. In this paper, a functional learning paradigm is exploited in a supervised fashion to derive continuous, smooth estimates of time series data (yielding aggregated local information), while simultaneously estimating a continuous shape function yielding optimal predictions. The proposed Supervised Aggregative Feature Extraction (SAFE) methodology can be extended to support nonlinear predictive models by embedding the functional learning framework in a Reproducing Kernel Hilbert Spaces setting. SAFE has a number of attractive features including closed form solution and the ability to explicitly incorporate first and second order derivative information. Using simulation studies and a practical semiconductor manufacturing case study we highlight the strengths of the new methodology with respect to standard unsupervised feature extraction approaches.

Parallel Time Series Analysis and Income Inequality: A New Approach to Comparative Case Studies

This case study deals with the role of time series analysis in sociology, and its relationship with the wider literature and methodology of comparative case study research. Time series analysis is now well-represented in top-ranked sociology journals, often in the form of ‘pooled time series’ research designs. These studies typically pool multiple countries together into a pooled time series cross-section panel, in order to provide a larger sample for more robust and comprehensive analysis. This approach is well suited to exploring trans-national phenomena, and for elaborating useful macro-level theories specific to social structures, national policies, and long-term historical processes. It is less suited however, to understanding how these global social processes work in different countries. As such, the complexities of individual countries - which often display very different or contradictory dynamics than those suggested in pooled studies – are subsumed. Meanwhile, a robust literature on comparative case-based methods exists in the social sciences, where researchers focus on differences between cases, and the complex ways in which they co-evolve or diverge over time. A good example of this is the inequality literature, where although panel studies suggest a general trend of rising inequality driven by the weakening power of labour, marketisation of welfare, and the rising power of capital, some countries have still managed to remain resilient. This case study takes a closer look at what can be learned by applying the insights of case-based comparative research to the method of time series analysis. Taking international income inequality as its point of departure, it argues that we have much to learn about the viability of different combinations of policy options by examining how they work in different countries over time. By taking representative cases from different welfare systems (liberal, social democratic, corporatist, or antipodean), we can better sharpen our theories of how policies can be more specifically engineered to offset rising inequality. This involves a fundamental realignment of the strategy of time series analysis, grounding it instead in a qualitative appreciation of the historical context of cases, as a basis for comparing effects between different countries.