MARCIO VALK

In the field of Statistical Process Control (SPC) there are several different approaches to deal with monitoring of batch processes. Such processes present a three-way data structure (batches × variables × time-instants), so that for each batch a multivariate time series is available. Traditional approaches do not take into account the time series nature of the data. They deal with this kind of data by applying multivariate techniques in a reduced two-way data structure, in order to capture variables dynamics in some way. Recent developments in SPC have proposed the use of the Vector Autoregressive (VAR) time series model considering the original three-way structure. However, they are restricted to control approaches focused on VAR residuals. This paper proposes a new approach to deal with batch processes using the VAR model, but focusing on coefficients instead of residuals. Through a simulated batch process, we illustrate the better performance of our approach over the residual-based control charts in both offline and online context.

Discrimination and classification time series becomes almost indispensable since the large amountof information available nowadays. The problem of time series discrimination and classification isdiscussed in [1]. In this work the authors propose a novel clustering algorithm based on a class ofquasi U-statistics and subgroup decomposition tests. The decomposition may be applied to any con-cave time-series distance. The resulting test statistics is proved to be asymptotically normal for eitheri.i.d. or non-identically distributed groups of time-series under mild conditions. In practice thereare many time series that are correlated among themselves. An example that can describe this fact isthe financial markets globalization. When one of these markets is affected by an exogenous factor, achain reaction can affect many others. So the independence condition fail.We are interested in analyzing how the correlation among the groups of time series can affectclassification and clustering methods especially the one proposed by [1]. Empirical results show thatthe proposed method is robust to the presence of correlation among time series. The convergence ofthe test statistic for dependent time series will be one of the goals in this work.

References[1]

Valk, M., Pinheiro, A. 2012: Time-series clustering via quasi U-statistics,J. Time Ser. Anal.,Vol. 33, 4, 608 -619.