Outliers in dynamic factor models

Dynamic factor models have a wide range of applications in econometrics and applied economics. The basic motivation resides in their capability of reducing a large set of time series to only few indicators (factors). If the number of time series is large compared to the available number of observations then most information may be conveyed to the factors. This way low dimension models may be estimated for explaining and forecasting one or more time series of interest. It is desirable that outlier free time series be available for estimation. In practice, outlying observations are likely to arise at unknown dates due, for instance, to external unusual events or gross data entry errors. Several methods for outlier detection in time series are available. Most methods, however, apply to univariate time series while even methods designed for handling the multivariate framework do not include dynamic factor models explicitly. A method for discovering outliers occurrences in a dynamic factor model is introduced that is based on linear transforms of the observed data. Some strategies to separate outliers that add to the model and outliers within the common component are discussed. Applications to simulated and real data sets are presented to check the effectiveness of the proposed method.Comment: Published in at http://dx.doi.org/10.1214/07-EJS082 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Fuzzy clustering of univariate and multivariate time series by genetic multiobjective optimization

COMISEF Working Papers Series WPS-028 08/02/2010 URL: http://comisef.eu/files/wps028.pd

General local search methods in time series

In time series problems often arise that involve large discrete solution spaces. It may happen that either searching such spaces cannot be accomplished by exhaustive enumeration or satisfactory methods do not exist which are able to yield the optimal solution for problems of moderate and large size. For instance, some nonlinear model parameter estimation, subset autoregression (possibly including moving average terms), outlier identification, clustering time series are all tasks that require the right combination of several parameters to be discovered. General local search methods, also called metaheuristics, or general heuristics, proved to be able to offer useful procedures that may solve such combinatorial-like problems in reasonable computing time. We consider the three most popular general local search methods, that is simulated annealing, tabu search and genetic algorithms. Their increasingly wide application in several fields, including many ”classical” problem (graph coloring, vehicle routing and salesman traveling, for instance), prompted the use of such methods in statistics and, in particular, in time series analysis. Examples of procedures will be discussed, and some comparisons between metaheuristics and well established techniques will be presented. Then, suggestions for future developments will be briefly outlined which include, for instance, filter design and wavelet filtering, outlier detection in vector time series, and threshold autoregressive moving average models