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6. Outliers in dynamic factor models

Author

Baragona, Roberto and Battaglia, Francesco

Subjects
Mathematics - Statistics Theory, 62M10, 62H25 (Primary) 62P20 (Secondary)
Abstract

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)

Published
2007
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7. Outliers in Time Series: An Empirical Likelihood Approach

Author

Baragona, Roberto, Cucina, Domenico, Vichi, Maurizio, Editor-in-chief, French Statistical Society (SFdS), Series editor, Italian Statistical Society (SIS), Series editor, Portugese Statistical Society (SPE), Series editor, Spanisch Statistical Society (SEIO), Series editor, Di Battista, Tonio, editor, Moreno, Elías, editor, and Racugno, Walter, editor

Published
2016
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10. Cluster Analysis

Author

Baragona, Roberto, Battaglia, Francesco, Poli, Irene, Baragona, Roberto, Battaglia, Francesco, and Poli, Irene

Published
2011
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11. Outliers

Author

Baragona, Roberto, Battaglia, Francesco, Poli, Irene, Baragona, Roberto, Battaglia, Francesco, and Poli, Irene

Published
2011
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15. Introduction

Author

Baragona, Roberto, Battaglia, Francesco, Poli, Irene, Baragona, Roberto, Battaglia, Francesco, and Poli, Irene

Published
2011
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19. Clusters of Multivariate Stationary Time Series by Differential Evolution and Autoregressive Distance

Author

Baragona, Roberto, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Kuznetsov, Sergei O., editor, Mandal, Deba P., editor, Kundu, Malay K., editor, and Pal, Sankar K., editor

Published
2011
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22. Genetic Algorithms-based Approaches for Clustering Time Series

Author

Baragona, Roberto, Vitrano, Salvatore, Bock, H. -H., editor, Gaul, W., editor, Vichi, M., editor, Arabie, Ph., editor, Baier, D., editor, Critchley, F., editor, Decker, R., editor, Diday, E., editor, Greenacre, M., editor, Lauro, C., editor, Meulman, J., editor, Monari, P., editor, Nishisato, S., editor, Ohsumi, N., editor, Opitz, O., editor, Ritter, G., editor, Schader, M., editor, Weihs, C., editor, Zani, Sergio, editor, Cerioli, Andrea, editor, Riani, Marco, editor, and Vichi, Maurizio, editor

Published
2006
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33. Introduction

Author

Baragona, Roberto, primary, Battaglia, Francesco, additional, and Poli, Irene, additional

Published
2010
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36. Outliers

Author

Baragona, Roberto, primary, Battaglia, Francesco, additional, and Poli, Irene, additional

Published
2010
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42. Periodic autoregressive models for time series with integrated seasonality.

Author

Baragona, Roberto, Battaglia, Francesco, and Cucina, Domenico

Subjects
*AUTOREGRESSIVE models, *ANALYSIS of variance, *TIME series analysis, *AUTOREGRESSION (Statistics)
Abstract

A comprehensive seasonally integrated periodic autoregressive model is suggested which is shown to be flexible enough to include both the stochastic seasonal integrated and random trigonometric polynomial-based models. The demonstration of the equivalence between the two approaches is the objective of two theorems that are stated and proved in some details. A nice advantage of our model building procedure is that it is able to provide the user not only with a detailed model for data description and forecasting purpose but in addition with a hint at the presence of seasonal unit roots. The model which is illustrated in the present paper may be considered parsimonious, i.e. the number of estimated parameters, for a given goodness-of-fit criterion, is taken as low as possible, in two ways. First, by imposing unit roots and seasonal unit roots so that some estimated parameters are replaced by a differencing operator with fixed coefficients, and, second, by adopting a subset periodic autoregressive model, so that some parameters do not need to be estimated as they are constrained to equal zero. The effectiveness of our model is highlighted by an extensive simulation experiment that supports our claim that the model building procedure described here may be of good use as well for checking the existence of seasonal unit roots. Applications to real-world time series data sets are reported, and promising results are obtained that allow us to suggest that the seasonally integrated periodic autoregressive model may be safely used for modelling a wide range of seasonal time series data. In addition, well-known widely used tests, such as HEGY and the Taylor variance ratio test, are shown to provide us with results that generally agree with our findings. [ABSTRACT FROM AUTHOR]

Published
2021
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43. Empirical likelihood for outlier detection and estimation in autoregressive time series

Author

Baragona Roberto, Battaglia Francesco, Cucina Domenico, Baragona, Roberto, Battaglia, Francesco, and Cucina, Domenico

Subjects
General estimating equation, Statistics and Probability, Innovation outlier, Applied Mathematics, Confidence regions, Statistics, confidence regions, hypothesis testing, additive outlier, innovation outlier, general estimating equations, ComputingMethodologies_PATTERNRECOGNITION, Hypothesis testing, Confidence region, General estimating equations, Additive outlier, Statistics, Probability and Uncertainty, Probability and Uncertainty, Statistic
Abstract

Identification and estimation of outliers in time series is proposed by using empirical likelihood methods. Theory and applications are developed for stationary autoregressive models with outliers distinguished in the usual additive and innovation types. Some other useful outlier types are considered as well. A simulation experiment is used for studying the behaviour of the empirical likelihood-based method in finite samples and indicates that the proposed methods are preferable when dealing with the non-Gaussian data. Our simulations suggest that the usual sequential procedure for multiple outlier detection is suitable also for the methods based on empirical likelihood.

Published
2016

45. Double threshold autoregressive conditionally heteroscedastic model building by genetic algorithms

Author

Baragona, Roberto, Cucina, Domenico, Baragona, Roberto, and Cucina, Domenico

Subjects
Statistics and Probability, Heteroscedasticity, autoregressive conditional heteroscedasticity, double-threshold autoregression, genetic algorithms, nonlinear time series models, Applied Mathematics, Double threshold, Brute-force search, Heteroscedastic model, Weighted least squares algorithm, Nonlinear system, Autoregressive model, Modeling and Simulation, Statistics, genetic algorithm, Applied mathematics, Statistics, Probability and Uncertainty, Volatility (finance), Mathematics
Abstract

Asymmetric behaviour in both mean and variance is often observed in real time series. The approach we adopt is based on double threshold autoregressive conditionally heteroscedastic (DTARCH) model with normal innovations. This model allows threshold nonlinearity in mean and volatility to be modelled as a result of the impact of lagged changes in assets and squared shocks, respectively. A methodology for building DTARCH models is proposed based on genetic algorithms (GAs). The most important structural parameters, that is regimes and thresholds, are searched for by GAs, while the remaining structural parameters, that is the delay parameters and models orders, vary in some pre-specified intervals and are determined using exhaustive search and an Asymptotic Information Criterion (AIC) like criterion. For each structural parameters trial set, a DTARCH model is fitted that maximizes the (penalized) likelihood (AIC criterion). For this purpose the iteratively weighted least squares algorithm is used. Then the best model according to the AIC criterion is chosen. Extension to the double threshold generalized ARCH (DTGARCH) model is also considered. The proposed methodology is checked using both simulated and market index data. Our findings show that our GAs-based procedure yields results that comparable to that reported in the literature and concerned with real time series. As far as artificial time series are considered, the proposed procedure seems to be able to fit the data quite well. In particular, a comparison is performed between the present procedure and the method proposed by Tsay [Tsay, R.S., 1989, Testing and modeling threshold autoregressive processes. Journal of the American Statistical Association, Theory and Methods, 84, 231-240.] for estimating the delay parameter. The former almost always yields better results than the latter. However, adopting Tsay's procedure as a preliminary stage for finding the appropriate delay parameter may save computational time specially if the delay parameter may vary in a large interval.

Published
2008

49. Portmanteau tests based on quadratic forms in the autocorrelations.

Author

Baragona, Roberto, Battaglia, Francesco, and Cucina, Domenico

Subjects
*QUADRATIC forms, *AUTOCORRELATION (Statistics), *LAPLACE distribution, *LINEAR statistical models, *RANDOM variables
Abstract

Many white noise and goodness-of-fit tests are (asymptotically) written as quadratic forms in the ordinary autocorrelation estimates. The properties of such tests are studied by investigating the structure of the matrix of the quadratic form. We suggest to choose the matrix of the quadratic form in such a way that the power is maximized according to the information available about the alternative hypothesis. A simulation study sheds some light on the behavior of the test in finite samples. It is generally found more powerful than the most popular portmanteau tests, i.e., the Box and Pierce and the Ljung and Box tests. [ABSTRACT FROM AUTHOR]

Published
2018
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