Publications of Dr. Manuel Rizzo

2020 [ nach oben ]

Battaglia, Francesco; Cucina, Domenico; Rizzo, Manuel Parsimonious periodic autoregressive models for time series with evolving trend and seasonalityStatistics and Computing 2020: 77–91
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This paper proposes an extension of Periodic AutoRegressive (PAR) modelling for time series with evolving features. The large scale of modern datasets, in fact, implies that the time span may subtend several evolving patterns of the underlying series, affecting also seasonality. The proposed model allows several regimes in time and a possibly different PAR process with a trend term in each regime. The means, autocorrelations and residual variances may change both with the regime and the season, resulting in a very large number of parameters. Therefore as a second step we propose a grouping procedure on the PAR parameters, in order to obtain a more parsimonious and concise model. The model selection procedure is a complex combinatorial problem, and it is solved basing on Genetic Algorithms that optimize an information criterion. The model is tested in both simulation studies and real data analysis from different fields, proving to be effective for a wide range of series with evolving features, and competitive with respect to more specific models.
@article{battaglia2019parsimonious, abstract = {This paper proposes an extension of Periodic AutoRegressive (PAR) modelling for time series with evolving features. The large scale of modern datasets, in fact, implies that the time span may subtend several evolving patterns of the underlying series, affecting also seasonality. The proposed model allows several regimes in time and a possibly different PAR process with a trend term in each regime. The means, autocorrelations and residual variances may change both with the regime and the season, resulting in a very large number of parameters. Therefore as a second step we propose a grouping procedure on the PAR parameters, in order to obtain a more parsimonious and concise model. The model selection procedure is a complex combinatorial problem, and it is solved basing on Genetic Algorithms that optimize an information criterion. The model is tested in both simulation studies and real data analysis from different fields, proving to be effective for a wide range of series with evolving features, and competitive with respect to more specific models.}, author = {Battaglia, Francesco and Cucina, Domenico and Rizzo, Manuel}, journal = {Statistics and Computing}, keywords = {sys:relevantfor:ae domenicocucina francescobattaglia manuelrizzo sc year2020}, pages = {77-91}, title = {Parsimonious periodic autoregressive models for time series with evolving trend and seasonality}, volume = 30, year = 2020 }

Friedrich, Tobias; Krejca, Martin S.; Lagodzinski, J. A. Gregor; Rizzo, Manuel; Zahn, Arthur Memetic Genetic Algorithms for Time Series Compression by Piecewise Linear ApproximationInternational Conference on Neural Information Processing (ICONIP) 2020: 592–604
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Time series are sequences of data indexed by time. Such data are collected in various domains, often in massive amounts, such that storing them proves challenging. Thus, time series are commonly stored in a compressed format. An important compression approach is piecewise linear approximation (PLA), which only keeps a small set of time points and interpolates the remainder linearly. Picking a subset of time points such that the PLA minimizes the mean squared error to the original time series is a challenging task, naturally lending itself to heuristics. We propose the piecewise linear approximation genetic algorithm (PLA-GA) for compressing time series by PLA. The PLA-GA is a memetic \((\mu + \lambda)\) GA that makes use of two distinct operators tailored to time series compression. First, we add special individuals to the initial population that are derived using established PLA heuristics. Second, we propose a novel local search operator that greedily improves a compressed time series. We compare the PLA-GA empirically with existing evolutionary approaches and with a deterministic PLA algorithm, known as Bellman's algorithm, that is optimal for the restricted setting of sampling. In both cases, the PLA-GA approximates the original time series better and quicker. Further, it drastically outperforms Bellman's algorithm with increasing instance size with respect to run time until finding a solution of equal or better quality -- we observe speed-up factors between 7 and 100 for instances of 90,000 to 100,000 data points.
@inproceedings{friedrich2020memetic, abstract = {Time series are sequences of data indexed by time. Such data are collected in various domains, often in massive amounts, such that storing them proves challenging. Thus, time series are commonly stored in a compressed format. An important compression approach is piecewise linear approximation (PLA), which only keeps a small set of time points and interpolates the remainder linearly. Picking a subset of time points such that the PLA minimizes the mean squared error to the original time series is a challenging task, naturally lending itself to heuristics. We propose the piecewise linear approximation genetic algorithm (PLA-GA) for compressing time series by PLA. The PLA-GA is a memetic \((\mu + \lambda)\) GA that makes use of two distinct operators tailored to time series compression. First, we add special individuals to the initial population that are derived using established PLA heuristics. Second, we propose a novel local search operator that greedily improves a compressed time series. We compare the PLA-GA empirically with existing evolutionary approaches and with a deterministic PLA algorithm, known as Bellman's algorithm, that is optimal for the restricted setting of sampling. In both cases, the PLA-GA approximates the original time series better and quicker. Further, it drastically outperforms Bellman's algorithm with increasing instance size with respect to run time until finding a solution of equal or better quality – we observe speed-up factors between 7 and 100 for instances of 90,000 to 100,000 data points.}, author = {Friedrich, Tobias and Krejca, Martin S. and Lagodzinski, J. A. Gregor and Rizzo, Manuel and Zahn, Arthur}, booktitle = {International Conference on Neural Information Processing (ICONIP)}, keywords = {arthurzahn gregorlagodzinski iconip manuelrizzo martinskrejca tobiasfriedrich year2020}, pages = {592-604}, title = {Memetic Genetic Algorithms for Time Series Compression by Piecewise Linear Approximation}, volume = 12534, year = 2020 }

2019 [ nach oben ]

Battaglia, Francesco; Cucina, Domenico; Rizzo, Manuel Detection and estimation of additive outliers in seasonal time seriesComputational Statistics 2019: 1–17
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The detection of outliers in a time series is an important issue because their presence may have serious negative effects on the analysis in many different ways. Moreover the presence of a complex seasonal pattern in the series could affect the properties of the usual outlier detection procedures. Therefore modelling the appropriate form of seasonality is a very important step when outliers are present in a seasonal time series. In this paper we present some procedures for detection and estimation of additive outliers when parametric seasonal models, in particular periodic autoregressive, are specified to fit the data. A simulation study is presented to evaluate the benefits and the drawbacks of the proposed procedure on a selection of seasonal time series. An application to three real time series is also examined.
@article{noauthororeditor, abstract = {The detection of outliers in a time series is an important issue because their presence may have serious negative effects on the analysis in many different ways. Moreover the presence of a complex seasonal pattern in the series could affect the properties of the usual outlier detection procedures. Therefore modelling the appropriate form of seasonality is a very important step when outliers are present in a seasonal time series. In this paper we present some procedures for detection and estimation of additive outliers when parametric seasonal models, in particular periodic autoregressive, are specified to fit the data. A simulation study is presented to evaluate the benefits and the drawbacks of the proposed procedure on a selection of seasonal time series. An application to three real time series is also examined.}, author = {Battaglia, Francesco and Cucina, Domenico and Rizzo, Manuel}, journal = {Computational Statistics}, keywords = {domenicocucina francescobattaglia manuelrizzo myown year2019}, pages = {1-17}, title = {Detection and estimation of additive outliers in seasonal time series}, year = 2019 }

Cucina, Domenico; Rizzo, Manuel; Ursu, Eugen Multiple changepoint detection for periodic autoregressive models with an application to river flow analysisStochastic Environmental Research and Risk Assessment 2019: 1137–1157
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River flow data are usually subject to several sources of discontinuity and inhomogeneity. An example is seasonality, because climatic oscillations occurring on inter-annual timescale have an obvious impact on the river flow. Further sources of alteration can be caused by changes in reservoir management, instrumentation or even unexpected shifts in climatic conditions. When such changes are ignored the results of a statistical analysis can be strongly misleading, so flexible procedures are needed for building the appropriate models, which may be very complex. This paper develops an automatic procedure to estimate the number and locations of changepoints in Periodic AutoRegressive (PAR) models, which have been extensively used to account for seasonality in hydrology. We aim at filling the literature gap on multiple changepoint detection by allowing several time segments to be detected, inside of which a different PAR structure is specified, with the resulting model being employed to successfully capture the discontinuities of river flow data. The model estimation is performed by optimization of an objective function based on an information criterion using genetic algorithms. The proposed methodology is evaluated by means of simulation studies and it is then employed in the analysis of two river flows: the South Saskatchewan, measured at Saskatoon, Canada, and the Colorado, measured at Lees Ferry, Arizona. For these river flows we build changepoint models, discussing the possible events that caused discontinuity, and evaluate their forecasting accuracy. Comparisons with the literature on river flow analysis and on existing methods for changepoint detection confirm the efficiency of our proposal.
@article{cucina2019multiple, abstract = {River flow data are usually subject to several sources of discontinuity and inhomogeneity. An example is seasonality, because climatic oscillations occurring on inter-annual timescale have an obvious impact on the river flow. Further sources of alteration can be caused by changes in reservoir management, instrumentation or even unexpected shifts in climatic conditions. When such changes are ignored the results of a statistical analysis can be strongly misleading, so flexible procedures are needed for building the appropriate models, which may be very complex. This paper develops an automatic procedure to estimate the number and locations of changepoints in Periodic AutoRegressive (PAR) models, which have been extensively used to account for seasonality in hydrology. We aim at filling the literature gap on multiple changepoint detection by allowing several time segments to be detected, inside of which a different PAR structure is specified, with the resulting model being employed to successfully capture the discontinuities of river flow data. The model estimation is performed by optimization of an objective function based on an information criterion using genetic algorithms. The proposed methodology is evaluated by means of simulation studies and it is then employed in the analysis of two river flows: the South Saskatchewan, measured at Saskatoon, Canada, and the Colorado, measured at Lees Ferry, Arizona. For these river flows we build changepoint models, discussing the possible events that caused discontinuity, and evaluate their forecasting accuracy. Comparisons with the literature on river flow analysis and on existing methods for changepoint detection confirm the efficiency of our proposal.}, author = {Cucina, Domenico and Rizzo, Manuel and Ursu, Eugen}, editor = {Springer}, journal = {Stochastic Environmental Research and Risk Assessment}, keywords = {domenicocucina eugenursu manuelrizzo myown serra year2019}, month = {jun}, number = 4, pages = {1137-1157}, title = {Multiple changepoint detection for periodic autoregressive models with an application to river flow analysis}, volume = 33, year = 2019 }

2018 [ nach oben ]

Rizzo, Manuel; Battaglia, Francesco Statistical and Computational Tradeoff in Genetic Algorithm-Based EstimationJournal of Statistical Computation and Simulation 2018: 3081–3097
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When a genetic algorithm (GA) is employed in a statistical problem, the result is affected by both variability due to sampling and the stochastic elements of algorithm. Both of these components should be controlled in order to obtain reliable results. In the present work we analyze parametric estimation problems tackled by GAs, and pursue two objectives: the first one is related to a formal variability analysis of final estimates, showing that it can be easily decomposed in the two sources of variability. In the second one we introduce a framework of GA estimation with fixed computational resources, which is a form of statistical and the computational tradeoff question, crucial in recent problems. In this situation the result should be optimal from both the statistical and computational point of view, considering the two sources of variability and the constraints on resources. Simulation studies will be presented for illustrating the proposed method and the statistical and computational tradeoff question.
@article{doi:10.1080/00949655.2018.1499740, abstract = {When a genetic algorithm (GA) is employed in a statistical problem, the result is affected by both variability due to sampling and the stochastic elements of algorithm. Both of these components should be controlled in order to obtain reliable results. In the present work we analyze parametric estimation problems tackled by GAs, and pursue two objectives: the first one is related to a formal variability analysis of final estimates, showing that it can be easily decomposed in the two sources of variability. In the second one we introduce a framework of GA estimation with fixed computational resources, which is a form of statistical and the computational tradeoff question, crucial in recent problems. In this situation the result should be optimal from both the statistical and computational point of view, considering the two sources of variability and the constraints on resources. Simulation studies will be presented for illustrating the proposed method and the statistical and computational tradeoff question.}, author = {Rizzo, Manuel and Battaglia, Francesco}, journal = {Journal of Statistical Computation and Simulation}, keywords = {francescobattaglia jscs manuelrizzo year2018}, number = 16, pages = {3081-3097}, publisher = {Taylor & Francis}, title = {Statistical and Computational Tradeoff in Genetic Algorithm-Based Estimation}, volume = 88, year = 2018 }

Battaglia, Francesco; Cucina, Domenico; Rizzo, Manuel Periodic Autoregressive Models with Multiple Structural Changes by Genetic AlgorithmsMathematical and Statistical Methods for Actuarial Sciences and Finance (MAF) 2018: 107–110
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We present a model and a computational procedure for dealing with seasonality and regime changes in time series. In this work we are interested in time series which in addition to trend display seasonality in mean, in autocorrelation and in variance. These type of series appears in many areas, including hydrology, meteorology, economics and finance. The seasonality is accounted for by subset PAR modelling, for which each season follows a possibly different Autoregressive model. Levels, trend, autoregressive parameters and residual variances are allowed to change their values at fixed unknown times. The identification of number and location of structural changes, as well as PAR lags indicators, is based on Genetic Algorithms, which are suitable because of high dimensionality of the discrete search space. An application to Italian industrial production index time series is also proposed.
@inbook{Battaglia2018, abstract = {We present a model and a computational procedure for dealing with seasonality and regime changes in time series. In this work we are interested in time series which in addition to trend display seasonality in mean, in autocorrelation and in variance. These type of series appears in many areas, including hydrology, meteorology, economics and finance. The seasonality is accounted for by subset PAR modelling, for which each season follows a possibly different Autoregressive model. Levels, trend, autoregressive parameters and residual variances are allowed to change their values at fixed unknown times. The identification of number and location of structural changes, as well as PAR lags indicators, is based on Genetic Algorithms, which are suitable because of high dimensionality of the discrete search space. An application to Italian industrial production index time series is also proposed.}, author = {Battaglia, Francesco and Cucina, Domenico and Rizzo, Manuel}, booktitle = {Mathematical and Statistical Methods for Actuarial Sciences and Finance (MAF)}, editor = {Corazza, Marco and Durbán, María and Grané, Aurea and Perna, Cira and Sibillo, Marilena}, keywords = {domenicocucina francescobattaglia maf manuelrizzo year2018}, pages = {107-110}, title = {Periodic Autoregressive Models with Multiple Structural Changes by Genetic Algorithms}, year = 2018 }

Cucina, Domenico; Rizzo, Manuel; Ursu, Eugen Identification of Multiregime Periodic Autoregressive Models by Genetic AlgorithmsInternational Conference on Time Series and Forecasting (ITISE) 2018: 396–407
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This paper develops a procedure for identifying multiregime Periodic AutoRegressive (PAR) models. In each regime a possibly dif- ferent PAR model is built, for which changes can be due to the seasonal means, the autocorrelation structure or the variances. Number and lo- cations of changepoints which subdivide the time span are detected by means of Genetic Algorithms (GAs), that optimize an identification cri- terion. The method is evaluated by means of simulation studies, and is then employed to analyze shrimp fishery data.
@inproceedings{cucina2018identification, abstract = {This paper develops a procedure for identifying multiregime Periodic AutoRegressive (PAR) models. In each regime a possibly dif- ferent PAR model is built, for which changes can be due to the seasonal means, the autocorrelation structure or the variances. Number and lo- cations of changepoints which subdivide the time span are detected by means of Genetic Algorithms (GAs), that optimize an identification cri- terion. The method is evaluated by means of simulation studies, and is then employed to analyze shrimp fishery data.}, author = {Cucina, Domenico and Rizzo, Manuel and Ursu, Eugen}, booktitle = {International Conference on Time Series and Forecasting (ITISE)}, keywords = {domenicocucina eugenursu itise manuelrizzo year2018}, pages = {396-407}, title = {Identification of Multiregime Periodic Autoregressive Models by Genetic Algorithms}, volume = 1, year = 2018 }

Battaglia, Francesco; Cucina, Domenico; Rizzo, Manuel Generalized Periodic Autoregressive Models for Trend and Seasonality Varying Time SeriesScientific Meeting of the Italian Statistical Society (SIS) 2018
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Many nonstationary time series exhibit changes in the trend and seasonality structure, that may be modeled by splitting the time axis into different regimes. We propose multi-regime models where, inside each regime, the trend is linear and seasonality is explained by a Periodic Autoregressive model. In addition, for achieving parsimony, we allow season grouping, i.e. seasons may consist of one, two, or more consecutive observations. Identification is obtained by means of a Genetic Algorithm that minimizes an identification criterion.
@inproceedings{battagliageneralized, abstract = {Many nonstationary time series exhibit changes in the trend and seasonality structure, that may be modeled by splitting the time axis into different regimes. We propose multi-regime models where, inside each regime, the trend is linear and seasonality is explained by a Periodic Autoregressive model. In addition, for achieving parsimony, we allow season grouping, i.e. seasons may consist of one, two, or more consecutive observations. Identification is obtained by means of a Genetic Algorithm that minimizes an identification criterion.}, author = {Battaglia, Francesco and Cucina, Domenico and Rizzo, Manuel}, booktitle = {Scientific Meeting of the Italian Statistical Society (SIS)}, keywords = {domenicocucina francescobattaglia manuelrizzo sis year2018}, title = {Generalized Periodic Autoregressive Models for Trend and Seasonality Varying Time Series}, year = 2018 }

Rizzo, Manuel Contributions on Evolutionary Computation for Statistical InferenceDoctoral Dissertation, Sapienza University of Rome 2018
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@phdthesis{rizzo2018contributions, annote = {Doctoral Dissertation, Sapienza University of Rome}, author = {Rizzo, Manuel}, keywords = {manuelrizzo phdthesis theses year2018}, school = {Sapienza University of Rome}, title = {Contributions on Evolutionary Computation for Statistical Inference}, type = {PhD Thesis}, year = 2018 }

2017 [ nach oben ]

Rizzo, Manuel On Variability Analysis of Evolutionary Algorithm-Based EstimationConference of the Classification and Data Analysis Group (CLADAG) 2017: 237–242
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A theoretical framework to analyze variability of parametric estimates obtained via Evolutionary Algorithms (EAs) is proposed. The nature of EAs, in fact, introduces a further source of variability, due to stochastic elements of the procedure. A simulation study employing Genetic Algorithms and Differential Evolution is also conducted in oder to make comments on the effect of these stochastic elements on variability.
@article{rizzo2017variability, abstract = {A theoretical framework to analyze variability of parametric estimates obtained via Evolutionary Algorithms (EAs) is proposed. The nature of EAs, in fact, introduces a further source of variability, due to stochastic elements of the procedure. A simulation study employing Genetic Algorithms and Differential Evolution is also conducted in oder to make comments on the effect of these stochastic elements on variability.}, author = {Rizzo, Manuel}, journal = {Conference of the Classification and Data Analysis Group (CLADAG)}, keywords = {cladag manuelrizzo year2017}, pages = {237-242}, title = {On Variability Analysis of Evolutionary Algorithm-Based Estimation}, year = 2017 }

2016 [ nach oben ]

Rizzo, Manuel; Battaglia, Francesco On the Choice of a Genetic Algorithm for Estimating GARCH ModelsComputational Economics 2016: 473–485
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The GARCH models have been found difficult to build by classical methods, and several other approaches have been proposed in literature, including metaheuristic and evolutionary ones. In the present paper we employ genetic algorithms to estimate the parameters of GARCH(1,1) models, assuming a fixed computational time (measured in number of fitness function evaluations) that is variously allocated in number of generations, number of algorithm restarts and number of chromosomes in the population, in order to gain some indications about the impact of each of these factors on the estimates. Results from this simulation study show that if the main purpose is to reach a high quality solution with no time restrictions the algorithm should not be restarted and an average population size is recommended, while if the interest is focused on driving rapidly to a satisfactory solution then for moderate population sizes it is convenient to restart the algorithm, even if this means to have a small number of generations.
@article{rizzo2016on, abstract = {The GARCH models have been found difficult to build by classical methods, and several other approaches have been proposed in literature, including metaheuristic and evolutionary ones. In the present paper we employ genetic algorithms to estimate the parameters of GARCH(1,1) models, assuming a fixed computational time (measured in number of fitness function evaluations) that is variously allocated in number of generations, number of algorithm restarts and number of chromosomes in the population, in order to gain some indications about the impact of each of these factors on the estimates. Results from this simulation study show that if the main purpose is to reach a high quality solution with no time restrictions the algorithm should not be restarted and an average population size is recommended, while if the interest is focused on driving rapidly to a satisfactory solution then for moderate population sizes it is convenient to restart the algorithm, even if this means to have a small number of generations.}, author = {Rizzo, Manuel and Battaglia, Francesco}, journal = {Computational Economics}, keywords = {ce francescobattaglia manuelrizzo year2016}, number = 3, pages = {473-485}, title = {On the Choice of a Genetic Algorithm for Estimating GARCH Models}, volume = 48, year = 2016 }