Rizzo, Manuel; Battaglia, Francesco Statistical and Computational Tradeoff in Genetic Algorithm-Based EstimationJournal of Statistical Computation and Simulation 2018: 3081–3097
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.
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
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.
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
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.
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
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.
Rizzo, Manuel Contributions on Evolutionary Computation for Statistical InferenceDoctoral Dissertation, Sapienza University of Rome 2018