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.
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, ManuelPeriodic Autoregressive Models with Multiple Structural Changes by Genetic Algorithms. Mathematical 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, EugenIdentification of Multiregime Periodic Autoregressive Models by Genetic Algorithms. International 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, ManuelGeneralized Periodic Autoregressive Models for Trend and Seasonality Varying Time Series. Scientific 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, ManuelContributions on Evolutionary Computation for Statistical Inference. Doctoral Dissertation, Sapienza University of Rome 2018
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.
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.
Our research focus is on theoretical computer science and algorithm engineering. We are equally interested in the mathematical foundations of algorithms and developing efficient algorithms in practice. A special focus is on random structures and methods.