A generalization of periodic autoregressive models for seasonal time series

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 consists of one, two, or more consecutive observations. Since the set of possible solutions is very large, the choice of number of regimes, change times and order and structure of the Autoregressive models is obtained by means of a Genetic Algorithm, and the evaluation of each possible solution is left to an identication criterion such as AIC, BIC or MDL. The comparison and performance of the proposed method are illustrated by a real data analysis. The results suggest that the proposed procedure is useful for analyzing complex phenomena with structural breaks, changes in trend and evolving seasonality

Autoregressive time series prediction by means of fuzzy inference systems using nonparametric residual variance estimation

We propose an automatic methodology framework for short- and long-term prediction of time series by means of fuzzy inference systems. In this methodology, fuzzy techniques and statistical techniques for nonparametric residual variance estimation are combined in order to build autoregressive predictive models implemented as fuzzy inference systems. Nonparametric residual variance estimation plays a key role in driving the identification and learning procedures. Concrete criteria and procedures within the proposed methodology framework are applied to a number of time series prediction problems. The learn from examples method introduced by Wang and Mendel (W&M) is used for identification. The Levenberg–Marquardt (L–M) optimization method is then applied for tuning. The W&M method produces compact and potentially accurate inference systems when applied after a proper variable selection stage. The L–M method yields the best compromise between accuracy and interpretability of results, among a set of alternatives. Delta test based residual variance estimations are used in order to select the best subset of inputs to the fuzzy inference systems as well as the number of linguistic labels for the inputs. Experiments on a diverse set of time series prediction benchmarks are compared against least-squares support vector machines (LS-SVM), optimally pruned extreme learning machine (OP-ELM), and k-NN based autoregressors. The advantages of the proposed methodology are shown in terms of linguistic interpretability, generalization capability and computational cost. Furthermore, fuzzy models are shown to be consistently more accurate for prediction in the case of time series coming from real-world applications.Ministerio de Ciencia e Innovación TEC2008-04920Junta de Andalucía P08-TIC-03674, IAC07-I-0205:33080, IAC08-II-3347:5626