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

Multi-regime models for nonlinear nonstationary time series

Nonlinear nonstationary models for time series are considered, where the series is generated from an autoregressive equation whose coe±cients change both according to time and the delayed values of the series itself, switching between several regimes. The transition from one regime to the next one may be discontinuous (self-exciting threshold model), smooth (smooth transition model) or continuous linear (piecewise linear threshold model). A genetic algorithm for identifying and estimating such models is proposed, and its behavior is evaluated through a simulation study and application to temperature data and a financial index.

Time-varying Multi-regime Models Fitting by Genetic Algorithms

Many time series exhibit both nonlinearity and nonstationarity. Though both features have often been taken into account separately, few attempts have been proposed to model them simultaneously. We consider threshold models, and present a general model allowing for different regimes both in time and in levels, where regime transitions may happen according to self-exciting, or smoothly varying, or piecewise linear threshold modeling. Since fitting such a model involves the choice of a large number of structural parameters, we propose a procedure based on genetic algorithms, evaluating models by means of a generalized identification criterion. The performance of the proposed procedure is illustrated with a simulation study and applications to some real data.Nonlinear time series; Nonstationary time series; Threshold model

Modelling the cohort effect in CBD models using a piecewise linear approach

This paper discusses a new pattern of mortality model which is built on the form and knowledge of the two-factor mortality model named after its designers Cairns, Blake and Dowd (2006). This model – the CBD model – is widely used and has been extended by the authors in a number of ways, including by the use of a cohort effect. In this paper, we propose a range of new parsimonious approaches to model the cohort effect. Instead of adding a cohort factor to an age-period model we model the effect by building discontinuities into the pattern of rates within each year. The fit of the resulting models is close to that available from the best of the CBD derivatives

Discussion of “An analysis of global warming in the Alpine region based on nonlinear nonstationary time series models” by F. Battaglia and M. K. Protopapas

The annual temperatures recorded for the last two centuries in fifteen european stations around the Alps are analyzed. They show a global warming whose growth rate is not however constant in time. An analysis based on linear Arima models does not provide accurate results. Thus, we propose threshold nonlinear nonstationary models based on several regimes both in time and in levels. Such models fit all series satisfactorily, allow a closer description of the temperature changes evolution, and help to discover the essential differences in the behavior of the different stations

A bi-objective genetic algorithm approach to risk mitigation in project scheduling

A problem of risk mitigation in project scheduling is formulated as a bi-objective optimization problem, where the expected makespan and the expected total cost are both to be minimized. The expected total cost is the sum of four cost components: overhead cost, activity execution cost, cost of reducing risks and penalty cost for tardiness. Risks for activities are predefined. For each risk at an activity, various levels are defined, which correspond to the results of different preventive measures. Only those risks with a probable impact on the duration of the related activity are considered here. Impacts of risks are not only accounted for through the expected makespan but are also translated into cost and thus have an impact on the expected total cost. An MIP model and a heuristic solution approach based on genetic algorithms (GAs) is proposed. The experiments conducted indicate that GAs provide a fast and effective solution approach to the problem. For smaller problems, the results obtained by the GA are very good. For larger problems, there is room for improvement