Abstract

Abstract
Real time series sometimes exhibit various types of "irregularities": missing observations, observations collected not regularly over time for practical reasons, observation times driven by the series itself, or outlying observations. However, the vast majority of methods of time series analysis are designed for regular time series only. A particular case of irregularly spaced time series is that in which the sampling procedure over time depends also on the observed values. In such situations, there is stochastic dependence between the process being modelled and the times of the observations. In this work, we propose a model in which the sampling design depends on all past history of the observed processes. Taking into account the natural temporal order underlying available data represented by a time series, then a modelling approach based on evolutionary processes seems a natural choice. We consider maximum likelihood estimation of the model parameters. Numerical studies with simulated and real data sets are performed to illustrate the benefits of this model-based approach.

Abstract
This work presents a framework of dynamic structural models with covariates for short-term forecasting of time series with complex seasonal patterns. The framework is based on the multiple sources of randomness formulation. A noise model is formulated to allow the incorporation of randomness into the seasonal component and to propagate this same randomness in the coefficients of the variant trigonometric terms over time. A unique, recursive and systematic computational procedure based on the maximum likelihood estimation under the hypothesis of Gaussian errors is introduced. The referred procedure combines the Kalman filter with recursive adjustment of the covariance matrices and the selection method of harmonics number in the trigonometric terms. A key feature of this method is that it allows estimating not only the states of the system but also allows obtaining the standard errors of the estimated parameters and the prediction intervals. In addition, this work also presents a non-parametric bootstrap approach to improve the forecasting method based on Kalman filter recursions. The proposed framework is empirically explored with two real time series.

Abstract
Cardiovascular variability is the result of the activity of several physiological control mechanisms, which involve different variables and operate across multiple time scales encompassing short term dynamics and long range correlations. This study presents a new approach to assess the multiscale complexity of multivariate time series, based on linear parametric models incorporating autoregressive coefficients and fractional integration. The approach extends to the multivariate case recent works introducing a linear parametric representation of multiscale entropy, and is exploited to assess the complexity of cardiovascular and respiratory time series in healthy subjects studied during postural and mental stress.

Abstract
Irregularly spaced time series are commonly encountered in the analysis of time series. A particular case is that in which the collection procedure over time depends also on the observed values. In such situations, there is stochastic dependence between the process being modeled and the times at which the observations are made. Ignoring this dependence can lead to biased estimates and misleading inferences. In this paper, we introduce the concept of preferential sampling in the temporal dimension and we propose a model to make inference and prediction. The methodology is illustrated using artificial data as well a real data set.

Abstract
Time series of (small) counts are common in practice and appear in a wide variety of fields. In the last three decades, several models that explicitly account for the discreteness of the data have been proposed in the literature. However, for multivariate time series of counts several difficulties arise and the literature is not so detailed. This work considers Bivariate INteger-valued Moving Average, BINMA, models based on the binomial thinning operation. The main probabilistic and statistical properties of BINMA models are studied. Two parametric cases are analysed, one with the cross-correlation generated through a Bivariate Poisson innovation process and another with a Bivariate Negative Binomial innovation process. Moreover, parameter estimation is carried out by the Generalized Method of Moments. The performance of the model is illustrated with synthetic data as well as with real datasets.