In areas of application, including actuarial science and demography, it is increasingly common to consider a time series of curves; an example of this is age-specific mortality rates observed over a period of years. Given that age can be treated as a discrete or continuous variable, a dimension reduction technique, such as principal component analysis (PCA), is often implemented. However, in the presence of moderate-to-strong temporal dependence, static PCA commonly used for analyzing independent and identically distributed data may not be adequate. As an alternative, we consider a dynamic principal component approach to model temporal dependence in a time series of curves. Inspired by Brillinger’s (1974, Time Series: Data Analysis and Theory. New York: Holt, Rinehart and Winston) theory of dynamic principal components, we introduce a dynamic PCA, which is based on eigen decomposition of estimated long-run covariance. Through a series of empirical applications, we demonstrate the potential improvement of 1-year-ahead point and interval forecast accuracies that the dynamic principal component regression entails when compared with the static counterpart.

We perform an analysis of the potential time inhomogeneity in the dependence between multiple financial time series. To this end, we use the framework of copula theory and tackle the question of whether dependencies in such a case can be assumed constant throughout time or rather have to be modeled in a time-inhomogeneous way. We focus on parametric copula models and suitable inference techniques in the context of a special copula-based multivariate time series model. A recent result due to Chan et al. (2009) is used to derive the joint limiting distribution of local maximum-likelihood estimators on overlapping samples. By restricting the overlap to be fixed, we establish the limiting law of the maximum of the estimator series. Based on the limiting distributions, we develop statistical homogeneity tests, and investigate their local power properties. A Monte Carlo simulation study demonstrates that bootstrapped variance estimates are needed in finite samples. Empirical analyses on real-world financial data finally confirm that time-varying parameters are an exception rather than the rule.

A new genetic factor model for multivariate phenotypic time series, iFACE, is presented which allows for the estimation of subject-specific model parameters of genetic and environmental factors. The iFACE was applied to multivariate EEG registrations obtained with single dizygotic twin pairs. The results showed evidence for considerable subject-specificity in heritabilities and environmental effects. The assumption that the population is homogeneous (i.e., that each case in the population obeys the same parametric model), does not hold for these psychophysiological data, and its use should be critically reconsidered. We conclude that the iFACE provides a powerful new methodology to assess heterogeneity (subject-specificity) based on phenotypic observations.

Fisheries exploitation systems are characterized by reciprocal interactions between fisheries activity and the harvested resource. Variability and changes affecting ‘natural’ and ‘socio-economic’ environments generate non stationarity of the variables used to describe the fishing activity, the resource and the yields. This characteristic needs to be taken into account in describing the evolution of the relationships between those variables, and in describing fisheries adaptability and sustainability. We present a dynamical system model with an application to data from surveys on activity and results of the Senegalese artisanal fishery from 1974 to 1992. A fitting procedure is proposed, giving estimates of the parameters of the model. A simulation is then made with the fitted model in order to apraise possible impacts of various events of different kind.

The paper derives the asymptotic properties of a class of estimators of the Walsh–Fourier spectral density of a stationary time series. The spectral density is defined in Kohn (1980).

We consider a general non-linear multivariate time series model which can be parameterized by a finite and fixed number of parameters and which can be rewritten, if necessary, in a form such that the disturbances are stationary martingale differences. Given a series of discrete, equally spaced observations we prove the strong consistency and asymptotic normality of the Gaussian estimators of the parameters, the parameters possibly being subject to non-linear constraints. Because the normal equations are usually highly non-linear it may be difficult to obtain explicit expressions for the Gaussian estimates. To overcome this problem we use a Gauss–Newton type algorithm to obtain a sequence of iterates which converge to, and have the same asymptotic properties as, the Gaussian estimates.