Background Providing support to others has been shown to be beneficial to older adults. As people age, their health and social relationships change. These changes may also relate to changes in social support provision. We examined the trajectory of instrumental support provision by older people in three European regions throughout 11 years of follow-up. We then examined the extent to which age at baseline, sex, and region (representing welfare state regime) influenced the variations in the trajectory. Methods Data collected from 8354 respondents who had completed at least waves 1 and 6 of the Survey of Health, Ageing and Retirement in Europe (SHARE) was analysed. Instrumental support provision was determined from asking a single question regarding whether the respondent provided help personally for people outside their household. Region, sex, and age at baseline were the main predictors tested. We used growth modelling to address the aims of this study. Results The northern European region (Sweden and Denmark) had the highest odds ratio of instrumental support provision. The likelihood of being involved in providing instrumental support decreased by 8% annually (OR: 0.916, 95%CI: 0.893,0.940) over the 11 years of follow-up. Older respondents were less likely to provide instrumental support and their trajectories declined faster than those of the younger respondents. Sex difference in instrumental support provision was more apparent among younger-older people in the southern European region. Conclusions Older European adults are an important source of instrumental support, especially for their families. The probability of instrumental support provision by European older adults declines over time. Age, sex, and welfare state regime predict this trajectory.

In this article, we combine the extensive literature on the analysis of life-course trajectories as sequences with the literature on causal inference and propose a new matching approach to investigate the causal effect of the timing of life-course events on subsequent outcomes. Our matching approach takes into account pre-event confounders that are both time-independent and time-dependent as well as life-course trajectories. After matching, treated and control individuals can be compared using standard statistical tests or regression models. We apply our approach to the study of the consequences of the age at retirement on subsequent health outcomes, using a unique data set from Swedish administrative registers. Once selectivity in the timing of retirement is taken into account, effects on hospitalization are small, while early retirement has negative effects on survival. Our approach also allows for heterogeneous treatment effects. We show that the effects of early retirement differ according to preretirement income, with higher income individuals tending to benefit from early retirement, while the opposite is true for individuals with lower income.

We present a family of spatio-temporal models which are geared to pro- vide time-forward predictions in environmental applications where data is spatially sparse but temporally rich. That is measurements are made at few spatial locations (stations), but at many regular time intervals. When predictions in the time di- rection is the purpose of the analysis, then spatial-stationarity assumptions which are commonly used in spatial modeling, are not necessary. The family of models proposed does not make such assumptions and consists of a vector autoregressive (VAR) specification, where there are as many time series as stations. However, by taking into account the spatial dependence structure, a model building strategy is introduced which borrows its simplicity from the Box-Jenkins strategy for univari- ate autoregressive (AR) models for time series. As for AR models, model building may be performed either by displaying sample partial correlation functions, or by minimizing an information criterion. A simulation study illustrates the gain re- sulting from our modeling strategy. Two environmental data sets are studied. In particular, we find evidence that a parametric modeling of the spatio-temporal cor- relation function is not appropriate because it rests on too strong assumptions. Moreover, we propose to compare model selection strategies with an out-of-sample validation method based on recursive prediction errors. In this article we present a model building strategy designed to work within a family of vector autoregressive models for time series being recorded at specific spatial locations. The methodology has been developed with environmental ap- plications in mind where measurements on a variable are made at regular time intervals and at several stations located within a specific area. More specifically, we focus on situations were measurements are available at a few stations −the spatio-temporal data is sparse in space but rich in time. We put the discussion into concrete form with two examples treated previously in the literature. The first data set we consider consists of average daily wind speeds mea- sured at 11 synoptic meteorological stations located in Ireland during the period 1961-78, 6,570 observations per location. Gneiting (2002) used this data set to

We analyze spatio-temporal data on U.S. unemployment rates. For this purpose, we present a family of models designed for the analysis and time-forward prediction of spatio-temporal econometric data. Our model is aimed at applications with spatially sparse but temporally rich data, i.e. for observations collected at few spatial regions, but at many regular time intervals. The family of models utilized does not make spatial stationarity assumptions and consists in a vector autoregressive (VAR) specification, where there are as many time series as spatial regions. A model building strategy is used that takes into account the spatial dependence structure of the data. Model building may be performed either by displaying sample partial correlation functions, or automatically with an information criterion. Monthly data on unemployment rates in the nine census divisions of the U.S. are analyzed. We show with a residual analysis that our autoregressive model captures the dependence structure of the data better than with univariate time series modeling.

An important problem in statistical practice is the selection of a suitable statistical model. Several model selection strategies are available in the literature, having different asymptotic and small sample properties, depending on the characteristics of the data generating mechanism. These characteristics are difficult to check in practice and there is a need for a data‐driven adaptive procedure to identify an appropriate model selection strategy for the data at hand. We call such an identification a model metaselection, and we base it on the analysis of recursive prediction residuals obtained from each strategy with increasing sample sizes. Graphical tools are proposed in order to study these recursive residuals. Their use is illustrated on real and simulated data sets. When necessary, an automatic metaselection can be performed by simply accumulating predictive losses. Asymptotic and small sample results are presented.

The purpose of this paper is to show how the stability properties of non-linear dynamic models may be characterized and studied, where the degree of stability is defined by the effects of exogenous shocks on the evolution of the observed stochastic system. This type of stability concept is frequently of interest in economics, e.g., in real business cycle theory.We argue that smooth Lyapunov exponents can be used to measure the degree of stability of a stochastic dynamic model. It is emphasized that the stability properties of the model should be considered when the volatility of the variable modelled is of interest. When a parametric model is fitted to observed data, an estimator of the largest smooth Lyapunov exponent is presented which is consistent and asymptotically normal. The small sample properties of this estimator are examined in a Monte Carlo study. Finally, we illustrate how the presented framework can be used to study the degree of stability and the volatility of an exchange rate.

In this paper a comparative study of the regime shift in inflation policies in New Zealand and Sweden is performed. A nonparametric regression method is used to decompose the inflation time series into three components of variation: a long-term trend, a medium-term (cyclical and transient variations) trend and a short-term shocks component. This allows study of the transition process from the high inflation characterizing the end of the 1970s and the 1980s to the low inflation observed during the 1990s. It is found that in New Zealand, although it is initially delayed, the decrease in inflation happens at a faster pace than in Sweden. This may indicate that reforms were more efficient in New Zealand. A clear link is also shown between the rising unemployment and the transition from high to low inflation. Furthermore, while in New Zealand a downward adjustment of the unemployment rate happens directly after the transition period, in Sweden there seems to be persistence in high unemployment.

In this paper we present guaranteed-content prediction intervals for time series data. These intervals are such that their content (or coverage) is guaranteed with a given high probability. They are thus more relevant for the observed time series at hand than classical prediction intervals, whose content is guaranteed merely on average over hypothetical repetitions of the prediction process. This type of prediction inference has, however, been ignored in the time series context because of a lack of results. This gap is filled by deriving asymptotic results for a general family of autoregressive models, thereby extending existing results in non-linear regression. The actual construction of guaranteed-content prediction intervals directly follows from this theory. Simulated and real data are used to illustrate the practical difference between classical and guaranteed-content prediction intervals for ARCH models. Copyright (C) 2001 John Wiley & Sons, Ltd.

How has the European monetary integration, with the creation of the EMU, affected the stability and volatility of foreign exchange? In order to answer this question, stability and volatility measures are defined and calculated. We then use these to investigate the changes in the stability and volatility of 16 European currencies, and in the volatility of the shocks to these currencies. The stability measures are based on smooth Lyapunov exponents, while the volatility measures utilize variances. The results indicate that when most of the currencies become more stable, a majority of them also become less volatile. For example, following the agreement of the Maastricht Treaty most currencies became more stable and less volatile, whereas they became less stable and more volatile when the Danish public voted against the treaty. Finally, there is no empirical support for the view that a decision to step aside from a closer monetary collaboration has a negative effect on the stability of the currency.

This article proposes a new approach to the robust estimation of a mixed autoregressive: and moving average (ARMA) model. It is based on the indirect inference method that originally was proposed for models with an intractable likelihood function. The estimation algorithm proposed is based on an auxiliary autoregressive representation whose parameters are first estimated on the observed time series and then on data simulated from the ARMA model. To simulate data the parameters of the ARMA model have to be set. By varying these we can minimize a distance between the simulation-based and the observation-based auxiliary estimate, The argument of the minimum yields then an estimator for the parameterization of the ARMA model. This simulation-based estimation procedure inherits the properties of the auxiliary model estimator. For instance, robustness is achieved with GM estimators. An essential feature of the introduced estimator, compared to existing robust estimators for ARMA models. is its theoretical tractability that allows us to show consistency and asymptotic normality. Moreover, it is possible to characterize the influence function and the breakdown point of the estimator. in a small sample Monte Carlo study it is found that the new estimator performs fairly well when compared with existing procedures. Furthermore, with two real examples, we also compare the proposed inferential method with two different approaches based on outliers detection.

The variability of parameter estimates is commonly neglected when constructing prediction intervals based on a parametric model for a time series. This practice is due to the complexity of conditioning the inference on information such as observed values of the underlying stochastic process. In this paper, conditional prediction intervals when using autoregression forecasts are proposed whose simple implementation will hopefully enable wide use. A simulation study illustrates the improvement over classical intervals in terms of empirical coverage.

Estimation in nonlinear time series models has mainly been performed by least squares or maximum likelihood (ML) methods. The paper suggests and studies the performance of generalized method of moments (GMM) and indirect estimators for the autoregressive asymmetric moving average model. Both approaches are easy to implement and perform well numerically. In a Monte Carlo study it is found that the MSE properties of GMM are close to those of ML. The indirect estimator performs poorly in this respect. On the other hand, the three estimation techniques lead to fairly similar power functions for a linearity test.