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Stationarity is a very general, qualitative assumption, that can be assessed on the basis of application specifics. It is thus a rather attractive assumption to base statistical analysis on, especially for problems for which less general qualitative assumptions, such as independence or finite memory, clearly fail. However, it has long been considered too general to be able to make statistical inference. One of the reasons for this is that rates of convergence, even of frequencies to the mean, are not available under this assumption alone. Recently, it has been shown that, while some natural and simple problems, such as homogeneity, are indeed provably impossible to solve if one only assumes that the data is stationary (or stationary ergodic), many others can be solved with rather simple and intuitive algorithms. The latter include clustering and change point estimation among others. In this volume I summarize these results. The emphasis is on asymptotic consistency, since this the strongest property one can obtain assuming stationarity alone. While for most of the problem for which a solution is found this solution is algorithmically realizable, the main objective in this area of research, the objective which is only partially attained, is to understand what is possible and what is not possible to do for stationary time series. The considered problems include homogeneity testing (the so-called two sample problem), clustering with respect to distribution, clustering with respect to independence, change point estimation, identity testing, and the general problem of composite hypotheses testing. For the latter problem, a topological criterion for the existence of a consistent test is presented. In addition, a number of open problems is presented.

Background Randomised controlled trials (RCTs) are considered the gold standard when evaluating the causal effects of healthcare interventions. When RCTs cannot be used (e.g. ethically difficult), the interrupted time series (ITS) design is a possible alternative. ITS is one of the strongest quasi-experimental designs. The aim of this methodological study was to describe how ITS designs were being used, the design characteristics, and reporting in the healthcare setting. Methods We searched MEDLINE for reports of ITS designs published in 2015 which had a minimum of two data points collected pre-intervention and one post-intervention. There was no restriction on participants, language of study, or type of outcome. Data were summarised using appropriate summary statistics. Results One hundred and sixteen studies were included in the study. Interventions evaluated were mainly programs 41 (35%) and policies 32 (28%). Data were usually collected at monthly intervals, 74 (64%). Of the 115 studies that reported an analysis, the most common method was segmented regression (78%), 55% considered autocorrelation, and only seven reported a sample size calculation. Estimation of intervention effects were reported as change in slope (84%) and change in level (70%) and 21% reported long-term change in levels. Conclusions This methodological study identified problems in the reporting of design features and results of ITS studies, and highlights the need for future work in the development of formal reporting guidelines and methodological work.

Time series econometrics is a rapidly evolving field. Particularly, the cointegration revolution has had a substantial impact on applied analysis. Hence, no textbook has managed to cover the full range of methods in current use and explain how to proceed in applied domains. This gap in the literature motivates the present volume. The methods are sketched out, reminding the reader of the ideas underlying them and giving sufficient background for empirical work. The treatment can also be used as a textbook for a course on applied time series econometrics. Topics include: unit root and cointegration analysis, structural vector autoregressions, conditional heteroskedasticity and nonlinear and nonparametric time series models. Crucial to empirical work is the software that is available for analysis. New methodology is typically only gradually incorporated into existing software packages. Therefore a flexible Java interface has been created, allowing readers to replicate the applications and conduct their own analyses.

\"Time-series, or longitudinal, data are ubiquitous in the social sciences. Unfortunately, analysts often treat the time-series properties of their data as a nuisance rather than a substantively meaningful dynamic process to be modeled and interpreted. Time-Series Analysis for Social Sciences provides accessible, up-to-date instruction and examples of the core methods in time-series econometrics.\"--Provided by publisher.

The volatility of financial returns changes over time and, for the last thirty years, Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have provided the principal means of analyzing, modeling and monitoring such changes. Taking into account that financial returns typically exhibit heavy tails - that is, extreme values can occur from time to time - Andrew Harvey's new book shows how a small but radical change in the way GARCH models are formulated leads to a resolution of many of the theoretical problems inherent in the statistical theory. The approach can also be applied to other aspects of volatility. The more general class of Dynamic Conditional Score models extends to robust modeling of outliers in the levels of time series and to the treatment of time-varying relationships. The statistical theory draws on basic principles of maximum likelihood estimation and, by doing so, leads to an elegant and unified treatment of nonlinear time-series modeling.

In response to public concerns and campaigns, some United Kingdom supermarkets have implemented policies to reduce less-healthy food at checkouts. We explored the effects of these policies on purchases of less-healthy foods commonly displayed at checkouts. We used a natural experimental design and two data sources providing complementary and unique information. We analysed data on purchases of small packages of common, less-healthy, checkout foods (sugary confectionary, chocolate, and potato crisps) from 2013 to 2017 from nine UK supermarkets (Aldi, Asda, Co-op, Lidl, M&S, Morrisons, Sainsbury's, Tesco, and Waitrose). Six supermarkets implemented a checkout food policy between 2013 and 2017 and were considered intervention stores; the remainder were comparators. Firstly, we studied the longitudinal association between implementation of checkout policies and purchases taken home. We used data from a large (n ≈ 30,000) household purchase panel of food brought home to conduct controlled interrupted time series analyses of purchases of less-healthy common checkout foods from 12 months before to 12 months after implementation. We conducted separate analyses for each intervention supermarket, using others as comparators. We synthesised results across supermarkets using random effects meta-analyses. Implementation of a checkout food policy was associated with an immediate reduction in four-weekly purchases of common checkout foods of 157,000 (72,700-242,800) packages per percentage market share-equivalent to a 17.3% reduction. This decrease was sustained at 1 year with 185,100 (121,700-248,500) fewer packages purchased per 4 weeks per percentage market share-equivalent to a 15.5% reduction. The immediate, but not sustained, effect was robust to sensitivity analysis. Secondly, we studied the cross-sectional association between checkout food policies and purchases eaten without being taken home. We used data from a smaller (n ≈ 7,500) individual purchase panel of food bought and eaten 'on the go'. We conducted cross-sectional analyses comparing purchases of common checkout foods in 2016-2017 from supermarkets with and without checkout food policies. There were 76.4% (95% confidence interval 48.6%-89.1%) fewer annual purchases of less-healthy common checkout foods from supermarkets with versus without checkout food policies. The main limitations of the study are that we do not know where in the store purchases were selected and cannot determine the effect of changes in purchases on consumption. Other interventions may also have been responsible for the results seen. There is a potential impact of checkout food polices on purchases. Voluntary supermarket-led activities may have public health benefits.

Background The workplace is an important determinant of health that people are exposed to for the first-time during adolescence or early adulthood. This study investigates how diet, physical activity, and sleep change as people aged 16–30 years transition into work and whether this varies for different individuals and job types. Methods Multilevel linear regression models assessed changes in fruit and vegetable intake, sleep duration, and physical activity among 3,302 UK Household Longitudinal Study (UKHLS) participants aged 16–30 years, who started work for the first time between 2015 and 2023. In line with interrupted time series analysis, models assessed behavioural trends in the period before starting work, the immediate effect of starting work, and changes in behaviour over time after employment. Stratified analyses examined differences by selected individual and job characteristics, adjusted for covariates. All analyses were conducted in R v.4.3.2. Results Sleep duration was stable over the years before and after starting work, but starting work was associated with an immediate reduction in sleep duration ( β -9.74 [95% CI:-17.32 to -2.17 min/night). Physical activity, measured in Metabolic Equivalent Tasks (METs), increased immediately after starting work ( β =  113.3, [95% CI: 80.49 to 146.11] MET-min/day), but subsequently decreased over time after starting work ( β= -26.7, [95% CI: -40.75 to -12.66] MET-min/day/year). The increase in physical activity was greater among males, among those with no degree and among those starting lower socioeconomic classification jobs. Starting a “work from home” job had an immediate negative effect on physical activity ( β= -126.42 [95% CI: -264.45 to 11.61] MET-min/day), whereas those who worked at their employer’s premises showed an initial increase ( β =  128.81 [95% CI: 89.46 to 168.16] MET-min/day). Starting work had little influence on fruit and vegetable consumption. Conclusions This is the first study to examine how diet, physical activity, and sleep in young adults change as they start employment in the UK. Starting work is associated with decreased sleep time and increased physical activity, with differences based on sociodemographic and job characteristics. Future research should consider these potential influences of the work environment when developing interventions to promote healthy behaviour in the workplace.