Surveillance of the covariance matrix of multivariate nonlinear time series

In this paper, sequential procedures for the surveillance of the covariance matrices of multivariate nonlinear time series are introduced. Two different types of control charts are proposed. The first type is based on the exponential smoothing of each component of a local measure for the covariances. The control statistic is equal to the Mahalanobis distance of this quantity with its in-control mean. In our second approach, the Mahalanobis distance is first determined and after that it is exponentially smoothed. We discuss three examples of local measures.

Several properties of the proposed schemes are discussed assuming the target process to be generated by a multivariate GARCH(1, 1) model. The generalization to the family of spherical distributions allows the modelling of frequently observed fat tails in financial data. Some results of an extensive Monte Carlo simulation study are provided in order to judge the performance of the presented control schemes. As a performance measure we use the average run length. An empirical example illustrates the importance of the fast detection of the changes in the covariance structure of the returns of financial assets.     

Simultaneous Canonization of Linear Models

Canonical form plays a similar role in linear models to spectral decomposition in matrix analysis. Let X = (X ₁,…, X _n )′ be a random vector with expectation Aβ and the variance–covariance matrix σV, where V is positive definite and let rank(A) = r. Then there exists a nonsingular linear transformation from X to T = (T ₁,…, T _n )′, such that ET _i  = η _i , for i = 1,…, r and zero for i > r, while cov(T _i , T _j ) = δ _ij σ. This canonical form, introduced by Ko?odziejczyk (1935 Ko?odziejczyk , S. ( 1935 ). On an important class of statistical hypotheses . Biometrika 27 : 161 – 190 .[Crossref] , [Google Scholar]), was used, among others, by Scheffé (1959 Scheffé , H. ( 1959 ). Analysis of Variance . New York : Wiley . [Google Scholar]) and by Lehmann (1959, 1986 Lehmann , E. L. (1959, 1986 ). Testing Statistical Hypotheses . New York : Wiley . [Google Scholar]). This technique is extended here for arbitrary (possibly singular) V and for simultaneous canonization of two models of this type.     

Some Remarks about Robust Estimation of the Scale Parameter in Weighted Models

Using Zieliński's (1977 Zieliński , R. ( 1977 ). Robustness: a quantitative approach . Bull. Acad. Polon. Sci., Ser. Sci. Math. Astronom. Phys. 25 : 1281 – 1286 . [Google Scholar]) concept of robustness, B?a?ej (2007 B?a?ej , P. ( 2007 ). Robust estimation of the scale and weighted distributions . Appl. Math. (Warsaw) 34 : 39 – 45 . [Google Scholar]) obtained the uniformly most bias-robust estimates (UMBREs) of the scale parameter for some statistical models, in a class of linear functions of order statistics. Violations of the models are generated by weight functions. In this article the UMBRE of the scale parameter, based on order statistics, a more general weighted model is derived. Extension of a result of B?a?ej (2007 B?a?ej , P. ( 2007 ). Robust estimation of the scale and weighted distributions . Appl. Math. (Warsaw) 34 : 39 – 45 . [Google Scholar]) is given.     

On the E-optimality of complete block designs under a mixed interference model

In experiments in which the response to a treatment can be affected by other treatments, the interference model with neighbor effects is usually used. It is known that circular neighbor balanced designs (CNBDs) are universally optimal under such a model if the neighbor effects are fixed (Druilhet, 1999) or random (4 and 7). However, such designs cannot exist for every combination of design parameters. In the class of block designs with the same number of treatments as experimental units per block, a CNBD cannot exist if the number of blocks, b  , is equal to p(t−1)±1$p(t-1)\pm 1$, where p is a positive integer and t is the number of treatments. Filipiak et al. (2008) gave the structure of the left-neighboring matrix of E-optimal complete block designs with p  =1 under the model with fixed neighbor effects. The purpose of this paper is to generalize E-optimality results for designs with p∈N$p\in \mathbb{N}$ assuming random neighbor effects.     

Social class,social networks and variety of weak and strong practices

Most research on the structural foundations of cultural consumption views tastes and practices as a better or worse emanation of social class or status. In contrast, this paper shows that cultural consumption is also embedded in a larger system of social networks. Not only does it examine whether having more diversified personal network translates into being involved in a wider range of cultural activities (omnivorousness), it also tests whether holding networks of different strength corresponds with different levels of cultural engagement (strong vs. weak). Based on the survey data collected in Poland in 2017, the analyses yield three main findings. First, cultural consumption continues to reflect social class divisions and is a potential mechanism for social exclusion. Second, network diversity is associated with cultural variety independently of class position. Third, the number of weak ties people hold is more strongly associated with the number of “weak” practices (that is practices of less frequency) and the number of strong ties is positively associated with the number of strong practices (voraciousness). These findings are discussed in terms of balance theory, interactional foci and weak versus strong culture. The implications of the article are that omnivorism both signifies class boundaries and indicates participation in different network structures.     

Notes and Communications REPLANNING FREQUENCIES FOR MASTER PRODUCTION SCHEDULES

Updating production plans typically is achieved by rolling the planning horizon forward one period at a time, each time including the latest information in order to determine the best course of action to pursue in the present period. Theoretical planning-horizon studies have identified the conditions by which the production decisions in the current and some specified number of future periods remain optimal given some set of future demands. Motivated by these findings, this study addresses the replanning frequency in a hierarchical production planning problem where no planning-horizon theorems are available. In this problem the aggregate production plan and the master production schedule are linked by a rolling-horizon practice. Empirical experimentation indicates that under certain cost and demand conditions the master production schedule need not be updated every period. If a schedule does not need to be updated for several periods, the schedule for these periods can be frozen to provide stability for planning components at lower levels in the bill of material of the products. The results of this study thus provide some reference for the determination of the frozen portion of the master production schedule.     

Transnational families: The experiences of Polish stayers from a lifelong perspective

In migration research, the voice is usually given to those who move, but in this article, those who stay are at the centre of attention. The study aims to present the stayers’ practices of everyday life in transnational families in an attempt to highlight the experience of staying and understand the stayers’ role in the migration project. The study is based on semi-structured life story interviews conducted in 2020 with people who in the 1980s stayed in the northeastern part of Poland when their relatives migrated internationally. In the almost four-decade perspective, staying appears as a powerful condition and an active process, closely interrelated with migration. Also, the migration project does not appear dependent so much on the range and availability of communication technologies – limited in the 1980s – but on transnational families’ engagement in that project and desire to accomplish it.     

Facing arrhythmia. Reconstructing time in the pandemic by the metropolitan creative classes in Poland

This paper shows how the metropolitan creative classes in Poland reacted to the changes in the organization of everyday life caused by the COVID-19 pandemic, especially its temporality and rhythmicity. The pandemic and lockdowns reorganized previous ways of experiencing and managing time. Based on our empirical research and research by other scholars, we have identified some of the most common disruptions of pandemic temporality. However, a vital element of the article is to specify how the social category we studied dealt with these disruptions. In doing so, we show that the response to the breakdown of the previous order of everyday life was to restore a sense of stability actively. We were also interested in the possible, also negative consequences of the findings for the social category under study. The empirical basis for the article are in-depth interviews conducted during the fourth phase of the ongoing research project [title anonymized], which began during the first weeks of the lockdown in Poland.     

Quality Management and Sustainable Development in Local Communes – Evidence from Poland

Public Organization Review - Sustainable development is usually investigated from a global or national rather than a regional or local perspective. However, it is local communes that decide on the...     

Parallel-machine scheduling of jobs with mixed job-, machine- and position-dependent processing times

Journal of Combinatorial Optimization - We consider a number of parallel-machine scheduling problems in which jobs have variable processing times. The actual processing time of each job is...