Discrimination of AR,MA and ARMA time series models

The problem of discrimination between two stationary ARMA time series models is considered, and in particular AR(p), MA(p), ARMA(1,1) models. The discriminant based on the likelihood ration leads to a quadratic form that is generally too complicated to evaluated explicitly. The discriminant can be expressed approximately as a linear combination of independent chi–squared random varianles each with one degree of freedom, the coefficients, of which are eigenvalues of cumbersome matrices. An analytical solution which gives the coefficients approximately is suggested.     

Analysis of stock market indices through multidimensional scaling

Two similarity measures are employed to compare historic stock market indices over time. The more traditional Euclidean similarity is employed to provide a reference. As a comparison, dynamic time warping is introduced as a similarity measure. Multidimensional scaling is employed to compare these dissimilarities on 15 financial indices sampled daily over a 10-year period. In addition to investigating the whole period, 1-year tranches are also considered. This analysis is compared to a recent study of Machado et al. [Analysis of stock market indices through multidimensional scaling, Commun. Nonlinear Sci. Numer. Simul. 16(12) (2011), pp. 4610–4618], who examined these same indices using correlation as a similarity measure. It is suggested that this approach may be problematic. Doubt is also cast on the efficacy of the ‘histogram’ similarity they also propose.     

Stepchildren's Views About Former Step‐Relationships Following Stepfamily Dissolution

Remarriages end in divorce more often than first marriages, so many stepchildren experience multiple parental divorces and the potential loss of significant family ties. Although there is substantial research on parent–child relationships after divorce, little is known about stepparent–stepchild relationships after divorce. Therefore, the authors conducted a grounded theory study of 41 adults who had undergone a stepfamily dissolution to explore their experiences with former stepparents. Postdivorce relationships with former stepparents are a function of whether stepchildren thought of their former stepparents as kin. Postdivorce step‐relationships were based on whether the stepchild had claimed the stepparent as kin, had once claimed them as kin but disclaimed them after the divorce, or had never claimed them as family members (unclaimed stepparents). Emotional reactions to parental divorce, patterns of support or resource exchanges, and parental encouragement or discouragement for continuing step‐relationships were identified. Implications for families, practitioners, and researchers are discussed.     

‘Unfit for reform or punishment’: mental disorder and discipline in Liverpool Borough Prison in the late nineteenth century

This article examines how Liverpool Borough Prison, opened in 1855 as one of the largest local prisons in England to adopt the separate system, categorized and dealt with mental distress and disorder amongst its prison population in the late nineteenth century. High prison committal rates in Liverpool, alongside high levels of recidivism, especially among female prisoners, led to severe overcrowding and encouraged a harsh disciplinary regime. Exacerbated by the poor physical and mental condition of the prisoners, this produced a challenging environment for maintaining the separate system of confinement and prisoners’ mental well-being. While official figures for the rates of mental disorder in local prisons are not readily available, Liverpool Prison’s diverse and under-exploited archives and official reports indicate that insanity caused prison officials and visiting justices great concern, and many prisoners were declared unfit for the rigours of prison discipline. Our article explores the implications of the ever more punitive, deterrent and physically taxing penal policy implemented in the late nineteenth century on the minds of prisoners. Despite the heavy toll on prisoners’ mental well-being, such cases were often retained by prison medical officers reluctant to acknowledge the failure of the prison to deter, reform and redeem.