Application of wavelets to the study of political history

\The idea that social processes develop in a cyclical manner is somewhat like a `Lorelei'. Researchers are lured to it because of its theoretical promise, only to become entangled in (if not wrecked by) messy problems of empirical inference. The reasoning leading to hypotheses of some kind of cycle is often elegant enough, yet the data from repeated observations rarely display the supposed cyclical pattern. (...) In addition, various `schools' seem to exist which frequently arrive at di erent conclusions on the basis of the same data." (van der Eijk and Weber 1987:271). Much of the empirical controversies around these issues arise because of three distinct problems: the coexistence of cycles of di erent periodicities, the possibility of transient cycles and the existence of cycles without xed periodicity. In some cases, there are no reasons to expect any of these phenomena to be relevant. Seasonality caused by Christmas is one such example (Wen 2002). In such cases, researchers mostly rely on spectral analysis and Auto-Regressive Moving-Average (ARMA) models to estimate the periodicity of cycles.1 However, and this is particularly true in social sciences, sometimes there are good theoretical reasons to expect irregular cycles. In such cases, \the identi cation of periodic movement in something like the vote is a daunting task all by itself. When a pendulum swings with an irregular beat (frequency), and the extent of the swing (amplitude) is not constant, mathematical functions like sine-waves are of no use."(Lebo and Norpoth 2007:73) In the past, this di culty has led to two di erent approaches. On the one hand, some researchers dismissed these methods altogether, relying on informal alternatives that do not meet rigorous standards of statistical inference. Goldstein (1985 and 1988), studying the severity of Great power wars is one such example. On the other hand, there are authors who transfer the assumptions of spectral analysis (and ARMA models) into fundamental assumptions about the nature of social phenomena. This type of argument was produced by Beck (1991) who, in a reply to Goldstein (1988), claimed that only \ xed period models are meaningful models of cyclic phenomena".We argue that wavelet analysis|a mathematical framework developed in the mid-1980s (Grossman and Morlet 1984; Goupillaud et al. 1984) | is a very viable alternative to study cycles in political time-series. It has the advantage of staying close to the frequency domain approach of spectral analysis while addressing its main limitations. Its principal contribution comes from estimating the spectral characteristics of a time-series as a function of time, thus revealing how its di erent periodic components may change over time. The rest of article proceeds as follows. In the section \Time-frequency Analysis", we study in some detail the continuous wavelet transform and compare its time-frequency properties with the more standard tool for that purpose, the windowed Fourier transform. In the section \The British Political Pendulum", we apply wavelet analysis to essentially the same data analyzed by Lebo and Norpoth (2007) and Merrill, Grofman and Brunell (2011) and try to provide a more nuanced answer to the same question discussed by these authors: do British electoral politics exhibit cycles? Finally, in the last section, we present a concise list of future directions.

Our place in history: young feminists at the margins

Feminisms in Portugal, as elsewhere, have been shaped historically. From the revolutions of the late 19th and early 20th centuries, which ended monarchy and established a republican system, women have taken a stand. In the late 1970s, after 48 years of dictatorship during which feminist issues were effectively silenced, feminist groups began to appear in Portugal. It was then, in 1976, that UMAR (Unia˜o de Mulheres Alternativa e Resposta [‘Union of Women for Alternatives and Answers’]) began its fight against discrimination and violence against women.

Childhood history of abuse and child abuse potential: the role of parent’s gender and timing of childhood abuse

It has been suggested that being physically abused leads to someone becoming a perpetrator of abuse which could be associated to parents' gender, timing of the physical abuse and specific socio-demographic variables. This study aims to investigate the role the parents' gender, timing of childhood abuse and socio-demographic variables on the relationship between parents' history of childhood physical abuse and current risk for children. The sample consisted of 920 parents (414 fathers, 506 mothers) from the Portuguese National Representative Study of Psychosocial Context of Child Abuse and Neglect who completed the Childhood History Questionnaire and the Child Abuse Potential Inventory. The results showed that fathers had lower current potential risk of becoming physical abuse perpetrators with their children than mothers although they did not differed in their physical victimization history. Moreover, the risk was higher in parents (both genders) with continuous history of victimization than in parents without victimization. Prediction models showed that for fathers and mothers separately similar socio-demographic variables (family income, number of children at home, employment status and marital status) predicted the potential risk of becoming physical abuses perpetrators. Nevertheless, the timing of victimization was different for fathers (before 13 years old) and mothers (after 13 years old). Then our study targets specific variables (timing of physical abuse, parents' gender and specific socio-demographic variables), which may enable professionals to select groups of parents at greater need of participating in abuse prevention programs.