The assessment of the comovement among international stock markets is of key interest, for example, for the international portfolio diversification literature. In this paper, we re-examine such comovement by resorting to a novel approach, wavelet analysis. Wavelet analysis allows one to measure the comovement in the time-frequency space. In this way, one can characterize how international stock returns relate in the time and frequency domains simultaneously, which allows one to provide a richer analysis of the comovement. We focus on Germany, Japan, UK and US and the analysis is done at both the aggregate and sectoral levels.

Nelson and Plosser (1982), in a classic paper, failed to find strong evidence against the null hypothesis of a generating process with a unit autoregressive root for thirteen US macroeconomic time series. Perron (1989) claimed that such evidence was available for a majority of these series if the alternative hypothesis was of trend stationarity with a break in 1929. Zivot and Andrews (1992) treated the break date as endogenous, then finding strong evidence agcainst the null for a minority of these series. Our own analysis extends theirs by permitting a break under the null as well as the alternative hypothesis, and allowing for the sequential nature of the testing. Our empirical findings complete the circle. We find no strong evidence against the unit root hypothesis for any of the thirteen Nelson–Plosser series.

A quasi-maximum likelihood estimator of the break date is analyzed. Consistency of the estimator is demonstrated under very general conditions, provided that the data-generating process is not integrated. However, the asymptotic distribution of the estimator is quite different for time series that are integrated of order one. In that case, when there is no break, the analyst can be spuriously led to the estimation of a break near the middle of the time series.

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The relative attractiveness of cities as places to live determines population movements in or out of them. Understanding the appealing features of a city is fundamental to local governments, particularly for cities facing population decline. Pull and push attributes of cities can include economic aspects, the availability of amenities and psychological constructs, initiating a discussion around which factors are more relevant in explaining migration. However, a pull-push approach has been underexplored in studies of shrinking cities. In the present study, we contribute to the discussion by identifying pull and push factors in Portuguese shrinking cities. Data were collected using a face-to-face questionnaire survey of 701 residents in four shrinking cities: Oporto, Barreiro, Peso da Régua and Moura. Factor analysis and automatic linear modelling were used to analyse the data. Our results support previous findings that the economic activity of a city is the most relevant feature for retaining residents. However, other characteristics specific to each city, especially those related to heritage and natural beauty, are also shown to influence a city's attractiveness as a place to live. The cause of population shrinkage is also found to influence residents' assessments of the pull and push attributes of each city. Furthermore, the results show the relevance of social ties and of place attachment to inhabitants' intention to continue living in their city of residence.