The degree of dependence inherent in a dataset, either in the time series domain or in multivariate analysis, commonly gives rise to two distinct types of processes: stationary and non-stationary (unit root). This thesis focuses on detecting the underlying degree of dependence in a certain dataset of unit (1; T) or higher (N; T) dimension. The rst part of the thesis aims at identifying the intrinsic strength of structure in a large dimensional setup. It is known that all informa- tion needed for this purpose is contained in the column-sum norm of the variance-covariance matrix of the dataset. This approaches in nity at rate N , 0 < 1. The strength of structure can then be determined by the value of . On this basis, a summary statistic is constructed as a means of quantifying this parameter . The resulting non-linear least squares estimator is consistent for relatively small N=T ratios. The accuracy of the statistic is further checked by use of a bootstrap procedure. An application to three major stock market indices is also incorporated. The second part of the thesis introduces alternative approaches to testing the hypothesis that a certain time series contains a unit root. Contrary to traditional unit root tests that assume speci c forms of de- 4 pendence in the errors of their stationary alternatives, it is argued that properties of partial sums can be used to provide limiting distributions for a wide range of stationary processes, with short or long memory. A rescaled variance type test making use of partial sums provides a simpler procedure for assessing the existence of a unit root in a time series with reasonable size and power. A further approach examined entails making use of the properties of the periodogram at low frequen- cies. Again a unit root/stationarity test based on this methodology is simple to implement and gives satisfactory results for size and power.
- Theses