We derive new stationarity results for derivative-free, generating set search methods for linearly constrained optimization. We show that a particular measure of stationarity is of the same order as the step length at an identifiable subset of the iterations. Thus, even in the absence of explicit knowledge of the derivatives of the objective function, we still have information about stationarit...

BACKGROUND Understanding complex brain networks using functional magnetic resonance imaging (fMRI) is of great interest to clinical and scientific communities. To utilize advanced analysis methods such as graph theory for these investigations, the stationarity of fMRI time series needs to be understood as it has important implications on the choice of appropriate approaches for the analysis of ...

In this contribution we generalize the test of sphericity as a test of stationarity for time-series. The sphericity statistics is in our case a measure of distance between the empirical correlations calculated on two contiguous segments of the same process. We prove that under the hypothesis of stationarity the logarithm of the sphericity converges in distribution to a quadratic form in a multi...

This paper provides a strict stationarity proof for general nonlinear regression models. In particular, it shows the existence of a strictly stationary solution to first order dynamic nonlinear models when the innovations are only assumed to satisfy a strict stationarity or strong mixing condition. The results of this paper can be applied to show the strict stationarity of threshold unit root m...

This paper proposes a new approach to measure dependences in multivariate financial data. Data in finance and insurance often cover a long time period. Therefore, the economic factors may induce some changes inside the dependence structure. Recently, two methods using copulas have been proposed to analyze such changes. The first approach investigates changes inside copula’s parameters. The seco...

This paper proposes a new approach to measure dependences in multivariate financial data. Data in finance and insurance often cover a long time period. Therefore, the economic factors may induce some changes inside the dependence structure. Recently, two methods using copulas have been proposed to analyze such changes. The first approach investigates changes inside copula’s parameters. The seco...

We discuss the components of validating credit default models with a focus on potential challenges to making inferences from validation under real-world conditions. We structure the discussion in terms of: (a) the quantities of interest that may be measured (calibration and power) and how they can result in misleading conclusions if not taken in context; (b) a methodology for measuring these qu...

This study re-examines the validity of Purchasing Power Parity (PPP) by focusing on the real effective exchange rates (REERs) for the post-Bretton Woods period, using newly developed unit root tests that account for both nonlinearity and smooth temporary multiple breaks in the data. The tests are applied to the REERs of 23 developed countries and are able to reject the null hypothesis of a unit...

This paper contributes new evidence relating to the hypothesis that there has been convergence between certain male and female offences over time. Using time-series data for adults charged with offences in Canada over the period 1983 to 2000, we conduct several formal econometric tests of the convergence hypothesis. This study allows for the non-stationarity of the data; structural breaks in so...