This paper deals with singular perturbation problems for vector fields on 2-dimensional manifolds. “Canard solutions” are solutions that, starting near an attracting normally hyperbolic branch of the singular curve, cross a “turning point” and follow for a while a normally repelling branch of the singular curve. Following the geometric ideas developed by Dumortier and Roussarie in 1996 for the ...

Methods for continuously monitoring business cycles are compared. A turn in a leading index can be used to predict a turn in the business cycle. Three likelihood based methods for turning point detection are compared in detail by using the theory of statistical surveillance and by simulations. One of the methods is a parametric likelihood ratio method. Another includes a non-parametric estimati...

In the prediction of oscillating time series, the interest is in the turning points of successive oscillations rather than the samples themselves. For this purpose a scheme has been proposed; the state space reconstruction is limited to the turning points and the local (nearest neighbor) model is modified in order to predict the turning point magnitudes and times. This approach is extended here...

A Hidden Markov Model (HMM) is used to classify an out of sample observation vector into either of two regimes. This leads to a procedure for making probability forecasts for changes of regimes in a time series, i.e. for turning points. Instead of maximizing a likelihood, the model is estimated with respect to known past regimes. This makes it possible to perform feature extraction and estimati...

Phonetic markedness regarding linguistically relevant tonal patterns (Accent 2, boundary tones) in Central Swedish is discussed. Both tonal markedness and F0 turning points are assumed to be important cues for anticipatory attention to grammatical structure during speech processing. Empirical evidence from neurolinguistic and psycholinguistic experiments for the assumed relation between anticip...

Dating business cycles entails ascertaining economy-wide turning points. Broadly speaking, there are two approaches in the literature. The first approach, which dates to Burns and Mitchell (1946), is to identify turning points individually in a large number of series, then to look for a common date that could be called an aggregate turning point. The second approach, which has been the focus of...