By Philip H. Franses, Richard Paap
An insightful and up to date research of using periodic types within the description and forecasting of financial info. Incorporating contemporary advancements within the box, the authors examine such parts as seasonal time sequence; periodic time sequence versions; periodic integration; and periodic integration; and peroidic cointegration. The research from the inclusion of many new empirical examples and effects.
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So far there is, however, no systematic theory of the dynamical aspects of the information contained in the EEG; first attempts to formulate such a theory on the basis of nonlinear dynamics were proposed 24Consequently a complete EEG recording is a multivariate time series; usually the univariate time series corresponding to the individual recording sites are called channels. 38 Dynamical systems, time series and attractors during the eighties of the 20th century. We will discuss these developments in chapter 12 in more detail; there and in chapter 13 we will also extend our discussion of the most relevant properties of EEG time series.
Basically two different kinds of noise in measured time series are distinguished [250]: • Additive measurement noise: The underlying system is completely deterministic and the noise is simply added to the true output of this system, without interfering with the dynamics of the system. The source of this kind of noise is located somewhere in the measurement apparatus; imprecisions due to finite precision of the A/D-conversion can also be regarded as a source of additive noise (sometimes known as quantisation noise).
We can think of p as a "probability mass" distributed somehow in state space, such that the total amount of this measure in state space equals unity. 3) where S is any subset of state space with nonvanishing volume. In the example of a limit cycle the invariant density is zero everywhere in state space except on the limit cycle; consequently p(l;) displays a non-continuous structure as a function of t;, at least for certain directions. More precisely p(l;) should not be regarded as a proper function, but rather as a distribution (a generalised function like the 6-function).
