All physical processes are nonstationary. When analyzing time series, it should be remembered that nature can be amazingly complex and that many of the theoretical constructs used in stochastic process theory, for example, linearity, ergodicity, normality, and particularly stationarity, are mathematical fairy tales. There are no stationary time series in the strict mathematical sense; at the ve...

Abstract Nonstationary fractional-order systems represent a new class of dynamic characterized by time-varying parameters as well memory effect and hereditary properties. Differential game described system linear nonstationary differential equations fractional order is treated in the paper. The involves two players, one which tries to bring system’s trajectory terminal set, whereas other strive...

The onset of stochastic oscillations in gyrotrons is studied by means of the self-consistent theory describing nonstationary processes. Complicated alternating sequences of regions of stationary, automodulation, and chaotic oscillations are found in the plane of the generalized gyrotron variables: cyclotron resonance mismatch and dimensionless current. The results of the investigations are impo...

∗Preliminary Comments are welcome. Paper written for the Handbook of Financial Econometrics edited by Yacine Aı̈t-Sahalia and Lars Peter Hansen. We thank Darrell Duffie, Benoit Perron and Mark Watson for discussions and Seoyeon Lee for research assistance. Bandi acknowledges financial support from the IBM Corporation Faculty Research Fund at the University of Chicago. Phillips thanks fhe NSF for...

This paper deals with the problem of classiication of nonstationary signals using signatures which are essentially independent of the signal length. This independence is a requirement in common classiication problems like stratigraphic analysis, which was a motivation for this research. We achieve this objective by developing the notion of an approximation to the Continuous Wavelet Transform (C...