UID:
almafu_9961652654402883
Umfang:
1 online resource (XXII, 500 p.)
ISBN:
9783111325033
Serie:
De Gruyter Studies in Mathematics , 98
Inhalt:
This book provides a self-contained account of continuous-parameter time series, starting with second-order models. Integration with respect to orthogonal increment processes, spectral theory and linear prediction are treated in detail. Lévy-driven models are incorporated, extending coverage to allow for infinite variance, a variety of marginal distributions and sample paths having jumps. The necessary theory of Lévy processes and integration of deterministic functions with respect to these processes is developed at length. Special emphasis is given to the analysis of continuous-time ARMA processes.
Anmerkung:
Frontmatter --
,
Preface --
,
Contents --
,
List of symbols and abbreviations --
,
1 Time series --
,
2 Hilbert spaces --
,
3 Second-order stochastic processes --
,
4 Orthogonal increment processes --
,
5 Spectral theory of MSC stationary processes --
,
6 Mean-square linear prediction of weakly stationary processes --
,
7 Second-order CARMA processes --
,
8 Infinitely divisible distributions --
,
9 The Lévy–Khintchine formula for infinitely divisible distributions --
,
10 Lévy processes --
,
11 Distributional properties of Lévy processes and the strong law of large numbers --
,
12 Lévy processes as random elements and their jump structure --
,
13 The Lévy–Itô decomposition of Lévy processes and consequences --
,
14 Examples of Lévy processes --
,
15 Integration of deterministic functions with respect to Lévy processes --
,
16 The distribution of the integral and consequences --
,
17 Ornstein–Uhlenbeck processes --
,
18 Lévy-driven CARMA processes: definition, existence, uniqueness and properties --
,
19 QML estimation for CARMA processes --
,
A Appendix: R Programs for generation of Lévy increments --
,
Bibliography --
,
Index
,
Issued also in print.
,
In English.
Weitere Ausg.:
ISBN 9783111325200
Weitere Ausg.:
ISBN 9783111324999
Sprache:
Englisch
DOI:
10.1515/9783111325033
URL:
https://doi.org/10.1515/9783111325033
URL:
https://www.degruyter.com/isbn/9783111325033
