Details
| Original language | English |
|---|---|
| Title of host publication | IX Hotine-Marussi Symposium on Mathematical Geodesy |
| Subtitle of host publication | Proceedings of the Symposium in Rome, June 18 – 22, 2018 |
| Editors | Pavel Novák, Mattia Crespi, Nico Sneeuw, Fernando Sansò |
| Place of Publication | Cham |
| Publisher | Springer Verlag |
| Pages | 183-189 |
| Number of pages | 7 |
| Edition | 1. |
| ISBN (Electronic) | 978-3-030-54267-2 |
| ISBN (Print) | 978-3-030-54266-5, 978-3-030-54269-6 |
| Publication status | Published - 22 Mar 2019 |
Publication series
| Name | International Association of Geodesy Symposia |
|---|---|
| Volume | 151 |
| ISSN (Print) | 0939-9585 |
| ISSN (Electronic) | 2197-9359 |
Abstract
The real-valued, time-discrete, one-dimensional and covariance-stationary autoregressive process of order p (AR(p) process) is a frequently used stochastic process for instance to model highly correlated measurement series with constant sampling rate given by satellite missions. In this contribution, a reformulation of an AR(p) to a moving average process with infinite order is presented. The Magic Square of this reformulated process can be seen as an alternative representation of the four quantities in time and frequency, which are usually given in the literature. The results will be evaluated by discussing an AR(1) process as example
Keywords
- Autoregressive process, Moving average process, Spectral analysis, Stochastic process, Time series analysis
ASJC Scopus subject areas
- Earth and Planetary Sciences(all)
- Computers in Earth Sciences
- Earth and Planetary Sciences(all)
- Geophysics
Cite this
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IX Hotine-Marussi Symposium on Mathematical Geodesy: Proceedings of the Symposium in Rome, June 18 – 22, 2018. ed. / Pavel Novák; Mattia Crespi; Nico Sneeuw; Fernando Sansò. 1. ed. Cham: Springer Verlag, 2019. p. 183-189 (International Association of Geodesy Symposia ; Vol. 151).
Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research › peer review
}
TY - CHAP
T1 - Non-recursive representation of an autoregressive process within the Magic Square
AU - Loth, Ina
AU - Kargoll, Boris
AU - Schuh, Wolf-Dieter
PY - 2019/3/22
Y1 - 2019/3/22
N2 - A stochastic process can be represented and analysed by four different quantities in the time and frequency domain: (1) the process itself, (2) its autocovariance function, (3) the spectral representation of the stochastic process and (4) its spectral distribution or the spectral density function, if it exits. These quantities and their relationships can be clearly represented by the “Magic Square”, where the quantities build the corners of this square and the connecting lines indicate the transformations into each other.The real-valued, time-discrete, one-dimensional and covariance-stationary autoregressive process of order p (AR(p) process) is a frequently used stochastic process for instance to model highly correlated measurement series with constant sampling rate given by satellite missions. In this contribution, a reformulation of an AR(p) to a moving average process with infinite order is presented. The Magic Square of this reformulated process can be seen as an alternative representation of the four quantities in time and frequency, which are usually given in the literature. The results will be evaluated by discussing an AR(1) process as example
AB - A stochastic process can be represented and analysed by four different quantities in the time and frequency domain: (1) the process itself, (2) its autocovariance function, (3) the spectral representation of the stochastic process and (4) its spectral distribution or the spectral density function, if it exits. These quantities and their relationships can be clearly represented by the “Magic Square”, where the quantities build the corners of this square and the connecting lines indicate the transformations into each other.The real-valued, time-discrete, one-dimensional and covariance-stationary autoregressive process of order p (AR(p) process) is a frequently used stochastic process for instance to model highly correlated measurement series with constant sampling rate given by satellite missions. In this contribution, a reformulation of an AR(p) to a moving average process with infinite order is presented. The Magic Square of this reformulated process can be seen as an alternative representation of the four quantities in time and frequency, which are usually given in the literature. The results will be evaluated by discussing an AR(1) process as example
KW - Autoregressive process
KW - Moving average process
KW - Spectral analysis
KW - Stochastic process
KW - Time series analysis
UR - http://www.scopus.com/inward/record.url?scp=85067368054&partnerID=8YFLogxK
U2 - 10.1007/1345_2019_60
DO - 10.1007/1345_2019_60
M3 - Contribution to book/anthology
SN - 978-3-030-54266-5
SN - 978-3-030-54269-6
T3 - International Association of Geodesy Symposia
SP - 183
EP - 189
BT - IX Hotine-Marussi Symposium on Mathematical Geodesy
A2 - Novák, Pavel
A2 - Crespi, Mattia
A2 - Sneeuw, Nico
A2 - Sansò, Fernando
PB - Springer Verlag
CY - Cham
ER -