Abstract
The Wold decomposition theorem says that under fairly general conditions, a stationary time series has a unique linear causal representation \(\displaystyle{ X_{t} =\sum _{ j=0}^{\infty }\psi _{ j}Z_{t-j},\,t \in \mathbb{Z}, }\) where \(\sum _{j=0}^{\infty }\psi _{j}^{2} <\infty\) and (Z t ) are uncorrelated random variables (r.v’s).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Diggle PJ, Ribeiro PJ (2007) Model-based geostatistics. Springer, New York
Diggle PJ, Moyeed RA, Tawn JA (1998) Model-based geostatistics. Appl Stat 47:299–350. (With discussion)
Heyde CC (1997) Quasi-likelihood and its application: a general approach to optimal parameter estimation. Springer, New York
Macedo ME (2006) Caracterização de Caudais Rio Tejo, Direção de Serviços de Monitorização Ambiental
Nisio M (1960) On polynomial approximation for strictly stationary processes. J Math Soc Jpn 12:207–226
Prado R, West M (2010) Time series: modeling, computation, and inference. Texts in statistical science. Chapman & Hall/CRC, Boca Raton
Priestley MB (1981) Spectral analysis and time series. Academic, London
Tong H (1990) Non-linear time series. Oxford Science Publications, Oxford
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Turkman, K.F., Scotto, M.G., de Zea Bermudez, P. (2014). Introduction. In: Non-Linear Time Series. Springer, Cham. https://doi.org/10.1007/978-3-319-07028-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-07028-5_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07027-8
Online ISBN: 978-3-319-07028-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)