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DEFINITIONS AND REPRESENTATIONS OF MULTIVARIATE LONG‐RANGE DEPENDENT TIME SERIES
Author(s) -
Kechagias Stefanos,
Pipiras Vladas
Publication year - 2015
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12086
Subject(s) - autocovariance , multivariate statistics , mathematics , series (stratigraphy) , range (aeronautics) , autoregressive model , extension (predicate logic) , time series , econometrics , statistics , mathematical analysis , fourier transform , computer science , paleontology , materials science , composite material , biology , programming language
The notion of multivariate long‐range dependence is reexamined here from the perspectives of time and spectral domains. The role of the so‐called phase parameters is clarified and stressed throughout. In particular, examples of causal (one‐sided) representations of multivariate long‐range dependent time series with general‐phase parameters are constructed. A multivariate extension of the autoregressive fractionally integrated moving‐average series is introduced with explicit formulas for its autocovariance function.