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Modelling Long‐memory Time Series with Finite or Infinite Variance: a General Approach
Author(s) -
Leipus Remigijus,
Viano MarieClaude
Publication year - 2000
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 - 10.1111/1467-9892.00173
Subject(s) - mathematics , series (stratigraphy) , long memory , covariance , connection (principal bundle) , class (philosophy) , convergence (economics) , pure mathematics , statistics , econometrics , volatility (finance) , paleontology , geometry , biology , economic growth , artificial intelligence , computer science , economics
We present a class of generalized fractional filters which is stable with respect to series and parallel connection. This class extends the so‐called fractional ARUMA and fractional ARMA filters previously introduced by e.g. Goncalves (1987) and Robinson (1994) and recently studied by Giraitis and Leipus (1995) and Viano et al. (1995). Conditions for the existence of the induced stationary S α S and L 2 processes are given. We describe the asymptotic dependence structure of these processes via the codifference and the covariance sequences respectively. In the L 2 case, we prove the weak convergence of the normalized partial sums.