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Uniform Limit Theory for Stationary Autoregression
Author(s) -
Giraitis Liudas,
Phillips Peter C. B.
Publication year - 2006
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/j.1467-9892.2005.00452.x
Subject(s) - autoregressive model , mathematics , limit (mathematics) , gaussian , econometrics , convergence (economics) , star model , mathematical analysis , statistics , autoregressive integrated moving average , time series , economics , physics , quantum mechanics , economic growth
. First order autoregression is shown to satisfy a limit theory which is uniform over stationary values of the autoregressive coefficient ρ = ρ n ∈ [0, 1) provided (1 − ρ n ) n → ∞. This extends existing Gaussian limit theory by allowing for values of stationary ρ that include neighbourhoods of unity provided they are wider than O ( n −1 ), even by a slowly varying factor. Rates of convergence depend on ρ and are at least but less than n . Only second moments are assumed, as in the case of stationary autoregression with fixed ρ .