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Consistent estimation and order selection for nonstationary autoregressive processes with stable innovations
Author(s) -
Burridge Peter,
Hristova Daniela
Publication year - 2008
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.1467-9892.2008.00579.x
Subject(s) - autoregressive model , mathematics , star model , selection (genetic algorithm) , consistency (knowledge bases) , distributed lag , ordinary least squares , lag , stability (learning theory) , variance (accounting) , econometrics , convergence (economics) , rate of convergence , setar , statistics , strong consistency , least squares function approximation , autoregressive integrated moving average , time series , computer science , economics , key (lock) , computer network , geometry , accounting , artificial intelligence , machine learning , estimator , economic growth , computer security
. A possibly nonstationary autoregressive process, of unknown finite order, with possibly infinite‐variance innovations is studied. The ordinary least squares autoregressive parameter estimates are shown to be consistent, and their rate of convergence, which depends on the index of stability, α , is established. We also establish consistency of lag‐order selection criteria in the nonstationary case. A small experiment illustrates the relative performance of different lag‐length selection criteria in finite samples.