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A Time‐Symmetric Self‐Normalization Approach for Inference of Time Series
Author(s) -
Lavitas Liliya,
Zhang Ting
Publication year - 2018
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.12303
Subject(s) - mathematics , normalization (sociology) , inference , centralizer and normalizer , series (stratigraphy) , asymmetry , algorithm , combinatorics , computer science , artificial intelligence , paleontology , physics , quantum mechanics , sociology , anthropology , biology
Self‐normalization has been celebrated as an alternative approach for inference of time series because of its ability to avoid direct estimation of the nuisance asymptotic variance. However, when being applied to quantities other than the mean, the conventional self‐normalizer typically exhibits certain degrees of asymmetry, an undesirable feature especially for time‐reversible processes. This paper considers a new self‐normalizer for time series, which (i) provides a time‐symmetric generalization to the conventional self‐normalizer, (ii) is able to automatically reduce to the conventional self‐normalizer in the mean case where the latter is already time‐symmetric to yield a unified inference procedure, and (iii) possibly leads to narrower confidence intervals when compared with the conventional self‐normalizer. For the proposed time‐symmetric self‐normalizer, we establish the asymptotic theory for its induced inference procedure and examine its finite sample performance through numerical experiments.