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Oracle M‐Estimation for Time Series Models
Author(s) -
Giurcanu Mihai C.
Publication year - 2017
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.12221
Subject(s) - estimator , mathematics , autoregressive model , series (stratigraphy) , oracle , block (permutation group theory) , consistency (knowledge bases) , thresholding , model selection , statistics , a priori and a posteriori , algorithm , computer science , artificial intelligence , combinatorics , paleontology , geometry , software engineering , image (mathematics) , biology , philosophy , epistemology
We propose a thresholding M‐estimator for multivariate time series. Our proposed estimator has the oracle property that its large‐sample properties are the same as of the classical M‐estimator obtained under the a priori information that the zero parameters were known. We study the consistency of the standard block bootstrap, the centred block bootstrap and the empirical likelihood block bootstrap distributions of the proposed M‐estimator. We develop automatic selection procedures for the thresholding parameter and for the block length of the bootstrap methods. We present the results of a simulation study of the proposed methods for a sparse vector autoregressive VAR(2) time series model. The analysis of two real‐world data sets illustrate applications of the methods in practice.