Oracle M‐Estimation for Time Series Models

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 th...

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Bibliographic Details
Published in:Journal of time series analysis 2017-05, Vol.38 (3), p.479-504
Main Author: Giurcanu, Mihai C.
Format: Article
Language:English
Subjects:
block bootstrap
Estimating techniques
M‐estimation
oracle property
Simulation
sparse models
Studies
thresholding
Time series
vector autoregressive time series
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Summary: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.
ISSN:0143-9782
1467-9892
DOI:10.1111/jtsa.12221