TY - JOUR
T1 - Modified LASSO estimators for time series regression models with dependent disturbances
AU - Xue, Yujie
AU - Taniguchi, Masanobu
N1 - Funding Information:
The first author would like to thank Mr. Fujimori for helping understand the high dimensional problem-solving idea. The second author thanks supports by Research Institute for Science and Engineering, Waseda University and JSPS Fundings: Kiban(A)(23244011, 15H02061) and Kiban(S)(18H05290).
Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/12
Y1 - 2020/12
N2 - This paper applies the modified least absolute shrinkage and selection operator (LASSO) to the regression model with dependent disturbances, especially, long-memory disturbances. Assuming the norm of different column in the regression matrix may have different order of observation length n, we introduce a modified LASSO estimator where the tuning parameter λ is not a scalar but vector. When the dimension of parameters is fixed, we derive the asymptotic distribution of the modified LASSO estimators under certain regularity condition. When the dimension of parameters increases with respect to n, the consistency on the probability of the correct selection of penalty parameters is shown under certain regularity conditions. Some simulation studies are examined.
AB - This paper applies the modified least absolute shrinkage and selection operator (LASSO) to the regression model with dependent disturbances, especially, long-memory disturbances. Assuming the norm of different column in the regression matrix may have different order of observation length n, we introduce a modified LASSO estimator where the tuning parameter λ is not a scalar but vector. When the dimension of parameters is fixed, we derive the asymptotic distribution of the modified LASSO estimators under certain regularity condition. When the dimension of parameters increases with respect to n, the consistency on the probability of the correct selection of penalty parameters is shown under certain regularity conditions. Some simulation studies are examined.
KW - High dimensional regression
KW - Long-memory disturbances
KW - Modified LASSO
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U2 - 10.1007/s10260-020-00506-w
DO - 10.1007/s10260-020-00506-w
M3 - Article
AN - SCOPUS:85095931114
SN - 1618-2510
VL - 29
SP - 845
EP - 869
JO - Statistical Methods and Applications
JF - Statistical Methods and Applications
IS - 4
ER -