Robust M-Estimation for Additive Single-Index Cointegrating Time Series Models

Chaohua Dong (), Jiti Gao, Bin Peng () and Yundong Tu ()

No 2/23, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: Robust M-estimation uses loss functions, such as least absolute deviation (LAD), quantile loss and Huber's loss, to construct its objective function, in order to for example eschew the impact of outliers, whereas the difficulty in analysing the resultant estimators rests on the nonsmoothness of these losses. Generalized functions have advantages over ordinary functions in several aspects, especially generalized functions possess derivatives of any order. Generalized functions incorporate local integrable functions, the so-called regular generalized functions, while the so-called singular generalized functions (e.g. Dirac delta function) can be obtained as the limits of a sequence of sufficient smooth functions, so-called regular sequence in generalized function context. This makes it possible to use these singular generalized functions through approximation. Nevertheless, a significant contribution of this paper is to establish the convergence rate of regular sequence to nonsmooth loss that answers a call from the relevant literature. For parameter estimation where objective function may be nonsmooth, this paper first shows as a general paradigm that how generalized function approach can be used to tackle the nonsmooth loss functions in Section two using a very simple model. This approach is of general interest and applicability. We further use the approach in robust M-estimation for additive single–index cointegrating time series models; the asymptotic theory is established for the proposed estimators. We evaluate the finite–sample performance of the proposed estimation method and theory by both simulated data and an empirical analysis of predictive regression of stock returns.

Keywords: additive single index models; generalized function; nonstationary time series; quadratic approximation; regular function sequence; robust M–estimation (search for similar items in EconPapers)
JEL-codes: C13 C22 G14 (search for similar items in EconPapers)
Pages: 53
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.monash.edu/business/ebs/research/publications/ebs/2023/wp02-2023.pdf (application/pdf)

Related works:
Working Paper: Robust M-Estimation for Additive Single-Index Cointegrating Time Series Models (2023)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:msh:ebswps:2023-2

Ordering information: This working paper can be ordered from
http://business.mona ... -business-statistics

Access Statistics for this paper

More papers in Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics PO Box 11E, Monash University, Victoria 3800, Australia. Contact information at EDIRC.
Bibliographic data for series maintained by Professor Xibin Zhang ().