EconPapers    
Economics at your fingertips  
 

Maximum likelihood estimation of autoregressive models with a near unit root and Cauchy errors

Jungjun Choi () and In Choi ()
Additional contact information
Jungjun Choi: Rutgers University

Annals of the Institute of Statistical Mathematics, 2019, vol. 71, issue 5, No 5, 1142 pages

Abstract: Abstract This paper studies maximum likelihood estimation of autoregressive models of order 1 with a near unit root and Cauchy errors. Autoregressive models with an intercept and with an intercept and a linear time trend are also considered. The maximum likelihood estimator (MLE) for the autoregressive coefficient is $$n^{3/2}$$ n 3 / 2 -consistent with n denoting the sample size and has a mixture-normal distribution in the limit. The MLE for the scale parameter of Cauchy distribution is $$n^{1/2}$$ n 1 / 2 -consistent, and its limiting distribution is normal. The MLEs of the intercept and the linear time trend are $$n^{1/2}$$ n 1 / 2 - and $$n^{3/2}$$ n 3 / 2 -consistent, respectively. It is also shown that the t statistic for the null hypothesis of a unit root based on the MLE has a standard normal distribution in the limit. In addition, finite-sample properties of the MLE are compared with those of the least square estimator (LSE). It is found that the MLE is more efficient than the LSE when the errors have a Cauchy distribution or a distribution which is a mixture of Cauchy and normal distributions. It is also shown that empirical power of the MLE-based t test for a unit root is much higher than that of the Dickey–Fuller t test.

Keywords: Autoregressive model; Near unit root; Cauchy distribution; Maximum likelihood estimator; Infinite variance (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
http://link.springer.com/10.1007/s10463-018-0671-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
Working Paper: Maximum Likelihood Estimation of Autoregressive Models with a Near Unit Root and Cauchy Errors (2016) Downloads
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:spr:aistmt:v:71:y:2019:i:5:d:10.1007_s10463-018-0671-z

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10463/PS2

DOI: 10.1007/s10463-018-0671-z

Access Statistics for this article

Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi

More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().

 
Page updated 2021-10-10
Handle: RePEc:spr:aistmt:v:71:y:2019:i:5:d:10.1007_s10463-018-0671-z