On the Irrelevance of Impossibility Theorems: The Case of the Long-run Variance

Pierre Perron and Ren Linxia
Additional contact information
Ren Linxia: SAS Institute Inc.

Journal of Time Series Econometrics, 2011, vol. 3, issue 3, 34

Abstract: It has been argued that estimating the spectral density function of a stationary stochastic process at the zero frequency (or the so-called long-run variance) is an ill-posed problem so that any estimate will have an infinite minimax risk (e.g., Pötscher 2002). Most often it is a nuisance parameter that is present in the limit distribution of some statistic and one then needs an estimate of it to obtain test statistics that have a pivotal distribution. In this context, we argue that such an impossibility result is irrelevant. We show that, in the presence of the discontinuities that cause the ill-posedness of the estimation problem for the long-run variance, using the true value of the spectral density function at frequency zero leads to tests that have either 0 or 100% size and, hence, lead to confidence intervals that are completely uninformative. On the other hand, tests based on standard estimates of the long-run variance will have well defined limit distributions and, accordingly, be more informative.

Keywords: ill-posed problems; robust inference; HAC estimates; spectral density function at frequency zero (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://doi.org/10.2202/1941-1928.1062 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
Working Paper: On the Irrelevance of Impossibility Theorems: The Case of the Long-run Variance (2010)
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:bpj:jtsmet:v:3:y:2011:i:3:n:1

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/jtse/html

DOI: 10.2202/1941-1928.1062

Access Statistics for this article

Journal of Time Series Econometrics is currently edited by Javier Hidalgo

More articles in Journal of Time Series Econometrics from De Gruyter
Bibliographic data for series maintained by Peter Golla ().