Central Limit Theorems When Data Are Dependent: Addressing the Pedagogical Gaps

32 Pages Posted: 10 Sep 2004 Last revised: 18 Aug 2009

See all articles by Timothy Falcon Crack

Timothy Falcon Crack

University of Otago - Department of Accountancy and Finance

Olivier Ledoit

University of Zurich - Department of Economics

Date Written: August 18, 2009

Abstract

Although dependence in financial data is pervasive, standard doctoral-level econometrics texts do not make clear that the common central limit theorems (CLTs) contained therein fail when applied to dependent data. More advanced books that are clear in their CLT assumptions do not contain any worked examples of CLTs that apply to dependent data. We address these pedagogical gaps by discussing dependence in financial data and dependence assumptions in CLTs and by giving a worked example of the application of a CLT for dependent data to the case of the derivation of the asymptotic distribution of the sample variance of a Gaussian AR(1). We also provide code and the results for a Monte-Carlo simulation used to check the results of the derivation.

Keywords: Central Limit Theorem, Dependent Data, Gaussian AR(1), Monte-Carlo, Asymptotic Distributions

JEL Classification: A23, C12, C22, G12

Suggested Citation

Crack, Timothy Falcon and Ledoit, Olivier, Central Limit Theorems When Data Are Dependent: Addressing the Pedagogical Gaps (August 18, 2009). Available at SSRN: https://ssrn.com/abstract=587562 or http://dx.doi.org/10.2139/ssrn.587562

Timothy Falcon Crack (Contact Author)

University of Otago - Department of Accountancy and Finance ( email )

Dunedin
New Zealand

Olivier Ledoit

University of Zurich - Department of Economics ( email )

Wilfriedstrasse 6
Z├╝rich, 8032
Switzerland

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
432
Abstract Views
2,717
rank
73,130
PlumX Metrics