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


Crack, Timothy Falcon; Ledoit, Olivier (2010). Central Limit Theorems When Data Are Dependent: Addressing the Pedagogical Gaps. Working paper series / Institute for Empirical Research in Economics No. 480, University of Zurich.

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 innCLTs 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.

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 innCLTs 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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Institute for Empirical Research in Economics (former)
Dewey Decimal Classification:330 Economics
Language:English
Date:February 2010
Deposited On:29 Nov 2011 15:09
Last Modified:17 Feb 2018 18:59
Series Name:Working paper series / Institute for Empirical Research in Economics
ISSN:1424-0459
OA Status:Green
Official URL:http://www.econ.uzh.ch/wp.html

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