Abstract #300348

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JSM 2003 Abstract #300348
Activity Number: 270
Type: Invited
Date/Time: Tuesday, August 5, 2003 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #300348
Title: Temporal Averaging and Nonstationarities
Author(s): Andrew W. Lo*+
Companies: Massachusetts Institute of Technology
Address: 50 Memorial Dr. Bldg. E52-432, Cambridge, MA, 02142-1347,
Keywords: time series ; nonstationarity ; nonparametrics ; financial econometrics ; finance ; econometrics
Abstract:

A common practice among quantitative financial analysts for dealing with nonstationary time series is to apply an exponentially declining weighting scheme to the data so that more distant observations are given less weight than more recent observations. We show that this practice is incorrect for all but linear estimators, implying that variances, covariances, betas, Sharpe ratios, Value-at-Risk, and many other common financial statistics are incorrectly estimated with exponentially weighted time series. We propose an alternative approach to exponentially weighting the data that yields unbiased estimators under the null hypothesis of independently and identically distributed observations, and which has attractive properties under several nonstationary alternative hypotheses. Using this approach, we derive exponentially weighted estimators for all the usual financial statistics and apply them to recent historical stock market data to demonstrate their empirical properties.

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