Backtesting Volatility Assumptions using Overlapping Observations

21 Pages Posted: 18 Mar 2019 Last revised: 26 Sep 2019

Date Written: September 25, 2019

Abstract

In this paper the ability of a variety of backtesting experiments to identify a model with misspecified volatility is examined. This quantitative testing assumes five years of risk factor observations, considers overlapping and non-overlapping backtest observations with horizons out to a year, and make use of Kolmogorov-Smirnov, Anderson-Darling and a likelihood ratio test statistics.

In doing so the `discriminatory power' of a test is defined, which is related to the average probability of correctly rejecting a model that is misspecified in a specific way, allowing tests to be quantitatively ranked in terms of this power. This is illustrated using a normal model with volatility misspecified by up to $25\%$, and it is shown the likelihood ratio test statistic is the most powerful of the considered test statistics for this purpose.

It is then demonstrated that test statistics that are adjusted for the correlation structure arising from the the use of overlapping return observations are more powerful than their unadjusted versions.

The result of this analysis is that the adjusted version of the likelihood ratio test statistic is the most powerful statistic to identify misspecified volatility. These adjusted test statistics are shown to have comparable discriminatory power to the (non-overlapping) 1-day backtest experiments, whereas overlapping experiments with the unadjusted statistics have a discriminatory power that rapidly deteriorates with increasing overlap.

Keywords: CCR Backtesting; Overlapping Observations; Discriminatory Power

JEL Classification: G32

Suggested Citation

Clayton, Michael A., Backtesting Volatility Assumptions using Overlapping Observations (September 25, 2019). Available at SSRN: https://ssrn.com/abstract=3342541 or http://dx.doi.org/10.2139/ssrn.3342541

Michael A. Clayton (Contact Author)

Michael A. Clayton Consulting, Inc. ( email )

Toronto, Ontario
Canada

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