calc_sd_ol_bias_fac: Calculate the overlapped bias factor for sample standard...

In PaulMTeggin/practechniques: Functions for the Practical Actuarial Techniques online book

Calculate the overlapped bias factor for sample standard deviation

Description

When overlapped data is used, the sample variance and standard deviation are biased. This function calculates a factor that corrects for the bias in the sample standard deviation. It assumes Bessel's correction has already been applied in the calculation of the sample standard deviation and removes this to avoid double-counting. In practice this means this factor can be applied to the results of sd.

Usage

calc_sd_ol_bias_fac(N, noverlap)

Arguments

N	The number of overlapped data points. There will be N + noverlap - 1 in the data prior to taking overlapped samples, which reduces to N after overlapping by noverlap. E.g. we need 11 more observations than N in order to have N annual monthly-overlapped observations.
noverlap	The extent of the overlap, e.g. 12 means annual overlaps from monthly data. 1 means no overlap.

Details

The factor is derived in a 2009 Risk.net article by Sun, Nelken et al. Where noverlap == 1 the factor is 1 and has no numerical effect.

Value

A factor to multiply the sample standard deviation by to give an unbiased estimate.

References

https://www.risk.net/risk-management/1509219/error-var-overlapping-intervals

Examples

calc_sd_ol_bias_fac(c(24, 60, 120, 180, 240), 12)

PaulMTeggin/practechniques documentation built on Aug. 19, 2023, 4:44 p.m.