Scaling laws in variance as a measure of long-term dependence

Many asset-pricing models require an annualized risk coefficient that is determined by the linear rescaling of the variance from other time intervals. However, this approach may not be appropriate for distributions that display linear dependence or leptokurtosis. Research in this paper investigated scaling relationships for spot month daily closing prices for four currency futures contracts (British pound [GBP]/United States dollar [USD], German mark [DMK]/USD, Japanese yen [JPY]/USD, and Swiss franc [CHF]/USD) traded on the Chicago International Money Market (IMM). Our results suggested that although all four series were non-Gaussian, they displayed similar scaling properties that were not consistent with their underlying level of long-term dependence. These results demonstrate that models of long-term dependence may be biased and that scaling laws can be used as an alternative and accurate proxy of dependence.