Effects of intervaling on high-frequency realized higher-order moments

In high-frequency finance, the statistical terms ‘realized skewness’ and ‘realized kurtosis’ refer to therealized third- and fourth-order moments of high-frequency returns data normalized (or divided) by‘realized variance’. In particular, before any computations of these two normalized realized momentsare carried out, one often predetermines the holding-interval and sampling-interval and thus implicitly influencing the actual magnitudes of the computed values of the normalized realized higher-ordermoments i.e. they have been found to be interval-variant. To-date, little theoretical or empiricalstudies have been undertaken in the high-frequency finance literature to properly investigate andunderstand the effects of these two types of intervalings on the behaviour of the ensuring measuresof realized skewness and realized kurtosis. This paper fills this gap by theoretically and empirically analyzing as to why and how these two normalized realized higher-order moments of marketreturns are influenced by the selected holding-interval and sampling-interval. Using simulated andprice index data from the G7 countries, we then proceed to illustrate via count-based signatureplots, the theoretical and empirical relationships between the realized higher-order moments and thesampling-intervals and holding-intervals