On the Difference Time Series (II)

Abstract

In my former report, I discussed on the autocorrelation coefficient of difference time series. In this paper, I point out some properties of time series that are investigated by taking difference, and discuss apparent periodicities coming out in the higher order difference series of purely random time series. Namely, according to E. L. Dodd, if {X_t} is purely random series the apparent period T of difference series {_??_ⁿX_t} is given by where, in our case, b₀=1, b_n+1=(-1)ⁿ⁺¹, Besides, corrections and supplements for the former report are appended.