Abstract:A first‐order autoregressive (AR(1)) model is analysed to investigate the relationship between a time dependent random variable Γt and its derivative . This is motivated by the problem of the turbulent dispersion of a gas cloud or plume in the atmosphere, where the square of the derivative, , is also of interest. It is shown that in general Γt and Dt are correlated, with their correlation proportional to the skewness of Γt. The probability distributions of the innovations and of Yt and Dt, and the joint distri… Show more
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