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It’s useful to study the mean and variance of the first-order autoregressive model (AR(1)), which is postulated as univariate:

We can determine an arm's length profit margin (expressed as operating profit divided by net sales) of a controlled taxpayer (“tested party”) by using a first-order autoregressive model, which we can show (like any stable first-order difference equation) to be equivalent to a range of comparable “routine” profit margins plus a weighted random error time series.

Computation of an arm's length operating profit margin is not as easy as it seems. As an example, we consider the directly proportional profit model postulated by the OECD Transfer Pricing Guidelines and the more likely power function that we may encounter when we analyze actual comparable data including small and large enterprises. In cases when the selected comparables include small, medium and large uncontrolled enterprises, an arm's length operating profit margin is more likely to be reliably measured by a double log or power function. The operating profit margin is defined as operating profits (before or after depreciation and amortization) divided by sales revenue.