How do I statistically differentiate a series of prices from a series of returns?

External question — Quantitative Finance Stack Exchange Author: SRKX Original post: https://quant.stackexchange.com/questions/3666 License: CC BY-SA 3.0 — https://creativecommons.org/licenses/by-sa/3.0/ Adaptation: HTML converted to plain text; contact email addresses removed. I developed an optimization algorithm that uses returns (among other parameters) as input and basically output an allocation. As I'm pretty happy with the results, I am in the process of putting the algorithm in production. As a matter of fact, I have to embed some checks into the algorithm to make sure that the input was right and that the output makes sense. For example, I check that the allocation sums to 1, I check that the time series provided are all of the same length and so on... I would like to add another test which allows me to display a warning if the input time series appear to be prices instead of returns (and people will do this mistake one day I'm sure). So, I would like to setup a statistical test on my set of points $x=x_1, ... , x_n$ to determine whether they are likely to be prices. Formally the statistical test if a function defined as follows: $$A(x) \rightarrow \{0,1\}$$ Ideally we would like to find a test that is sufficient and necessary for a time series to be returns (as compared to prices, not to "a random time series"). There are three types of interesting statistical tests: Type I (necessary and sufficient) $$A(x)=1 \iff x ~ \text{are returns}$$ Type II (sufficient) $$A(x)=1 \Longrightarrow x ~ \text{are returns}$$ Type III (necessary) $$A(x) \neq 1 \Longrightarrow x ~ \text{are prices}$$ The following test is a dummy one: $$A_{\text{dummy}}(x)=\frac{1}{n} \sum_{i=1}^n x_i > 1$$ This is not good because a Forex time series are prices of a currency expressed in the base currency of the portfolio, and such a series would produce a result of 1. I came up with a Type II test: $$A_\text{Type II}(x) = \exists i ~ x_i<0$$ Note that I assume that the input could be either prices or returns . A series of prices with non-negative returns would fool this test so it is not necessary. I believe it is impossible to come up with a Type I test, which implies that I can't come up with a Type III test either (otherwise I could construct a Type I test easily). I would be looking for extra Type II tests to improve the probability of wrong input detection. Have you ever had to do such test? What method would you recommend?