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Is there an example for a pair of random variables to be correlated in first differences...

Is there an example for a pair of random variables to be correlated in first differences but not in levels?

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Answer:

Yes it is possible.

For an instance, consider two stocks, Stock A and Stock B. Stock A has a share price that is increasing with some stable positive slope and stock B which has a stock price that is declining with some stable negative slope. Then, the variability in the stock prices of stocks A and B are perfectly correlated but the price of these stocks stock A and stock B is "uncorrelated".

The two stock prices are atleast uncorrelated linearly because the mean price of each series(levels) is not constant

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