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I have 2 time-series datasets. I am trying to find co integration between them. Now the thing is they are negatively correlated. So if I want to look at the distance between them, would I be right in just inverting one (1/value) of them and looking at the distance they maintain over time? Is this approach right?

I am looking at currency pairs EURUSD and USDJPY

Mathematically speaking if y=mx+c and y=-mx+d, i could take a negative of mx and see the difference between the new series so obtained and y=mx+c.

However, intuitively I am not able to connect if taking the inverse of prices, I would get the same. If i invert USDJPY, I would get JPYUSD and can run it against EURUSD. But I don't really tie it up, whether taking an inverse makes sense

Thanks, Cheers!

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You would have to inverse them, USD priced in JPY, and EUR priced in USD will almost always be inversely correlated. It is like pricing the SP500 in USD, and comparing it to USD priced in DOW30, It makes no sense! You will get the opposite result, but it will make more sense (inversing it).

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    $\begingroup$ A paper called "Common Risk Factors in Currency Markets" shows that the world's currencies are driven by 2 main factors: the "dollar risk factor" which basically is currencies moving up or down together vis a vis the USD, and a "slope factor" which has to do with differences in interest rates across countries. Therefore it is important to price all currencies with respect to the USD, otherwise the first factor is mis-specified in the currencies that are quoted "backwards". So use JPYUSD, not USDJPY. $\endgroup$
    – Alex C
    Aug 31, 2016 at 23:16
  • $\begingroup$ I had a look at the paper and it was very fascinating. However it seems for many commodity currencies It would be important to factor in trade weighted commodity price changes. $\endgroup$
    – FX_NINJA
    Sep 1, 2016 at 14:02
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I think the answer lies not in the technicalities of cointegration but rather in the reality of currency markets and international economics. I don't think EUR/USD is cointegrated with USD/JPY or JPY/USD. If they were, EUR and JPY would move in parallell w.r.t USD, apart from short-term deviations.

  • This does happen to the extent of how strong/weak USD generally is (e.g. driven by the macroeconomic situation of the U.S.).
  • However, this is only half of the story. There are also separate driving forces behind the strength/weakness of EUR and JPY (their respective macroeconomic situations), respectively, and those need not always coincide (Europe does not always go down when Japan is going down, even though this may sometimes happen).

Thus there is a common trend between EUR/USD and JPY/USD, but there also are separate trends extra to it, and that prevents cointegration.

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