Why Inverting Currency Quotes Does Not Establish Cointegration
Summary
The discussion considers whether reversing one currency quote can make two negatively correlated exchange rates suitable for a cointegration or distance based strategy. It uses EUR/USD and USD/JPY as examples, noting that quote direction changes the way currency strength appears in a comparison. Inverting USD/JPY expresses JPY/USD, which may make the shared USD influence easier to interpret, but does not itself show that the resulting series are cointegrated.
The economic explanation distinguishes a common driver from a stable long run relationship. Both exchange rates can respond to broad dollar strength, while euro and yen values also move with separate economic forces. Those independent trends can prevent a stationary spread even when the rates share some broad movements. The answers offer conceptual reasoning rather than statistical tests, data, or a trading evaluation; any proposed relationship would need to be tested on suitably transformed series and an appropriate sample.
Key ideas
- Changing the quote direction reverses how currency movements are represented, but does not prove cointegration.
- EUR/USD and JPY/USD may share exposure to broad changes in the dollar.
- Separate economic forces affecting the euro and yen can create distinct trends.
- A common driver alone does not ensure a stable long run spread.
Tags
Full text
# Co integration of diverging time series # Co integration of diverging time series 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! ## Answer by FX_NINJA (score 1) https://quant.stackexchange.com/a/29924 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). ## Answer by Richard Hardy (score 1) https://quant.stackexchange.com/a/29925 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.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.