發散時間序列的協整
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!
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).
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.