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Interesting Mike! I run a model that looks like this:

D(Z) = - 0.03312117393 * ( Z(-1) + 0.0067250946 * PCNE(-1) - 2.19469359 ) + 0.1188193949 * D(Z(-1)) + 0.0007333664481 * D(PCNE(-1)) - 0.0184800283 - 0.006406242209 * (CDTB - USTB) - 0.00140106491 * OIL - 0.0001347297381 * OIL(-1) + 0.001874154885 * OIL(-2) + 0.001278679394 * (YG - YG_US)

where z is the quarterly real exchange rate (and where a decrease means an appreciation in the CAD) PCNE is the Bank of Canada non-energy price index, cdtb and ustb are Canadian and US 3-month treasury yield, and yg - yg_us is a GDP growth rate differential.

It has proved to be very accurate out of sample over short horizons (1-4 quarters).


I think there is something special - probably psychological - that what happens when we hit parity and beyond. In my graphs of commodity prices and the exchange rate (most recent version), there's a pretty clear kink at parity.

Out of interest, have you tried using other interest rate differentials?

"Out of interest, have you tried using other interest rate differentials?"

No, but I really should. One thing I've been thinking of doing is using the actual values for the rates rather than the target rates. I should see if that makes a difference.

I agree Stephen - its almost like either parity or oil over $100 represents some threshold for the commodity price/loonie relationship at which it completely breaks down. Though the sample is small so who knows.

Brendon: Interesting model! Any insights on where the Canadian dollar is likely headed?

Well, the one drawback is that it is a quarterly average so misses a lot of the action. I've got the dollar at 97-98 cents for 2010 and I would guess we'll see parity soon if oil keeps rising and if, as you say, we get a strong jobs report next week.

You might try including a measure for official reserves in your model, although the effect could wash out on a quarterly basis as the effectiveness of the central bank leaning against the market will tend to dissipate over time.

In the late 80s, I developed a simple model to predict monthly changes in official international reserves which worked remarkably well. If I recall correctly, the explanatory variables were Canada-US interest rate differentials (short-term treasury bills I think) and changes in the C$/US$ exchange rate. Of course, the Bank of Canada was somewhat more proactive at the time in managing the exchange rate through foreign exchange interventions.

Cool "toy", thanks for sharing!

Now it appears to me that the "toy" might be so effective because WTI is strongly correlated to the inverse of the US dollar. I wonder how well the "toy" performs when WTI diverges from the US dollar (or more accurately, the inverse of US dollar)?

I took a look at log(WTI), inverse US dollar index, CAD/EUR and CAD/USD, and I have a (busy) chart of those four variables here: http://special----k.blogspot.com/2010/04/more-on-cadusd-wti.html . I think there are some observations.

First, to the eye log(WTI) fits the inverse of the US dollar much better than straight WTI. This suggests tht log(WTI) might better predict CAD/USD. Have you looked at using log(WTI) in your toy model?

Second, there are multiple periods where log(WTI) diverges from inverse US dollar index. During these periods CAD/EUR appears to follow the US dollar index. That is if the US dollar weakens without corresponding strength in log(WTI), CAD/EUR weakens. Similarly, if log(WTI) strengthens without corresponding weakness in the US dollar, CAD/EUR falls.

I'm using CAD/EUR as an indicator of Canadian dollar strength independent of the US dollar. I'm curious about how your "toy" handles these periods where log(WTI) diverges from inverse US dollar index? The sense I get from my chart is that during these periods, CAD/EUR tracks USD. So it would seem that during these periods, WTI would underpredict CAD/USD.

Hi Kosta,

Thanks for your comments!

"This suggests tht log(WTI) might better predict CAD/USD. Have you looked at using log(WTI) in your toy model?"

No, though I really should. My idea when I created the toy was to make a model that was as simple as possible that could still estimate the value of the Canadian dollar. In particular I was looking for something I can calculate in my head to see if the loonie is over or undervalued (when doing a quick mental calculation I omit the interest rate portion, and use the parameter values 0.5 for the intercept and 0.6 for WTI). I should try making a more complex version. log(WTI) would be a good place to start.

"I'm curious about how your "toy" handles these periods where log(WTI) diverges from inverse US dollar index?"

The toy seems to work well for 1996-2010. Which periods do log(WTI) diverge from the inverse US dollar index? I'd love to test it out.


I think your "toy" is absolutely brilliant in its simplicity and I can see why you haven't looked at other terms or modifications. Now a casual look at log(WTI) and inverse US dollar suggests they are strongly correlated from 2003 on (see the chart in the link in my previous comment).

Post 2003 there are three obvious periods where the two diverge. For about 3 months around both the end of 2004 and the end of 2005, inverse US dollar is above log(WTI), and then for about 3 month in the fall of 2005 log(WTI) is above inverse US dollar. I'm curious about your "toy's" performance here especially as your INTGAP term is probably playing a role as well. But I wonder if any additional information could be gleaned from these periods where log(WTI) and inverse USD diverge.

There's also the 2000-mid 2002 period where the US dollar was strong but oil prices first started moving up. Just considering WTI's contribution , I wonder if your "toy" had a systematic bias in predicting USD/CAD over this period. But again, I don't know about the INTGAP contribution during this period.


Please don't worry about replying to my queries. I tracked down the interest rate data and I'll just run your MERT and answer my questions by myself. But, I think you might still be interested in looking into using log(WTI).


One thing that you might be interested in toying with is the increasing gap between production and consumption - forecasted to continue to grow as more oil sands projects come onstream.


Mike: a recent article in the National Post stated that Bank of Canada has just released a sophisticated correlation study to predict the Canadian dollar and found that the main parameters for a long term correlation, in order of importance is:
1. Price of commodities (the article did not mention oil, probably as an abbreviation)
2. the size of the Canadian deficit.
For a short term correlation, the interest rate differential with the US gov is the second parameter and the size of the deficit is the third.

This is real rough, you might want to check it out. KShen

Hi K Shen:

I'll have to track down that article! I've been playing around with the data a little. Will post a follow-up with what I've found.



Mike: Love the toy! Thanks for doing this. Here are a bunch of possible reasons why your prediction error increase near parity:

+ The toy model uses spot oil prices whereas much oil trades through longer-term contracts. So as spot oil rices rocket up, they become increasingly less representative of prices actually paid.

+ The benchmark oil prices capture the market prices of light, sweet crude. Given refining bottlenecks, spot prices of light, sweet, relatively clean, easy to refine crude may spike while heavier grades of oil enjoy relatively modest price increases by comparison.

+ Earlier in the decade, natural gas prices were more correlated with oil prices or is my impression. In light of the current glut, North American natural gas prices have become more uncoupled from oil prices.

+ I would also tend to think that commodities like base metals and coal are positively correlated with oil (prices) but do not necessarily move together when oil prices spike enough to drive the dollar to near parity. Once again, longer-term contracts are frequent.

Of course the higher Canadian dollar could be drying up export opportunities and related investments in non-resource sectors. (Not that anybody would notice in western Canada.)

Instead of overnight rate differences, target or observed, I would look for the bond rate or market rate that most captures the type of fixed income assets that will respond quickly to rate shocks and whose value is somewhat correlated with other similar market-traded assets like corporate bonds. Exactly which one, I'm not sure. 5-year government bond yields maybe?

I hope you manage to keep the model parsimonious. Feel free to post pictures of the residuals when you get a chance. Would also be most curious to see how well the toy performs in logged first-differences. -w

Pre-1995 - well, John Crow was governor of the B of C until 1994 - Mr. Corw wanted 0% inflation - maybe you need a different variable for different governors of the various central banks too.

My guess is that using short term interest rates is inadequate - you need to also plug in long term interest rates and inflation in both countries, or else use real interest rates.

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