Lag Difference results

[alim]

1 September 2014

Dear TomDoam

Trust you are well. I need your help again. I have two time series variables. Australian steam coal export is dependent variable and Australian dollar exchange rate is independent variable. The data are quarterly. I consider Australian dollar exchange rates lag1, lag2 and lag3 (Independent variables) to check how exchange rates affect the Australian steam coal export quarterly. Both variables at level have unit root but 1st difference they have not unit root and they are not co-integrated. Therefore, I take 1st difference data for estimation. But my supervisor comments the following:
" The tests for lag effects are probably wrong because you are treating the lagged variables as independent. However, they will be highly correlated. It would be better to test one lagged variable at a time, and then just report the model with the best fit, or come up with a single composite variable that is an average of the independent variable over time".

Please confirm me whether my supervisor comments are right or wrong. If wrong please explain it for me.

Secondly, I don't understand this part of his comments "and then just report the model with the best fit, or come up with a single composite variable that is an average of the independent variable over time" . For example, does he mean that if lag1 is the best fit of the model then I explain only "1 cent increase Australian dollar value against US dollar, Australian steam coal export decrease by 54,870 tonnes second quarter. Other part of the model I would not explain.

I would be highly glad if you kindly provide me your advice and explain it little bit more that I understand easily.

Thanking you

with regard
Alim

[TomDoan]

Whenever you do any sort of "distributed lag", there is a question of how or whether to even attempt to interpret individual lag coefficients. First, however, given that your explanatory variables are (I assume) first differences of the log exchange rate, there is little concern that those are highly correlated---if they were, you should quit graduate school and start trading currency. But if they were highly correlated (if, for instance, they were just log ex rate rather than its differences), I wouldn't really recommend just trying the lags one at a time and seeing which is most significant. First, if they are highly correlated, each lag is a reasonable proxy for its neighbors, so it's likely that if one is significant, all will be. Also, if the true best fitting combination requires more than one lag, you can't capture that by doing one lag a a time. Whether there is single sensible linear combination that somehow models the effect is unclear---in some cases, there might be, in others, not really. You can run the distributed lag, see if a pattern suggests itself and test the restriction. For instance, if you get a lag pattern of -.2,-.15,-.23,-.17, it looks like a flat response might fit almost as well and would be easier to interpret.

[alim]

Dear TomDoam

Trust you are well. I need your quick help. I have a ten time series data. At level, they are non-stationary but 1st difference, they are all stationary. But at level, they are co-integrated. Can you please let me know whether I will take at level data for estimation ( because they are co-integrated at level) or 1st difference?

I am looking your best help in this regard.

Thanking you for your help.

with kinds

Alim

[TomDoan]

I've made this same recommendation to others: Try reading an early paper on error correction models like Davidson, Hendry, Srba, Yeo(1978), "Econometric Modelling of the ....", Economic Journal. That came out before the original cointegration paper, so they weren't obsessed with the I(x)-ness of the data. Start with the economics of the model, not the statistics.