Monday, April 12, 2010

Debate on Unit Roots in Temperature Series

A huge debate with 1672 comments erupted on Bart Verheggen's blog regarding the issue of unit roots in temperature series. I didn't read much of it, but the main point seems to be that when there are unit roots in time series you need to take that in account when determining if there is a trend in the series and it is harder to reject the null of no trend. This is all true but you can also exploit the unit root property to find the fingerprint of other unit root variables that might be driving your series of interest. And that is what Robert Kaufmann and I did in our research on this topic. Apart from our 1997 paper in Nature it hasn't garnered a lot of citations. So it's not surprising that not many people know about it. Anyway, you can check out all the papers by following this link.


  1. Hi David,

    Thank you for your comment at Bart's blog, here:

    However, I found your concluding remark a bit unsettling:

    "But I wouldn’t be too dogmatic about what the best approach is."

    Are you suggesting that researchers are free to pick the (fundamental) assumption they like (here: stationarity/nonstationarity), and ignore the results of formal testing?

    That's a very awkward approach to 'science' in general, and econometrics in particular. It definitely defies everything I was taught.

    Also, the certainty with which you propagate the untested 'nonstationarity is caused by GHG's' thesis, in order to 'explain' the (near) unit root in the instrumental record, is in my opinion unwarranted. Do note that what you are in fact claiming is that all climatic variables are in fact stationary, and that the non-stationarity of all these variables (e.g. sea-level heights) is in fact caused by the nonstationarity of GHG's, which in its turn is caused by the nonstationarity of GDP.

    I believe this assumption to be a bit of a stretch, especially because to my knowledge, it hasn't been put to a proper test. In that sense, and please do not take this the wrong way, I believe that a part of your results is driven by your particular model specification.

    All the best, VS

    PS. I'm not posting at Bart's blog anymore, for obvious reasons.

    PPS. If you dig through the thread, you will find some results relevant for your own research. These concern the size distortions of the PP family of tests in the presence of a moderate negative inverted MA root, whose (biased) results are undermining your conclusions/methods (i.e. cointegration).

    PPPS. I'm also curious to hear what your take is on the BR paper, here:

  2. The reason I said not to be too dogmatic is because the time series nature of a series can look different depending on how long a time frame one looks at. What might be a good approximation over one time frame might not be over another. It's very hard to tell between a unit root process and a near unit root process as you know. At this aggregate level all models are approximations to the real processes going on. So I am open to ongoing research finding better or more useful ways to the model the system. So, whereas certainly there is a lot of autocorrelation in the series and this needs to be taken into account I'm not dogmatic about the series having unit roots or cointegration analysis being needed. Maybe this comes from being an economist - we know that no economic model is supposed to be an actual representation of the system. It's a useful platform for exploring some ideas about the behavior/nature of the actual system. This is different to some natural sciences where the ideal is to exactly model the actual process.

    The finding that unit root behavior is due to greenhouse gases etc. is mainly based on cointegration results - i.e. finding the fingerprint of the unique time series pattern of the input variables appearing in the temperature. I think it is a reasonable assumption that in the absence of changes in greenhouse gases, solar irradiance, and aerosols the climate would be stationary around a constant mean. i.e. in a dynamic equilibrium.

    I certainly don't think that anthropogenic emissions are the only thing perturbing the climate. Changes in irradiance, volcanic eruptions etc. would all be perturbing the system and we include as many of these as possible in our models.

    I'd certainly be happy to see publications which challenge my results. If you have some findings go ahead and publish them. I'll take a look at that Hebrew U. paper (my undergrad alma mater BTW).

  3. Hi David, thank you for your reply.

    I think you misunderstood my PS :) The results in the thread I'm referring to suggest that the PP tests are severely size-distorted (5%->75%+, n=128) in the case of (near) unit root and an ARIMA(-like) strucuture we measure. Note that the PP tests reject the unit root. In this sense the results posted in the thread *support* your approach, rather than dispute it.

    As for the time frame, I think we are on the same page. My central argument is that the (trend) stationarity assumption is not (automatically) justified on the time frame (interval) xe are dealing with (for the giss, 128 years), simply because the long-term process is stationary.

    Your own work suggests, rightfully in my opinion, that in small samples it is more appropriate to treat a near unit root process as a pure unit root process, rather than a trend stationary one.

    Best, VS

  4. As you'll see I put up a post on B&R now. Thanks for pointing me to their paper.