Hi

Yes, spuriuos relationships are easy to create in timeseries. In fact, that is the reason I went looking for cointegration in the first place. Linear regression in time series often leads to spurious relationships being identified, so it is no surprise you have found one with this.

As to the cointegration you have said -“Claims are being made that co-integration is different than correlation,” — yes, these claims have been made and well established for many years. eg see:

  1. Johansen, S. 1988. Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12: 231–254.
  2. Johansen, S. 1991. Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59: 1551–1580.
  3. Johansen, S. 1995. Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford: Oxford University Press
  4. https://en.wikipedia.org/wiki/Cointegration
  5. Yule, U. (1926). “Why do we sometimes get nonsense-correlations between time series? — A study in sampling and the nature of time series”. Journal of the Royal Statistical Society. 89 (1): 11–63. doi:10.2307/2341482. JSTOR 2341482.
  6. etc…

In short, cointegration is a better indication of relation than correlation in non-stationary time series, due to the exhaustively tested and researched reasons already given in the many peer reviewed articles available on the subject.

Of course, it is entirely possible to “create” a cointegrating series (i.e. generate a series (or sample from some unrelated series)). However, if there is no plausible relationship there then there is no point in testing for cointegration.

The difference between the series you have here is actually large. You are using monthly time steps on one series, from the past, on a totally unrelated series- as such the do not cointegrate (when you use the correct timesteps).

Now, you *could* invent a timestep (lets say that each month is equal to one day in the other time series) to try to coerce them to cointegrate, but what is the point of that?

I put it to you, that your argument is a formal logical fallacy: denying the antecedent. You have essentially communicated that if these series do not cointegrate, then the stock to flow hypothesis is correct, and if they do then it isn’t. This is equivalant logic to if P then Q; but not P then not Q (which is the formal statement of the aformentioned fallacy).

If we found no cointegration with stock to flow, then that would be a reason to reject the hypothesis. However we have found it and whilst it is cointegrated, it also has fundamental reasoning behind why it should be a predictor (outlined in planb’s article).

I may in the future put together a bit more of a thorough explanation in another medium article, but for now I hope this helps.

Cheers

Nick

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