Comments on: Spurious Significance #2 : Granger and Newbold 1974

By: Trying to Replicate Moberg « Climate Audit

Trying to Replicate Moberg « Climate Audit — Sat, 04 Dec 2010 18:19:51 +0000

[...] in the spurious regression range. It is unacceptable for the hockey Team to simply ignore this. See my discussion of Granger and Newbold [1974] who said over 30 years ago: It is very common to see reported in applied econometric literature [...]

By: Paul

Paul — Wed, 24 Aug 2005 11:18:28 +0000

#5.

Indeed. Especially for forecasting purposes! (multiple equation models employing lagged endogenous variables exhibiting autocorrelation and all that)

By: Steve McIntyre

Steve McIntyre — Wed, 24 Aug 2005 00:06:11 +0000

Paul, one of the interesting features of the temperature series is that, modeled as ARMA(1,1), their AR coefficients are >>0.9 (and a negative MA1 coefficient), quite a bit higher than modeled as ARMA(1,0), which is the more usual comparison. I don’t entirely know where this leads, but I’m going to get to some econometric models raising real issues about spurious significance in this type of context.

By: Ross McKitrick

Ross McKitrick — Tue, 23 Aug 2005 22:13:16 +0000

Re #2: Individual series need to be tested for unit roots, but this is different from applying a DW test on a regression model. And there certainly are papers that examine geophysical data for nonstationarity prior to proceeding with trend modeling or other analysis. But the result is a body of literature that is divided on whether temperature is nonstationary or highly autocorrelated; either way it means the data need to be handled and interpreted carefully.

By: Steve McIntyre

Steve McIntyre — Tue, 23 Aug 2005 13:39:18 +0000

Some of the articles that have interested me the most pertain to situations where the DW statistic does not work. That accounts for much of my present interest in ARMA(1,1) statistics, where Feng [2005] appears to have used “almost integrated almost white” (ARMA(1,1) processes to explain spurious regressions in Ferson et al [2003]. I’m hoping to get there in these notes without stumbling too much.

By: Paul

Paul — Tue, 23 Aug 2005 09:33:45 +0000

I would go further than this:

not performing a DW statistic on a regression relating highly autocorrelated series would be inconceivable for any econometrician after 1974

Any reasonably knowledgable econometrician would perform such tests on ALL the time series in use PRIOR to any regression, in order to determine the existance of units roots and hence understand the nature of the data being analysed and the potential statistical pitfalls that could result.

That has always been one of the glaring omissions on all hte time series work on temperature or proxies – some basic unit root test on the data and a description of whether they are stationary or not.

By: Ross McKitrick

Ross McKitrick — Tue, 23 Aug 2005 05:46:49 +0000

Durbin-Watson is part of the standard introductory treatment of econometrics and has been for decades, because it comes up a lot and autocorrelation matters a lot. However DW has a couple of limitations. It’s got an obscure distribution (but so what, there are tables and Shazam can compute the exact p-value), it’s not valid if there are lagged dependent variables, and it only tests for AR1. There’s another test that has a fancy-sounding name and is easy to do (2 big advantages, in my view), called the LM test, which is more general and which is steadily getting into the texts. Or there’s the brute force method of estimating models with ARMA residuals and testing lags for insignificance.
The connection to the term “spurious” is building across these notes, but already a key point is worth stressing. When you do a regression the package mechanically computes the ratio of the estimated parameter to the estimated standard error and sticks it in a column under the heading “t-statistic”. But that is no guarantee the number therein came from a data generating process that follows a t-distribution. You have to be able to rule out some influential model misspecification problems. Otherwise you might be comparing your “t-statistic” to the wrong critical values. In the case of Granger and Newbold they looked at regressing random walks on each other. In that case a “t-stat” of, say, 4.0 does not mean the relationship is significant since the ratio in question doesn’t follow a t distribution. “Spurious significance” in this sense means comparing your test statistic to the wrong benchmark and concluding you have significance when in reality you do not.