Comments on: Satellite Measurements #2: Arima

By: Another pro-global warming comment, effective PR at work! « Fabius Maximus

Another pro-global warming comment, effective PR at work! « Fabius Maximus — Mon, 01 Dec 2008 00:02:45 +0000

[...] data — An archive here. Esp note here, here, here, here, and [...]

By: John Creighton

John Creighton — Wed, 06 Sep 2006 03:46:34 +0000

I was thinking about the figure in the original post and how to compare it with estimates obtained at different sampling rates. One thing I thought of was transforming the estimate obtained as a fit to the annual data to a model that is sampled yearly instead of monthly. Clearly the fit would be considerably worse. I am of yet unsure of the significance of this somewhat obvious observation.

By: John Creighton

John Creighton — Sun, 03 Sep 2006 03:07:15 +0000

Thank you for the script. When I first saw the data the fit looked spectacular. I noticed two things that make the fit look less impressive. The first is that the sample time of the ARMA model is monthly as opposed to yearly. Although a good prediction from monthly data may still be impressive the smaller the time interval the easier it is to predict the future data from the past data and consequently the better a low order ARMA model will fit. There is a type of analog to digital converter called a sigma delta converter. When the sampling rate is fast the sigma delta converter only needs a constant function to predicted future values from past values.

The second thing I notice is in the algorithm is the moving average part is a function of the errors and not known inputs.

X[t] = a[1]X[t-1] + … + a[p]X[t-p] + e[t] + b[1]e[t-1] + … + b[q]e[t-q]
http://www.ualberta.ca/CNS/RESEARCH/Rdoc/R/library/ts/html/arima.html

I do not know the likelihood function and how it constrains these values of the error. None the less if this algorithm fits the satellite data much better then the instrumental data I will accept the satellite data is better suited for building models. Unfortunately I do not see the same procedure applied to the instrumental data.

By: Steve McIntyre

Steve McIntyre — Sat, 02 Sep 2006 22:35:47 +0000

Plot Script

By: John Creighton

John Creighton — Sat, 02 Sep 2006 21:22:01 +0000

Steve, the results look surprisingly good. I was just looking up satellite data prior to discovering this thread
http://en.wikipedia.org/wiki/Satellite_temperature_measurements
and the satellite data appeared to agree closely with the instrumental data, yet I have not seen anyone fit the instrumental data this well. What was your input for the ARMA model and what sampling period did you use (Year month?).

By: Michael Jankowski

Michael Jankowski — Thu, 18 Aug 2005 17:47:36 +0000

Do your walking experiments include the effect of the rise in body temp on the perception of a change in air temp?

It would have to be considered, of course. I’d prefer to remove human body effects altogether by getting some big grant $$$ to put continuously-monitored weather stations on a grid system…

By: J. Sperry

J. Sperry — Fri, 12 Aug 2005 16:38:17 +0000

Re: 44 (somewhat tongue-in-cheek)
Do your walking experiments include the effect of the rise in body temp on the perception of a change in air temp?

By: Steve McIntyre

Steve McIntyre — Fri, 12 Aug 2005 15:39:16 +0000

Here’s an interesting article which appears germane to these issues: Helle Bunzel & Timothy Vogelsang, 2003. “Powerful Trend Function Tests That are Robust to Strong Serial Correlation with an Application to the Prebisch Singer Hypothesis,” Econometrics http://econwpa.wustl.edu:80/eps/em/papers/0304/0304002.pdf . I’m trying to figure out how to implement these and would welcome any thoughts on it.

By: TCO

TCO — Fri, 12 Aug 2005 14:08:38 +0000

I can’t find it again, don’t remember exact search terms. BTW, I did not find a good overview description of ARMA basics. Many assumed that you knew the basics or that you knew AR and MA to start with. The one that I made offhand reference to was regarding issues in using ARMA, common mistakes etc. I didn’t follow that much of it either. and it was late.

By: Steve McIntyre

Steve McIntyre — Fri, 12 Aug 2005 13:56:35 +0000

Peter (Ha.), I’ve been intrigued with extreme autocorrelation from the proxy aspect. I’ll post up the ACFs of the NOAMER PC1, the Gaspe tree ring set and some others to give a flavor.

However, in the satellite data with a trend model, there’s an outright Durbin-Watson failure, so one doesn’t need fancy spurious regression theories.

I’m intrigued with Ferson and Deng, because they appear to identify some situations with spurious regression that are resistant to Durbin-Watson. Some of the situations that they considered had high theta’s. Obviously low theta is classic spurious regression. The effect that I’ve noticed with series like Tornetrask is that the AR1 coefficient is much higher in a ARMA(1,1) model than in the ARMA(!,0), which is the usual benchmark (if one is used at all) and that the ARMA(1,1) is much better than the ARMA(1,0) model. Thinking out loud, the question is then – maybe moderate theta’s e.g -.3 or maybe -0.6 in combination with a very high AR1 >0.9 or even >0.95, are sufficient to provide DW resistance: maybe you don’t need to be “almost white”, maybe just a little bit.

TCO, I’m not advocating ARMA as a magic bullet – what’s the reference that you had in mind?