OK, just so we know you are unable to address the professional time series experts on this topic. That way I know where you stand.
Mr. Glenn Morton takes exception to the SAS Institute and a PhD statistician and he can't explain why they are wrong and he is right.
Got it!
Sigh, I have addressed it several times, but you are too thick to understand it. In the note that you are replying to, I addressed it.
grmorton said:
You then claimed that the low frequency component in the satellite data means there is a secular trend. You are in the process of changing by now claiming that it can mean a secular trend. It can, but your logic is highly flawed. While secular trends will have some low frequency, you cant do what you did and look at an FFT and conclude that there is a secular trend. It is a one way gate. Most secular trends require low frequency (unless it is very steep) but not all low frequencies indicate a secular trend. Below is a power spectra from seismic data. It has no secular trend, yet it has a huge amp at 1 hz. Thus, you can't look at the satellite data and claim that the FFT proves there is a secular trend any more than you can say one exists in a box function or on seismic data. Flawed logic leads to flawed conclusions.
As you said earlier, you have never done time series analysis before and now you are an add-water-become-instant-expert. You got over your head in a debate about GW, an area you thought would be an easy slam-dunk and now you are just looking for anything with which to salvage something. But you continue to make mistake after mistake. You dont even recognize responses to the things you are demanding a response for.
Your logic is turned about. All crows are black, but not all black things are crows. Can you comprehend that???
Trends CAN cause low frequency spikes, but as Chalnoth and I have repeatedly told you, you cant reverse the logic (all black things are crows) and be successful. Not all low frequency peaks are due to trends. If you are incapable of understanding this, then this really is a waste of time.
All babies have bottoms, but not all bottoms are on babies! Some are on adults, some bottoms are on jars, some bottoms are on ships etc ad nauseum.
You are trying to look at a power spectra and determine that the peak represents a trend. YOU CANT DO THAT anymore than you can claim that every bottom you see belongs to a baby.
The above fits what the SAS says and the statistician said. Trends can cause low frequencies, But as I showed with the boxcar function, not every low frequency peak is due to a trend. How hard is that, mr. New to time series analysis and showing it??
I think I could come up with some time series with trends that didnt have such a spike. Add a low slope with 100 hz data that has 5000 times the amplitude as the trend. That wouldnt come out with a peak at 1 hz but would peak at 100 hz. I havent done this but that is what I would expect.
Now, look Glenn, you are clearly an amateur in statistics and I hate to have to keep correcting your freshman mistakes, but a p-value like that on a fit means there's a 99.99% chance that it is non-zero (ie a trend).
How rich. Given all the mistakes you have made (and you did this on the yearly data) I am amazed that you are still claiming what you are claiming.
Thaumaturgy said:
But from what I can tell, Fisher's Kappa indicates no such "cyclicity" among the noise to a 99% level of assurity.
. . .
Thaumaturgy said:
I think I was mistaken about the Kappa function. It does show a statistical significance for cyclcity when it is low on the p-value.
No problem. We see from the graph that, as Glenn has pointed out, there is, indeed, cyclicity. AND it has a multi-year period. The residuals bear this out
Do you want me to cite more of your errors? you are the one who averaged the yearly values, you are the one who cant seem to understand that temperature gauges on air conditioner exhausts would bias the results, and you are the one who cant seem to understand the simple fact that when the measurement error is larger than the presumed signal, it is a meaningless measurement. You continually claim that I know nothing, but it is you that keeps making the mistakes.
Now, notice, T, I have no doubt that the regression will show a trend. Shoot, taking the regression on a sine function from 0 to pi/2 will show a regression trend. That doesnt make the sine function a linear function. The reality is, if you look at the 80s on the Satellite data, you will see it is highly periodic. The ups and downs are clearly NOT random noise. This is clearly a cyclical function with a wide range of frequencies. It isnt a linear change with random noise. Random noise in a Fourier transform is a bias in the frequency domain. Random noise has a constant energy across all frequencies. The transform doesnt show that. But of course, you wont understand this any more than you understood
Whatever the big picture really is, there is no doubt there is some kind of trend within the time span of your data.
I havent denied that from start to finish, over 30 years, one can see a small rise in tropospheric temperature. What you have never addressed that I have seen is the fact that it is far smaller than what you posted about land, which, as far as I recall, you didnt explain why it exaggerated the global warming rise. The IPCC says .74 deg C over the past 100 years (I finally found it in the 2004 volume. But you have well over a degree on your chart.
No, what I said was there is a measurable, statistically significant linear trend, and that it was up to you to prove the data was dominated by a cyclic function. That was before I educated myself on time-series analysis.
LOL. I see you are still trying to say that a trend lies in the low frequencies. It may, but it doesnt have to as you are claiming.
THEN ADDRESS THE POINTS BY THE SAS INSTITUTE AND A PhD STATISTICIAN.
I did. See above. See my previous posts on this.
In the note to which you are responding I also replied to it. You ignored it. From the post you are replying to and now demanding that I respond to the SAS institute and the Ph. D. Statistician, I wrote:
grmorton said:
You then claimed that the low frequency component in the satellite data means there is a secular trend. You are in the process of changing by now claiming that it can mean a secular trend. It can, but your logic is highly flawed. While secular trends will have some low frequency, you cant do what you did and look at an FFT and conclude that there is a secular trend. It is a one way gate. Most secular trends require low frequency (unless it is very steep) but not all low frequencies indicate a secular trend. Below is a power spectra from seismic data. It has no secular trend, yet it has a huge amp at 1 hz. Thus, you can't look at the satellite data and claim that the FFT proves there is a secular trend any more than you can say one exists in a box function or on seismic data. Flawed logic leads to flawed conclusions.
I think I am in agreement with what those two sources of yours are saying.
I said, that a trend could show up as a low frequency peak but that your logic was backwards. Obviously you ignored it and now demand that I state it again.
1. Do you or do you not think that low frequency wavelengths will show up as a low frequency spike on a periodogram
What in the heck is this? Of course a single frequency, low frequency wave, of one, will appear as a spike on the power spectra. So will a high frequency wave appear as a spike. Your terminology here is not very clear as to what you are asking
2. Do you or do you not think an extreeeeemely low frequency cyclic trend in the data can show up as a steady increase when sampled over a shorter time frame (ie much, much, much shorter than its wavelength)
For about the 3rd (or 4th) time, yes, they CAN, but you cant turn the logic around and say that just because you have low frequency energy, that you have a trend. The box car function has a low frequency peak. I showed this. You were too thick to follow it. So, I will post a picture from the Robert Sheriff, Encyclopedic Dictionary of Applied Geophysics. 2002 P. 149
Now, on the box car function, show me the secular trend? I dare you. It starts at precisely zero and ends at precisely zero. The peak in the spectrum is at zero Hz. Why Zero hertz? Because this function does have some DC shift, or as Chalnoth put it, it has an average value. Zero frequency is about as low frequency as it gets. And if you try to claim that the low frequency represents a secular trend, Mr. Instant-time-series-analyst, please show that trend in the data which starts at zero at infinity, rises to some value at -1/2, and then returns to zero at +1/2 remaining at zero to positive infinity.
Where is the trend. Until you understand what the statistician is saying and what the SAS book is saying, you will wander in the darkness.
3. Do you or do you not believe that such a trend, if sampled at a small enough fraction of its wavelength could appear to be a linear trend.
Of course but irrelevant. We started this with the satellite data, which for the life of me is the weaker data for your position, which you now go to the mat over. If you are saying that the warming of the past century is part of a 500 year long cycle, then of course, it would appear as a linear trend, but, and this is important, it wouldnt be a trend, it would be a cycle. No matter how much you proclaimed it as a trend, it wouldnt be a trend because eventually it goes back to the value it started atwhich is what the satellite data did from Dec 1978 to May 2005it returned to its value---a cycle, not a trend! Gosh, you make things hard.
I suggest you answer these questions.
Then we'll get back to your "understanding" of the difference between confidence intervals and standard deviations.
First off you have to understand something. I am not writing here for a scientific article. I am writing for the people who are reading us. I want them to understand what is said. Jargon laced language is bad for that. I am not even really writing to you any more, given all the errors you have had to acknowledge in this discourse, yet refuse to actually discuss the temperature record. You are the one who over and over is forced to admit errors. Now explain either where the secular trend is in the boxcar function or admit that a big peak in the low frequency range doesnt necessarily mean a secular trend.
Here is some more data on California (for those who might have interest, as Thaumaturgy doesnt seem to). The maximum yearly temperature change is plotted for each station. Note that Electra had one year in which the temperature changed by 18 degrees F. Now anyone who knows the heating and energy industry knows that degree days are an important number. They tell the power companies what to expect in the way of demand. Usually it is degree days above or below some reference. Well in Electra CA, one year got an additional 6570 degree days.
I looked up Electras degree days, If you cool your house when the temperature is above 65 deg F, you have 602 degree days annually. But the temperature record says that in this maximum change, Electra suddenly got 6570 more degree days. And people believe the temperature record. Data from
http://www.nahbrc.org/evha/HDD.pdf
btw, being a blackbelt is not a very important criteria for addressing Fourier transforms.