Loehle and Scafetta Bart
steven mosher says:
July 25, 2011 at 8:35 pm
“Now, enthusiasts have a standard counter to that argument, namly that their cycles are real, but ‘intermittent’ [i.e. come and go].”
hehe like gremlins
Willis Eschenbach says:
July 25, 2011 at 10:03 pm
You can easily find such cycles in a variety of chaotic systems, like say the stock market. The problem is that the cycles come and go. When you look at chaotic systems, you’ll often find what look like cycles. But the problem is, they don’t last. You may find a period with say a sixty and a twenty year cycle, but then the twenty year cycle fades out and is replaced by a thirty-five year cycle. Or the sixty year cycle simply narrows over time and becomes a fifty year cycle.
You guys do not understand stochastic systems. This is precisely how a system of lightly damped modes of a system described by partial differential equations with random input behaves. Precisely. This is how the real world works. I see it every single god**ed day analyzing structural resonances. Cycles come and go. For a given time period, they can look similar to a steady state oscillation, but eventually, they are randomly amplitude and frequency modulated.
It is wholly unremarkable, standard workaday, cut and dried, basic, elementary stuff. If I had any hair left, I would be tearing it out over all this foolishness. In a room of my peers, there would be no question about it, just affirming nods and sympathetic murmurs. I tried explaining it to Leif once, but he does not understand it and does not want to understand it. You probably won’t either, but I’m telling you what is, regardless of how you receive it.
The example I gave to Leif is the Sun spot cycle. As I showed here, the Sun spot cycle is dominated by two processes with resonances corresponding to periods of roughly 20 and 23.6 years. A simple two-mode system can be used to model the process, as shown here. The resonances are driven by random inputs which, for all practical purposes, can be modeled as white noise. When I simulate this system, I get results which qualitatively look very similar in character to the actual Sun spot data, as here, and here.
As you can see, the cycles grow and fade over time. This is what real world systems do. If I had the time, I could formulate a Kalman Filter which I would prime with the historical data, and I could then project optimal estimates and associated uncertainty bounds for the process forward (or backward) in time. But, I do not have the time. I am busy doing important things which actually have application in the real world – besides which, like primitive people who cannot be made to believe that there is no Rain God, I’d likely only get grief for my efforts to enlighten (like I got from Leif). But, it just kills me to see neophytes to the world of stochastic systems analysis make such a hash of things, laughing up their sleeves at things they do not understand, when it is so simple, and has been known for decades, and is done every day in scientific and technical trades the world over.