Dust flux, Vostok ice core

Dust flux, Vostok ice core
Two dimensional phase space reconstruction of dust flux from the Vostok core over the period 186-4 ka using the time derivative method. Dust flux on the x-axis, rate of change is on the y-axis. From Gipp (2001).

Wednesday, January 28, 2015

House prices seek stability of long-term relationship

. . . somewhere in phase space.

I have often used the the index of home prices in the United States (the Case Shiller index) as an example of a complex system showing multistability. The data are updated monthly here.

The multistable nature of such systems is demonstrated in reconstructed phase space portraits, which can be generated by two principal methods--the time-delay approach and the time-derivative approach.


For nearly 40 years, the system remained confined to the area of the yellow circle. In fact, house prices were confined to this small area for much longer than that--for the longer term chart I've presented previously shows that this yellow area has been occupied for a total of about 70 years.

It looks like there was some kind of redefinition or recalculation of the time series on the Shiller website sometime in the last year or so, as the current time series available on the site (from which the above chart is drawn) differs from the previous time series available (from which my older graphs are drawn). For instance, in my older figure, the house price appears to have been above 100 over the last 60 years--this does not appear to be the case in the graphs I have produced in previous years.

The overall story has not changed--after 50 years of relative stability (the bubble of 1989-90 looks benign in the above figure), the system broke out of its area of Lyapunov stability, and has been meandering through phase space ever since. Two years ago, it seemed to be on a trajectory to return to the yellow area of stability. In the last two years the system trajectory veered away from that target, and is now headed . . . where?

Normally we expect it to migrate to an area which has previously acted as an area of stability--but both such areas are at much lower prices than is currently the case.

It is possible for the system to carve out a new area of stability. For reasons of geometry, stable areas must be located on the y = x line. Since we are close to that line now, it implies that perhaps Yellen can engineer a soft landing for housing at close to the current price range. Unfortunately, the future level of the trajectory in state space is partially determined by the past trajectory--and in 2013, the housing index was in the low 130s (on the horizontal axis). In two years, therefore, the trajectory will dip to the same level on the vertical axis. If house prices remain where they are now, the trajectory will be far enough from the y = x line to be unstable, and a further decline in house prices would be indicated.

If house prices rise again, we will find ourselves in a bubble destined for collapse, just as we were in about 2004. If the yellin' wants to bring housing to stability, the thing to do would be to engineer a slight decline in house prices over the next two years. Unfortunately, I don't think she wants to do that.

Friday, January 23, 2015

Thursday, January 22, 2015

Near-term struggle for gold

We have a new visitor with an interest in gold.


So let's give him (her?) something to read about, shall we?

Over the past few years I have use reconstructed phase space portraits to try to gain some insight into dynamic systems. Key features that we can identify in these diagrams are areas of stability, where some parameter is trapped into a fairly narrow range for a period of time. It appears to be nearly universal in interesting systems that there are multiple metastable equilibria, meaning more than one area where the system is stable--such systems are characterized by long periods of quiescence punctuated by rapid bursts of activity (volatility).


Since the plot shows the trajectory of the system through time, an area of stability is an area of phase space in which the system remains trapped for a long period of time relative to the shorter periods of time in which the system shifts from one region of the graph to another.

In the above phase space plot of gold x USDX, there are three regions of stability--one centered at about the 650 level, one at about the 1050 level, and one at about the 1350 level. The system has been locked into the area of stability at the 1050 level since about July 2013.

These areas of stability actually have nothing to do with gold or the US dollar. They exist because of mass psychology; and the sudden changes from one region of stability to another is a function of a rapid change in the perception of value.

What I usually look for in these plots is a sign of a breakout from an area of attraction. For instance, last week's print appears just outside the middle region of attraction. It isn't far enough outside the border (which has been placed in completely arbitrary fashion), but if the system trajectory continues to extend in its current direction for a couple more weeks, I would conclude the system is heading towards the area of attraction at the 1350 level.

Complicating this simple picture is the phase space portrait just for gold, seen below.


This graph looks remarkably like the phase space diagram for gold x USDX: there are three areas of attraction, and the system has been mired in the middle one for about a year-and-a-half. But there is a major difference--the present gold price is nowhere near to breaking out of its current area of attraction. It is currently somewhere in the middle of it, having spent most of the past year near the bottom of it.

So one chart suggests an imminent breakout, and one does not. Can they both be true?

The target for gold x USDX (assuming we do get a breakout) would be in the 1350 range, and it would be reached in about 18 weeks. Given the rate of rise of the US dollar, it would not be surprising if it reaches the 100 level in this time. The 1350 level, in this case, would be reached with a gold price of $1350 per oz, which would still be within the current area of attraction for the gold price.

It doesn't seem reasonable for both gold and the US dollar to rise so far together, unless we either accept Richard Russel's suggestion that debt represents a short position against the US dollar, or we are seeing the beginnings of a move in money down Exter's Pyramid.

Monday, January 19, 2015

Grottoes and hobbit holes of Luo Yang

Driving around over the Great Loess Plain of China, you eventually come to Luo Yang, home of the peony festival. Not too many peonies around this time of year, but the city is famous for other reasons, including the Longmen Grottoes, a UNESCO World heritage site.


The grottoes are small caves that have carved out of a limestone cliff. They are decorated with sculptures representing buddha, boddhisatvas, guardians, and pagodas. The sculptures were all created between the late fifth century (C.E.) and the early 12th century.



View from Xiangshan temple


There are about 1400 caves and over 100,000 carvings (including some very small ones).




Progressive details in Leigutaizhongdong Cave.





Large sculptures of Feng Xian Si (the large grotto in the top two images).

A small reflection of the grottoes is found in the loess cliffs along the highway near Luo Yang. I call these hobbit holes, even though they aren't dwellings. Some of them are brick-lined, but most appear to be for manufacture.



Loess is quite cohesive, and there are regions in China where people live in the stuff. It is pretty stable until there is an earthquake, at which point the casualties can be horrific.


Big hobbit hole.