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).

Friday, August 28, 2015

Recent behaviour of the Case Shiller index (or where are we now?)

One example of multistability I have used in the past few years is the reconstructed state space portrait of the Case Shiller index.

I have been studying state space of complex systems in the hope to better understand them. My original interest was in natural systems-I have gotten dragged into economic data sets because they are generally better.

Data for the Case Shiller index is found here (click the link labelled "US Home Prices 1890 to present"). The first two plots have been posted before, showing the index plotted against itself with a four-year lag.

The first plot shows the annual index to 2012, along with predictions of where in state space the system would plot in 2015, for declining house prices, constant house prices, or rising house prices (in inflation-adjusted terms). The major features are two very long-term islands of stability, at about the 70 level (from 1915 to 1945) and around the 110 level (until 1999); and the large crashing loop that has been traced out since 1999.

This plot shows the same information, but monthly from 1954. The area of stability occupied until 1999 is circled in yellow, and the large "cycle" is also visible, showing that the system was following the trajectory of rising house prices in 2014.

The last plot represents the most recently available data, projected monthly, but it shows the same thing--the long-term area of stability at lower left, and the big loop, now nearly closed. The last available point is reasonably close to the projected state for 2015 (which itself would be averaged over the year).

Is this a potential area of stability? Sadly, no. In this type of plot, long-term stability will have to occur along the y = x line shown on the second graph in this posting. Presently, we are far below or to the right of this line.

If house prices had been frozen at the levels of the end of 2011, we could have developed a region of stability. But the stable state would have been within the large area of stability that existed prior to 1999. Who the hell wants that (apart from young people hoping to buy a house)? So we are embarking on yet another price increase, once again into a market with no ability to support the higher prices. The long term prognosis is for another rise and collapse. Time will tell how big it gets.

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