In October S&P 500 index is likely to retest recent lows

This post is an update to the S&P500 prediction posted on this blog earlier in July. The prediction comes true as well as oil bubble burst forecast issued here. However the S&P index did not plunge as low as 1150 points but the critical time prediction was quite accurate. Also it has to be remembered that critical time obtained from LPPL models is only the most probable point of trend reversal. Financial markets are complex and open systems and its valuation oscillations are driven both by endogenous end exogenous factors. In July In my assessment S&P500 price dynamics was strongly affected by SEC naked short-selling ban on the stocks of major financial institution. But take me correct I don’t think that SEC decision was wrong on contrary I think it was absolutely correct and needed as it break negative feedback loop.



Here I want to make an update to my earlier prediction of S&P500 based on LPPL model. An LPPL model applies concepts of criticality from statistical physics however I will not focus here on the theory complex systems (nice and easy to read easy on complex system and LPPL models you can find here .)

A complex system is a system composed of interconnected parts that as a whole exhibit one or more properties (behavior among the possible properties) not obvious from the properties of the individual parts. Financial markets and economy as a whole is a complex system buildup with a large number of interconnected elements.

The characterization and understanding of complex systems is a difficult task, since they cannot be split into simpler subsystems without tampering the dynamical properties.
One approach in studying such systems is the recording of long time series of several selected variables (observables), which reflect the state of the system in a dimensionally reduced representation

Data series generated by complex systems exhibit fluctuations on a wide range of time scales and/or broad distributions of the values. Some systems are characterized by periodic or nearly periodic behavior. In these cases, the dynamics can be characterized by scaling laws. Such dynamics are usually denoted as fractal or multifractal, depending on the question if they are characterized by one scaling exponent or by a multitude of scaling exponents.

If one finds that a complex system is characterized by fractal dynamics with particular scaling exponents, this finding will help in obtaining predictions of the future behavior of the system.
In 2000-2003 anti-bubble/bear phase The S&P500 index shows clear oscillations with 5 sharp local minima and the self similar structure and the scaling exponent was easy to find.

The local minima are dated as follows: m5=12-Oct-2000; m4=20-Dec-2000; m3=04-APR-2001; m2=21-SEP-2001; m1=23-July-2002.

Log-Periodicity means that that the ratios of the distances between the consecutive repeatable minima should be constant equal to the preferable scaling ratio λ which is a signature of Discrete Invariance Scale(DSI)

(Mn-Mn+1)/(Mn+1-Mn+2)=(Mn+1-Mn+2)/(Mn+2-Mn+3)=λ
Using the previously determined minima M1,…,M5 we get

(m1-m2)/(m2-m3)=λ1=1.79
(m2-m3)/(m3-m4)=λ2=1.62
(m3-m4)/(m4-m5)=λ3=1.52

It shows that all scaling ratios are comparable and if it would be known ex-ante it would help to find next local minima in the bearish trend giving significant upper hand. More detailed discussion about 2000-2003 S&P500 index anti-bubble period you can find in D.Sornete works (link here 1 2 3)

The main disadvantage of the Shrank’s transform presented above it that it needs quite a long time series to determine the preferable scaling factor of the system. Although in the current bearish pattern of the S&P 500 index also shows strong oscillations but the time series is much shorter and its much harder to determine the scaling parameters. So instead of Shrank’s transform I implemented the Lomb spectral analysis. I done the computation in Matlab using procedure written by Brett Sholeson. After visual analysis of the S&P500 index I chose for critical time tc=10-10-2007, then the data was detrended.



The Lomb periodogram (chart 2) exhibit an extremely significant peak close to log-frequency f=w/2π=2.6 with the amplitude larger than 60. Second peak is close to 2w log frequency which suggest the presence of harmonic anagular. The visual structure of the current S&P500 time series with double minima pattern also suggest suggest the presence of a rather strong harmonic at the angular logfrequency.

The data fit quite well to the formula. Numbers on horizontal are counting the distance in trading days from the critical time tc=10-10-2007
Below I put the chart with the forecast for S&P 500 index from the LPPL model. The forecast suggest that the next minima S&P500 index will reach in October/November and the index should rally into year 2009 when the trend should turnaround toward new minma.