Forex Automaton

Fig.1:Top: evolution of SPDR (SPY), day scale. Time axis is labeled in MM-YY format and spans the interval from August 2, 2007 to January 29, 2009.

Fig.2: Evolution of Pearson correlation coefficient between the logarithmic returns in SPY and AUD/JPY, day scale. Time bin is two weeks wide. Time axis is labeled in MM-YY format and spans the interval from August 2, 2007 to January 29, 2009.

Fig.3: Evolution of the correlation between SPY and AUD/JPY correlation peak structure during the financial crisis, day time scale. The peak structure is represented by three correlation values: the one for the zero lag (essentially a volatility measure) downscaled by 5 for easier visual comparison, the one at (plus or minus) one day lag and the one at (plus or minus) two day lag. Negative lags are in the top panel, positive lags -- in the bottom panel. Time axis is labeled in MM-YY format and spans the interval from August 2, 2007 through January 29, 2009.

As before, I define the visible phase of the present financial crisis to begin on August 16, 2007, the day of Countrywide Financial near-bankruptcy event, followed by an extraordinary half-percent Fed discount rate cut next day. This study covers 78 weeks from August 2, 2007 through January 29, 2009. Fig.3 shows the time evolution of the correlation peak by plotting the correlation values for the negative and positive lags in separate panels.

The time lag is defined as

t_d = t₁ - t₂,

where index "1" denotes SPY and index "2" denotes AUD/JPY. Therefore, negative correlation value at negative lags means that movements of the same direction in SPY and JPY/AUD happen at an earlier time in SPY, or SPY is a leading indicator for JPY/AUD. Likewise, a negative correlation value at positive lags means that movements of the same direction in SPY and JPY/AUD happen at an earlier time in JPY/AUD, or JPY/AUD is a leading indicator for SPY. Both types or correlation are seen in Fig.3, however it is not clear at this time whether this is an indepenent effect or a consequence of AUD/JPY and SPY being autocorrelated in a particular way, with no extra value to be extracted from the intermarket correlation.

The time evolution of the correlation peak structure (Fig.3) resembles what has been seen in the corresponding plots of SPY and forex autocorrelations such AUD/JPY: the increased volatility (zero time lag shooting up) is accompanied by increased next-to-zero bin signal (shooting down). I say next-to-zero because the AUD/JPY post dealt with the hour time scale while the SPY one -- with day time scale. Same pattern has been seen in many other plots in the Patterns of Financial Crisis series.

The fact that same or similar pattern has been seen for both time frames (scales), hour and day, is remarkable -- and makes one recall the idea of self-similarity (or fractality) applied to markets by Benoit Mandelbrot ("The (Mis)behavior of Markets"). The pattern or texture of a self-similar object has a property to reproduce itself as the scale of analysis (trading time frame in our case) changes. This is familiar from everyday experience -- for example, due to self-similarity of turbulence, it is very difficult to estimate by eye the size of a body of a human bathing in the ocean surf, when watching from ashore -- one can easily mistake an adult for a child or vise versa. The textures you see in turbulence provide no benchmark to gauge the size of an embedded object, due to self-similarity and lack of characteristic scale.