Patterns of financial crisis: EUR/GBP 2007-2008.

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Written by Forex Automaton   
Monday, 02 February 2009 15:21

Both the initial autocorrelation structure of EUR/GBP at the onset of the present crisis and its modification during the volatile phase of the crisis resemble those of EUR/JPY, EUR/USD, and GBP/USD: the autocorrelation function of logarithmic returns, with initially visible positive tails of the zero-lag peak, becomes oscillatory in the vicinity of zero lag as the EUR/GBP rally unfolds in the late 2008. Thus the abnormal volatility is accompanied by a specific correlation structure, and EUR/GBP is consistent with the broader picture of "bipolar disorder" correlation being the characteristic pattern of the financial panic.

Evolution of EUR/GBP exchange rate during the financial crisis, hour.

Fig.1:EUR/GBP during the financial crisis, hour time scale. Time axis is labeled in MM-YY format and spans the interval from August 2, 2007 through December 31, 2008.

Evolution of EUR/GBP autocorrelation peak structure during the financial crisis, hour.

Fig.2: Evolution of EUR/GBP autocorrelation peak structure during the financial crisis, hour time scale. Time bin is two weeks wide. The peak structure is represented by three correlation values: the one for the zero lag (essentially a volatility measure) downscaled by 10 for easier visual comparison, the one at one hour lag and the one at two hour lag. Time axis is labeled in MM-YY format and spans the interval from August 2, 2007 through December 31, 2008. Only trading hours from 1am to 1pm New York time (European trading hours), usually rich in non-trivial correlations, are included.

As before, the time interval starting in August 2007 is split into two parts, the "moderate" and the high volatility one, whose features are then compared. 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 74 weeks from August 2, 2007 through December 31, 2008.

In terms of EUR/GBP trends (Fig.1), the range under study can be subdivided into upward (up to beginning of April 2008), sideways (from April to end of October), and the fast upward trend which started in November. Thus, EUR/GBP was already abnormally volatile while still in the sideways trend in September 2008.

Fig.2 shows the evolution of the correlation structure in the vicinity of zero time lag, representing the correlation structure as a triplet of correlation values: those at zero, one and two hour lags. The increased volatility shows up as the increase in the magnitude of all these values, with variance (a measure of volatility) being fairly well represented by the magnitude of the zero time lag value.

The sub-range of extreme volatility can be roughly defined as the last 18 weeks of this 74-week range. Thus, I divide the time interval under study in two unequal parts, those of (relatively speaking) low and high volatility. The low volatility phase is from August 2, 2007 through August 27, 2008. The high volatility phase is from August 28 through the end of 2008. For the two time intevals defined, the autocorrelation is investigated in Fig.3 as a function of its time lag, rather than function of time as in Fig.2.

 

In this study, I only look at trading activity taking place from 1am to 1pm New York time, since the experience shows it to be the richest in non-trivial correlations.

Autocorrelation of logarithmic returns in EUR/GBP,  European trading hours, hour scale, from August 2, 2007 to August 27, 2008. Autocorrelation of logarithmic returns in EUR/GBP,  European trading hours, hour scale, from August 28, 2008 to January 01, 2009.

Fig.3: Autocorrelation of logarithmic returns in EUR/GBP for the European (Eurasian) trading shown against the backdrop of statistical noise (red). Top panel: the measurement time range is for the relatively low volatility phase of the crisis, from August 2, 2007 through August 27, 2008. Bottom panel: same for the high volatility phase, from August 28, 2008 through the end of 2008. The noise is obtained from martingale simulations based on the recorded volatilities of EUR/GBP in the trading hours under study for the period. The noise is presented as mean plus-minus 1 RMS, where RMS characterizes the distribution of the correlation value obtained for each particular bin by analyzing 20 independent simulated uncorrelated time series of the same average volatility.

In Fig.3, the pattern in the vicinity of the zero time lag bin is quite different in top and bottom panels. In the top panel, it looks like the zero-lag correlation peak has tails which fill the one-hour lag bins. In the bottom panel, it's the familial pattern of "bipolar disorder", a tendency to form quickly alternating rises and falls on next-hour time scale, more pronounced than in a fully unpredictable time series of the same volatility. This pattern shows up as negative deeps surrounding the zero-time lag peak, as has been seen before in forex exchange rates with high interest rate differential at stake, and also in LIBOR time series analyses. The significant positive signal at 2-hour lag in Fig.3, bottom panel, does not contradict the "bipolar disorder" pattern, since oscillation (of patient's mood, as it were) fits well into the pattern of such a disorder.

The data used are from the period 2002-08-02 00:00:00 to 2009-01-01 00:00:00, New York time.

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Last Updated ( Monday, 04 January 2010 12:41 )