Patterns of financial crisis: CHF/JPY 2007-2009

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Written by Forex Automaton   
Tuesday, 24 March 2009 14:56

CHF/JPY dropped during the crisis, as did the interest rate differential between the currencies. The autocorrelation "pattern" of logarithmic returns resembles those of EUR/GBP, GBP/USD, EUR/JPY, and EUR/USD, with the hour-scale "bipolar disorder", seen in the analysis as a significant negative correlation value at one hour lag, growing in prominence during the volatile phase of the crisis. Still, in CHF/JPY it falls short of the magnitude seen in EUR/CHF (ironically, one of the least volatile in forex), not to mention AUD/USD. In short, not just the increased volatility discussed in the media, but also the "bipolar disorder", a particular form of pre-history dependence, is seen as the signature pattern of financial panic.

Evolution of CHF/JPY exchange rate during the financial crisis, hour.

Fig.1:CHF/JPY during the financial crisis, hour time scale. Time axis is labeled in MM-YY format and spans the interval from August 2, 2007 through February 11, 2008.

Evolution of CHF/JPY autocorrelation peak structure during the financial crisis, hour.

Fig.2: Evolution of CHF/JPY 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. Only trading hours from 1am to 1pm New York time (European trading hours), usually rich in non-trivial correlations, are included.

I define the visible phase of the present financial crisis to begin on August 16, 2007, the day of Countrywide Financial near-bancruptcy event, followed by an extraoridinary half-percent Fed discount rate cut next day. This study covers 82 weeks from August 2, 2007 through February 12, 2008. The choice of February 12 is motivated by purely technical considerations -- there is no indication that the crisis ends there! The sub-range of extreme volatility (as will be seen in Fig.4) can be roughly defined as the last 28 weeks of this range. 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.

Speaking of CHF/JPY trends, the advent of the high volatility regime coincides with CHF/JPY breaking out of the range-bound evolution in August 2008.

Fig.2 shows the corresponding evolution of the autocorrelation of logarithmic returns in the vicinity of zero time lag. The correlation structure is represented 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.

Ideally one would like to be able to estimate significance of the observed correlation values. I do this by constructing many uncorrelated time series with volatility of the real one, running the analysis on them, and obtaining the mean and the variance of the correlation values at each time lag as a sample mean and variance -- or mean and RMS. These are shown as the mean and the range of the red background sequence in Fig.3. The problem however is the increase in volatility from "phase 1" to "phase 2", which would make a simple approach based on stationary time series (that is, constructed on the basis of the same distribution) invalid. Since the question of potential changes brought about by the crisis is interesting in itself, we separate the "phase 1" and "phase 2" correlations, see Fig.3.

Autocorrelation of logarithmic returns in CHF/JPY,  European trading hours, hour scale, from August 2, 2007 through August 27, 2008. Autocorrelation of logarithmic returns in CHF/JPY,  European trading hours, hour scale, from August 28, 2008 through February 12, 2009.

Fig.3: Autocorrelation of logarithmic returns in EUR/JPY for the European (Eurasian) trading shown against the backdrop of statistical noise (red). "Phase 1": the measurement time range is for the relatively low volatility phase of the crisis, from August 2, 2007 through August 27, 2008. "Phase 2": same for the high volatility phase, from August 28, 2008 through February 12, 2009. The noise is obtained from martingale simulations based on the recorded volatilities of EUR/JPY 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. From top to bottom, the shape of the autocorrelation in the vicinity of the zero-time lag peak sees some change.

The pattern of "bipolar disorder" has been seen before in forex exchange rates with high interest rate differential at stake, and also in LIBOR time series analyses. The "bipolar disorder" feature, a tendency to form alternating rises and falls on next-hour time scale, more pronounced than in a fully unpredictable time series of the same volatility, shows up as negative deeps surrounding the zero-time lag peak. The difference between top and bottom panels of Fig.3 can be summed up as an increase in "bipolar disorder" during the volatile phase of the crisis.

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Last Updated ( Monday, 04 January 2010 12:38 )