|Written by Mikhail Kopytine|
|Tuesday, 13 January 2009 12:15|
Page 2 of 5
In the autocorrelation distribution for the time series of zero mean, the magnitude of the zero time-lag peak equals variance of the varibale which constitutes the time series (logarithmic return of LIBOR in our case). Dramatic changes in this variance with time (variations in volatility) obscure visual comparison of features common to different time periods in the same figure. For this reason, below I prescale all histograms (of autocorrelations) by the factor which equals inverse magnitude of the zero time-lag peak. After that, the histograms "match" each other at the peak. Large prescale factors correspond to low volatility and vice versa.
A few basic facts about autocorrelations may help interpreting the plots:
The "bipolar disorder" feature, a tendency to form quickly alternating rises and falls on next-day 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, and is seen in time series of some interest rates and forex exchange rates, especially the ones with high interest rate differential. In USD LIBOR, as seen from top vs bottom comparison in Fig.2, this feature appears more pronounced in the falling interest rates climate.
Both panels of Fig.2 show periodic structures. The period and the peak positions ("phase" of the structure) show a fair degree of stability year from year, and despite the change in the interest rates dynamics.
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