USD LIBOR 2002-2008: predictability in times of credit tightening and expansion

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Written by Forex Automaton   
Tuesday, 13 January 2009 12:15
Article Index
USD LIBOR 2002-2008: predictability in times of credit tightening and expansion
USD LIBOR s/n-o/n autocorrelations, year-by-year comparison
USD LIBOR 1-week autocorrelations, year-by-year comparison
USD LIBOR 1-month autocorrelations, year-by-year comparison
USD LIBOR autocorrelations, 3-month and longer terms, year-by-year comparison
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The original USD LIBOR technical predictability note presented a time-integrated measurement of autocorrelations and cross-correlations associated with the USD LIBOR of various maturities. This note follows up on the topic with a time-evolution study, splitting the 2002-2008 range into separate year-long intervals. Due to changes in volatility, the integrated picture might be dominated by a few time periods of the highest volatility.  For this and other reasons, a time-evolution study is useful. It's interesting that LIBOR correlations from 2008, the year of credit crisis, look neither uninformative nor artificial. While the LIBOR patterns of 2008 are quantitatively different from other years, they do not look fundamentally different from other years with falling interest rates -- once the monstrous volatility of 2008 is taken out of the picture by proper normalization. The main finding is that the correlation patterns in the years of falling interest rates are similar among themselves and different as a class from those found in the years of rising interest rates  The interest-rate hike regime is seen as more predictable for the money markets, predictability being defined purely technically as a non-zero correlation at non-zero time lags.

BBA tracks LIBORs for various loan durations (maturities). For this study, I focus on spot-next/overnight (s/n-o/n), 1 week, 1 month, 3 month, 6-month and 1 year maturities.

History of s/n-o/n USD LIBOR 2002-2008 History of 1 month USD LIBOR 2002-2008 History of 12-month USD LIBOR 2002-2008

Fig.1: Historical USD LIBOR rates charts, top to bottom: s/n-o/n, 1-month and 12-month. Time axis is labeled in MM-YY format.

Based on Fig.2, I identify years of rising and falling spot LIBOR. Years of rising LIBOR are 2003, 2004, 2005, and 2006. Years of falling LIBOR are 2002, 2007, and 2008. These will be grouped together (into the "rising" group and the "falling" group) in this study.


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.

USD s/n-o/n LIBOR autocorrelation, day time scale, rising rates USD s/n-o/n LIBOR autocorrelation, day time scale, falling rates

Fig.2: Autocorrelation of logarithmic returns in the historical s/n-o/n USD LIBOR. Top: as measured in the years of rising interest rates: 2004, 2005, and 2006. Bottom: as measured in the years of falling interest rates: 2002, 2003, 2007, and 2008.

A few basic facts about autocorrelations may help interpreting the plots:

  • A positive autocorrelation in returns, associated with a certain time lag, means that you can bet that the current trend (be it up or down) will continue at the moment separated from now by that time lag.
  • A negative autocorrelation in returns means the opposite -- that a trend reversal is likely over that time lag.
  • Thus, the autocorrelation of a wave -- a highly predictable pattern -- looks like a wave.
  • The positive peak at zero lag by itself tells you nothing useful for prediction -- its magnitude is a measure of volatility.

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.


USD 1-week LIBOR autocorrelation, day time scale, rising rates USD 1-week LIBOR autocorrelation, day time scale, falling rates

Fig.3: Autocorrelation of logarithmic returns in the historical 1-week USD LIBOR. Top: as measured in the years of rising interest rates: 2004, 2005, and 2006. Bottom: as measured in the years of falling interest rates: 2002, 2003, 2007, and 2008.

Interest rates on 1-week terms in times of aggressive interest rates policy, Fig.3, show a lot of predictability: markets go through steps of interest rate hikes separated by certain intervals, as seen from the positive peaks around certain time-lag values. The time lags of 30 days or so seem somewhat strange though since the 7-week regular FOMC meeting interval corresponds to 70 business days. One is not so sure of the future when it comes to softening the interest rates policy, as seen from the bottom panel of Fig.3. The positive correlation is much subdued although some of it remains in the immediate vicinity of the zero-lag peak, that is on short time intervals. The "bipolar disorder" feature figures prominently again in the bottom panel, characterizing the nervousness of the money markets.


USD 1-month LIBOR autocorrelation, day time scale, rising rates USD 1-month LIBOR autocorrelation, day time scale, falling rates

Fig.4: Autocorrelation of logarithmic returns in the historical 1-week USD LIBOR. Top: as measured in the years of rising interest rates: 2004, 2005, and 2006. Bottom: as measured in the years of falling interest rates: 2002, 2003, 2007, and 2008.

The difference between the two economic regimes -- of rising and falling interests -- is amplified going over from 1-week to 1-month USD LIBOR. In the rising rates regime (Fig.4, top) the distinct positive peaks merge creating an overall positive correlation, modulated by a wave-like pattern. The interest-drop regime shows oscillatory patterns without the overall positive offset of the top plot.


USD 3-month LIBOR autocorrelation, day time scale, rising rates USD 3-month LIBOR autocorrelation, day time scale, falling rates

Fig.5: Autocorrelation of logarithmic returns in the historical 1-week USD LIBOR. Top: as measured in the years of rising interest rates: 2004, 2005, and 2006. Bottom: as measured in the years of falling interest rates: 2002, 2003, 2007, and 2008.

The evolution of the patterns continues in the 3-month data (Fig.5). In the interest-hike regime, the wave disappears and is replaced by a smoothly varying positive plateau, whereas the interest-drop regime shows stronger oscillations, 2008 being off-phase with the rest of the data, even though equally oscillatory. The organized structures weaken in 6-month data (Fig.6) and largely disapper in the 12-month LIBOR data (Fig.7).

USD 6-month LIBOR autocorrelation, day time scale, rising rates USD 6-month LIBOR autocorrelation, day time scale, falling rates

Fig.6: Autocorrelation of logarithmic returns in the historical 1-week USD LIBOR. Top: as measured in the years of rising interest rates: 2004, 2005, and 2006. Bottom: as measured in the years of falling interest rates: 2002, 2003, 2007, and 2008.

USD 12-month LIBOR autocorrelation, day time scale, rising rates USD 12-month LIBOR autocorrelation, day time scale, falling rates

Fig.7: Autocorrelation of logarithmic returns in the historical 1-week USD LIBOR. Top: as measured in the years of rising interest rates: 2004, 2005, and 2006. Bottom: as measured in the years of falling interest rates: 2002, 2003, 2007, and 2008.

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Last Updated ( Monday, 04 January 2010 12:42 )