USD LIBOR predictability 20072010: shorter maturities show the way 
Written by Forex Automaton  
Friday, 22 October 2010 09:59  
A series of LIBOR correlation articles published on this site in late 2008early 2009 were very well received by the readers. The financial panic of 2008 was the most extreme event for LIBOR, and for reasons of timing, was not covered very well in these articles. Now, I am coming back to the topic with more data and the same statistical analysis framework. The data presented here cover the period from August 16, 2007 (the day Countrywide Financial made the news, triggering a change in the Fed stance) through July 30, 2010. The period chosen is the one characterized by the US Fed singleminded focus on lowering the short and longerterm interest rates. Not surprisingly, this definite trend shows up in the correlation analysis as a broad positive correlation peak. Crosscorrelation analysis of different maturities shows shorter maturities to play the role of leading indicators for the longer ones. The effect has a characteristic time length of up to ten days. It is the most prominent when combining overnight LIBOR with the 1month one, or combining the 1week LIBOR with longer terms. LIBOR charts
The credit crunch of 2008 is seen in the charts as a series of spikes in the overnight LIBOR and a more solid local maximum of LIBOR for longer maturities. Traditionally, the Fed manipulates the short term rates through the Open Market mechanism. These are seen to hit the ground as early as December 2008. The longer term rates continued to move down for another year. Which ones lead and which ones follow is not at all obvious from the charts, and requires correlation analysis. LIBOR autocorrelationsIn the analysis, the time series of the actual LIBOR quotes is replaced by the time series of the logarithmic returns, or logarithmic differences in the adjacent quotes. This eliminates the trivial positive component to the correlation coming merely from the positiveness of the interest rate. The zerotime lag value, essentially a variance, is a measure of volatility and does not address the issue of forecasting. Typically, the full magnitude of the zero time lag bin is left outside the scope of the plots. We are interested in the magnitudes of correlation values for the nonzero time lag bins. By definition, an autocorrelation function is symmetric around zero. Thanks to this symmetry, only left side of the plots (negative lag values) will be shown.
Fig.2 and subsequent figures ascertain the significance of the patterns by comparing with the statistical noise estimate, based on simulations devoid of correlations, but with volatility of the actual data. The most prominent nontrivial feature is the nonzero width of the correlation peak centered at zero lag. The shape of the peak evolves with maturity; one could say that what looked like a definite peak in 1month data degenerates into a broad positive "base" around lag zero in 6month data (barely significant) and disappears altogether in 12month data. None of this is visible in the traditional charts. Crosscorrelations of LIBOR termsNext, I am going to look at correlation between LIBOR rates of different maturities for various time lags. These help answer the question to what extent one LIBOR term can be predicted on the basis of any others. The figures focus on the correlation shapes at the time lags surrounding the zerolag peak. The correlation of different maturity terms (which is roughly the square root of the zero timelag peak amplitude) is seen to go down as the difference in maturities grows; similar maturities are correlated tighter. Correlations between overnight and longer term LIBOR rates
Fig.3 and Fig.4 are arguably the most interesting figures in the article. Correlation between overnight and 1month is where you see the most asymmetry in the correlation peaks. Positive values at nonzero lags mean that the data (two different LIBOR series) "do the same thing with a lag". Which one is the leader, follows from the definition of time lag. It is always defined to be t_{d} = t_{1}t_{2}, where 1 and 2 label the time series, the overnight one being "1". Therefore, a positive peak at negative lags is interepreted as the overnight LIBOR being the leader, the rest  followers. The width of the peak is important and indicates, for how many days this "echo" lasts. Correlations between 1week and longer term LIBOR ratesA very similar leaderfollower effect is seen in the correlations between 1week and 1month, 6month and 12month LIBOR.
Correlations between 1month and longer term LIBOR ratesCorrelations between 1month and longer terms exhibit a broad positive peak arond zero time lag. The leaderfollower effect is gone for these longer maturities.


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