USD LIBOR predictability 2007-2010: shorter maturities show the way

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Written by Forex Automaton   
Friday, 22 October 2010 09:59
Article Index
USD LIBOR predictability 2007-2010: shorter maturities show the way
USD LIBOR autocorrelations
Correlations between USD LIBOR maturities, overnight and longer terms
Correlations between USD LIBOR maturities, 1-week and longer terms, 1-month and longer terms
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A series of LIBOR correlation articles published on this site in late 2008--early 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 single-minded focus on lowering the short- and longer-term interest rates. Not surprisingly, this definite trend shows up in the correlation analysis as a broad positive correlation peak. Cross-correlation 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 1-month one, or combining the 1-week LIBOR with longer terms.

LIBOR charts

History of overnight USD LIBOR 2007-2010 History of 1-week USD LIBOR 2007-2010 History of 6-month USD LIBOR 2007-2010 History of 12-month USD LIBOR 2007-2010

Fig.1: Historical USD LIBOR charts, top to bottom: overnight, 1-week, 6-month, and 12-month maturity. Time axis is labeled in MM-YY format. The data covers the time range from 2007-08-16 to 2010-07-30.

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 autocorrelations

In 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 zero-time 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 non-zero 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.

USD overnight LIBOR autocorrelation, 1 day time scale USD 1-week LIBOR autocorrelation, 1 day time scale USD 1-month LIBOR autocorrelation, 1 day time scale USD 6-month LIBOR autocorrelation, 1 day time scale USD 12-month LIBOR autocorrelation, 1 day time scale

Fig.2: Autocorrelations of logarithmic returns in the historical USD LIBOR are shown against the backdrop of statistical "noise". The noise is obtained from martingale simulations based on the historical volatilities of LIBOR for the period under study. The noise is presented as mean plus-minus 1 RMS, where RMS characterizes the distribution of the correlation value obtained for each particular time lag bin by analyzing 20 independent simulated uncorrelated time series. The RMS is a measure of accuracy in the determination of the correlation values, an irreducible uncertainty dependent on the amount of data and the time scale. Top to bottom: overnight, 1-week, 1-month, 6-month, and 12-month data.

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 non-trivial feature is the non-zero 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 1-month data degenerates into a broad positive "base" around lag zero in 6-month data (barely significant) and disappears altogether in 12-month data. None of this is visible in the traditional charts.


Cross-correlations of LIBOR terms

Next, 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 zero-lag peak.

The correlation of different maturity terms (which is roughly the square root of the zero time-lag 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

Correlation between logarithmic returns in overnight and 1-week USD LIBOR rates as a function of time lag, days Correlation between logarithmic returns in overnight and 1-month USD LIBOR rates as a function of time lag, days Correlation between logarithmic returns in overnight and 6-month USD LIBOR rates as a function of time lag, days Correlation between logarithmic returns in overnight and 12-month USD LIBOR rates as a function of time lag, days

Fig.3: Correlation between logarithmic returns in overnight and, top to bottom: 1-week, 1-month, 6-month and 12-month USD LIBOR rates as a function of time lag, days, shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the historical LIBOR volatilities for the period under study. 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 pairs of uncorrelated time series.

Fig.3 and Fig.4 are arguably the most interesting figures in the article. Correlation between overnight and 1-month is where you see the most asymmetry in the correlation peaks. Positive values at non-zero 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

td = t1-t2,

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 1-week and longer term LIBOR rates

A very similar leader-follower effect is seen in the correlations between 1-week and 1-month, 6-month and 12-month LIBOR.

Correlation between logarithmic returns in 1-week and 1-month USD LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 1-week and 6-month USD LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 1-week and 12-month USD LIBOR rates as a function of time lag, days

Fig.4: Correlation between logarithmic returns in 1-week and, top to bottom: 1-month, 6-month and 12-month USD LIBOR rates as a function of time lag, days, shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the historical LIBOR volatilities for the period under study. 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 pairs of uncorrelated time series.

Correlations between 1-month and longer term LIBOR rates

Correlations between 1-month and longer terms exhibit a broad positive peak arond zero time lag. The leader-follower effect is gone for these longer maturities.

Correlation between logarithmic returns in 1-month and 6-month USD LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 1-month and 12-month USD LIBOR rates as a function of time lag, days

Fig.5: Correlation between logarithmic returns in 1-month and, top to bottom: 6-month and 12-month USD LIBOR rates as a function of time lag, days, shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the historical LIBOR volatilities for the period under study. 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 pairs of uncorrelated time series.

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Last Updated ( Saturday, 05 May 2012 15:08 )