Forex Automaton

The results for EUR/JPY and the respective LIBOR ratio, obtained in the inter-market correlation technique for logarithmic returns, look somewhat disappointing. The sharp zero-lag peaks seen in USD/JPY for LIBOR durations longer than 3 months are absent here. The quantitative analysis of time lag dependence of the correlation shows the EUR/JPY movement during the crisis to precede, rather than to follow the interest rate developments, however this seems to be more of a single long-range event than a repetitive and predictive temporal connection required for trading system formulation.

This post continues the work of Forex-LIBOR correlation started last week with EUR/USD: using inter-market correlation to get a first-hand understanding of the connection between the interest rates and forex on the basis of real data. The milder volatility pre-crisis period ("A") and the present crisis ("B") are studied separately and compared.

Executive summary: LIBORs with maturity below 3 months appear uncorrelated with forex, whereas longer maturities are correlated with it. Surprisingly, the volatility-adjusted (via Pearson normalization) correlation seems to become stronger in period B despite the interest rate cuts and doubts about relevancy of LIBOR fixing amidst the credit crunch.

I use inter-market correlation to get a first-hand understanding of the connection between the interest rates and forex. I start with EUR/USD and, for the sake of uniformity, the respective ratio of LIBORs of various maturities. The correlation is a function of the time lag and in real life, in contrast with the efficient market assumption, its behavior with time lag is often informative. As usual, I pay particular attention to the non-zero time lags since these, when non-zero in a statistically significant way, quantify predictability of the time series, provided there are reasons to expect that some aspects of the time series repeat themselves over time. The present crisis and the preceding milder volatility period are studied separately and compared.

Executive summary: the correlation between LIBOR interest rates and forex should not be taken for granted. For example, in the pre-crisis period of 2002-2007, no correlation between shorter LIBOR maturities and EUR/USD is detected. During the crisis, long range correlations are seen in the movements of the instruments -- again surprising given the interest rate cuts and doubts about relevance of LIBOR fixing in the midst of a credit crunch.

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.

The New Zealand Dollar LIBOR has been mostly rising during the period under study, like it did for the Australian Dollar. Motivation for publishing LIBOR correlation analysis on a forex trading system site has been outlined in the first USD LIBOR analysis article. This document begins with historical LIBOR charts for the currency, continues with volatility analysis, and culminates with autocorrelations and correlations of logarithmic returns for various NZD LIBOR terms. As for the Aussie, the predominant predictive pattern for the NZD LIBOR interest rate is a "damped oscillation", but unlike AUD, the pattern stays well pronounced not just for the spot-next/overnight and 1-week, but even for the 6-month and 12-month duration terms. Another common feature is positive correlation peaks in the vicinity of the zero time lag, getting wider as the duration term grows. The cross-correlation of different maturities is oscillatory, but the trend is seen for the shorter term to be of predictive influence on the longer term (with either positive or negative "feed-back"), rather than the other way round as is the case with CAD and to some extent, USD LIBORs. The data cover the period from July 2003 up to December 2008.

Like the Danish Krone, the Swedish Krona LIBOR has been mostly rising during the period under study. Motivation for publishing LIBOR correlation analysis on a forex trading system site has been outlined in the USD LIBOR analysis. This document begins with historical LIBOR charts for the currency, continues with volatility analysis, and culminates with autocorrelations and correlations of logarithmic returns for various SEK LIBOR terms. The main predictive patterns in SEK LIBOR are broad correlation peak around zero time lag, whose width varies with maturity, and periodic (wave-like) oscillations. The data cover the period from February 2006 up to December 2008.

Among the other LIBOR rates, the Danish Krone LIBOR is remarkable for its positive autocorrelations, peculiar and very strongly pronounced short-range pattern of the overnight interest rate, and the weakness of the correlation between different duration terms. Like the previous LIBOR predictability overviews, this document begins with historical LIBOR charts for the currency, continues with volatility analysis, and culminates with autocorrelations and correlations of logarithmic returns for various DKK LIBOR terms. As with many other currencies, the predictable patterns in DKK LIBOR evolve with loan duration term from short-range but strong and regular oscillation in the overnight through smooth waves in 3-month and into relative featurelessness of the 12-month LIBOR. Motivation for publishing this type of study on a forex trading system site has been outlined in the USD LIBOR analysis. Here I can only add that for a student of financial correlations, LIBOR is a nice real-life intuition-building tool, for the correlations are so strong you can learn to identidy features in the charts with features in the correlations visually.

Like the previous LIBOR predictability overviews, this document begins with historical LIBOR charts for the Canadian Dollar, continues with volatility analysis, and culminates with autocorrelations and correlations of logarithmic returns for various CAD LIBOR terms. 1-week LIBOR shows wave-like correlation pattern with a period of about 30 days on top of a positive autocorrelation. As the loan duration gets longer, the wave disappers and a more uniform positive autocorrelation emerges for the range of time lags of up to 70 days. That gets reduced to a 2-3 days wide peak around zero time lag for 12-month LIBOR. Cross-correlations between different LIBOR terms show srong predictability of the shorter range LIBOR on the basis of longer range. Motivation for this type of study has been outlined in the USD LIBOR analysis.

Like the previous LIBOR predictability overviews, this document begins with historical LIBOR charts for the Australian Dollar, continues with volatility analysis, and culminates with autocorrelations and correlations of various LIBOR terms. You will see that predictable patterns in AUD LIBORs are quite unique. Autocorrelations of short-term LIBORs show oscillations with about 7-8 day pediod, similar to USD but localized in the short range lags. For 3-month, 6-month and 12-month terms, broad (a few days) correlation peaks around 0 time lag are seen. For 3-month and 6-month LIBORs, the correlation is seen to be overall positive for the range of lags up to 70 or 80 days.

I've outlined the original motivation to study historical LIBOR data from predictability point of view in the USD LIBOR article. I continue with the logarithmic returns technique that proved useful in forex. Like the previous reports, this document begins with historical LIBOR charts for the Swiss Franc, continues with volatility analysis, and culminates with autocorrelations and correlations. You will see that predictable patterns in CHF LIBORs vary with duration term. Autocorrelations of short-term LIBORs show fast (about 4-day period) oscillation. For 3-month and 6-month terms, the main correlation pattern does not develop 70-day period waves on top of positive background, in contrast to USD and EUR LIBORs, but keeps oscillating between positive and negative autocorrelation values, with the oscillation period longer than that of the shorter terms. The autocorrelation of 12-month LIBOR remains similar to 6-month instead of becoming more uniformly positive as it does for JPY or more jittery as it does for USD, EUR and GBP.