A time-integrated study of hourly time-scale lagged correlation between USD/TRY and EUR/JPY reveals hints of a correlation whereby EUR/JPY leads and TRY/USD follows with a lag on one hour.

Compared to the series of intermarket correlation reports generated in 2008-2009 (not covering Turkish Lira), the new reports adopt a somewhat different approach to statistical uncertainty estimation. Instead of synthesizing mock time series with the volatility distribution of the real ones, producing their autocorrelations (and intermarket correlations), and inferring the uncertainty from a comparison of many such analyses, as was done in 2008-2009, I now infer the uncertainty of the correlation coefficients directly as a standard deviation of the sum, knowing the terms entering the sum. As before, hourly data are used and the quantity correlated is hourly logarithmic return.

The data used cover the period from November 14, 2010 till December 09, 2012.

**1.1** **1.2**

The time lag between the USD/TRY and EUR/JPY time series is defined as

t_{d} = t_{USD/TRY} – t_{EUR/JPY}.

The negative correlation content in the +1 hour time lag bin is seen with about 2.5 standard deviations. This means that a move (the present analysis is insensitive to the direction of that move) in USD/TRY and time t and a move in EUR/JPY at time t-1 are negatively correlated over the time of observation. This is the same as saying the TRY/USD follows (trails) a movement in EUR/JPY with a lag of one hour. Due to the discrete nature of binning, the actual ticks that create the effect could be separate by a time interval from anything about zero to anything below two hours and still land in the separate adjancent hourly periods, creating a 1-hour lag effect. The average such time interval is one hour.

Speaking of pair trading, when forming a pair of EUR/JPY and USD/TRY, due to the negative correlation, both positions must be held short or long at the same time. The relative weight with which EUR/JPY and USD/TRY enter the pair must be optimized to increase the one-lag correlation with respect to the one at lag zero. Qualitatively speaking, the features around zero in Fig.2 (zero autocorrelation at 1-hour lag in EUR/JPY and negative autocorrelation at 1-hour lag in USD/TRY) will not cancel the feature in Fig.1 (also negative). The resulting pair will be a mean-reverting autocorrelated time series.