Introducing monthly correlation reports

Sunday, 19 February 2012 12:56

Forex Automaton is launching a new type of information product: a monthly correlation analysis report. The reports are computer-generated and follow a pre-defined format. This document explains the purpose and structure of the reports and is intended to serve as a brief user manual to the new information product. It also collects in one place any other information necessary to understand the reports, which otherwise would have to be repeated in every report. The document explains the quantities shown in the plots and relationships between the plots.

Intended audience and the purpose of the reports

Regularly updated quantitative information about the correlations in foreign exchange time series on various time scales, including lagged correlations (a.k.a. leader-follower effects) is of value to hedgers, speculators, execution traders, portfolio managers, investment advisors, and analysts. The least ambitious use of this information is construction of multi-currency portfolios with desired volatility. Availability of information about lagged correlation opens up a new dimension of analysis, related to the problem of forecasting.

Foreign exchange rate notation

Notation like EURUSD may be used to mean EUR/USD, and so on for other currency pairs.

Time series granularity and the period of measurement

To conduct correlation analysis, two characteristic time scales need to be defined.
  • First, one needs to define a duration of time such that one is able to talk with certainty about the price quote being found somewhere with a time interval of that duration. The higher the liquidity, the shorter this time scale can potentially be. This time scale defines the "granularity" of the time series being analyzed. For the present reports, this time scale is defined to be one hour -- certainly not the shortest possible.
  • Second, one needs the time scale of data aggregation, since correlations are properties of time series of certain length. This time scale is set to one month.

Quantities and definitions

The reports track the 14 most popular foreign exchange rates: AUD/JPY, AUD/USD, CHF/JPY, EUR/AUD, EUR/CHF, EUR/GBP, EUR/JPY, EUR/USD, GBP/CHF, GBP/JPY, GBP/USD, USD/CAD, USD/CHF, USD/JPY, in this order, constructing correlation functions within each time series (14 autocorrelations) and 14×(14-1)/2 = 91 unique correlations among the different time series.

Fig.1.  January 2012.  Left panel: Correlation between hourly logarithmic returns in AUD/JPY and USD/JPY.  Right panel: Correlation between hourly logarithmic returns in CHF/JPY and USD/CHF. The correlation are normalized to form Pearson correlation coefficients.

  Vertical bars assigned to the points characterize the statistical precision of measurements. Leader-follower effects manifest themselves in measured correlation coefficients at non-zero time lags significantly in excess of statistical uncertainty.  

When looking for leader-follower effects, pay attention to the order in which the currency pairs are mentioned in the title of the correlation plot. The 14 currency pairs form 14×(14-1)/2 = 91 unique combinations, and for each of these, a correlation plot is prepared. However, due to permutations in the order of the combinations, the total number of intermarket combinations is 14×13 = 182. For each of the two combinations differing only by the ordering of pairs, only a single plot is made. For example, the AUD/JPY and AUD/USD correlation is represented as AUD/JPY being market 1 and AUD/USD being market 2, and this plot is included in the AUD/JPY as well as AUD/USD correlation section.

Time lag between two time series (time series 1 and time series 2) is defined as

td = t1-t2

Obviously, when the time series are renumbered such that 1 becomes 2 and vice versa, td flips sign.

2D 0-lag FX intermarket correlation pattern for AUD/JPY, AUD/USD, CHF/JPY, EUR/AUD, EUR/CHF, EUR/GBP, EUR/JPY, EUR/USD, GBP/CHF, GBP/JPY, GBP/USD, USD/CAD, USD/CHF, USD/JPY 2D 1-lag FX intermarket correlation pattern for AUD/JPY, AUD/USD, CHF/JPY, EUR/AUD, EUR/CHF, EUR/GBP, EUR/JPY, EUR/USD, GBP/CHF, GBP/JPY, GBP/USD, USD/CAD, USD/CHF, USD/JPY

Fig.2.  January 2012. Left (top) panel: The zero-lag correlation heatmap is a 2D arrangement of Pearson correlation coefficients such that any bin in the i-th row and j-th column contains the correlation coefficient between time series i and time series j, with numbers assigned in the following order: 1 -- AUD/JPY, 2 -- AUD/USD, 3 -- CHF/JPY, 4 -- EUR/AUD, 5 -- EUR/CHF, 6 -- EUR/GBP, 7 -- EUR/JPY, 8 -- EUR/USD, 9 -- GBP/CHF, 10 -- GBP/JPY, 11 -- GBP/USD, 12 -- USD/CAD, 13 -- USD/CHF, 14 -- USD/JPY. Right (bottom) panel: The unit-lag correlation heatmap is a 2D arrangement of Pearson correlation coefficients such that any bin in the i-th row and j-th column contains the correlation coefficient between time series i and time series j, with numbers assigned in the same order.

Example: take row 14 (14 along the axis labeled as "FX time series 2"), column 1 (1 along the axis labeled as "FX time series 1") from Fig.2, right panel. 14 is USD/JPY, 1 is AUD/JPY. The color corresponds to the Pearson correlation coefficient for time lag

td = t[AUD/JPY]-t[USD/JPY] = 1

This is the bin with time lag 1 in the correlation plot for AUD/JPY and USD/JPY, labeled AUDJPY_USDJPY and shown in Fig.1. The fact that a negative correlation signal is seen in this bin indicates that AUD/JPY follows USD/JPY in the opposite direction. The fact that it is AUD/JPY who follows is seen from the positive sign of td: the time the follower movement happens in AUD/JPY is greater than when the leader movement happens in USD/JPY.

  Another example: take row 3 (3 along the axis labeled as "FX time series 2"), column 13 (13 along the axis labeled as "FX time series 1") from Fig.2, right panel. 3 is CHF/JPY, 13 is USD/CHF. The time lag is 1 if defined as t[USD/CHF]-t[CHF/JPY], but in the chart, the pair is ordered as CHF/JPY being time series 1, and USD/CHF being time series 2. Therefore this correlation coefficient is found at lag -1 in the CHFJPY_USDCHF correlation plot, shown in Fig.1.  

Monthly correlation analysis reports of the hourly FX time series are found in this section of the site.

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