

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 computergenerated and follow a predefined 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 reportsRegularly updated quantitative information about the correlations in foreign exchange time series on various time scales, including lagged correlations (a.k.a. leaderfollower 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 multicurrency 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 notationNotation like EURUSD may be used to mean EUR/USD, and so on for other currency pairs.Time series granularity and the period of measurementTo conduct correlation analysis, two characteristic time scales need to be defined.
Quantities and definitionsThe 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×(141)/2 = 91 unique correlations among the different time series.
Vertical bars assigned to the points characterize the statistical precision of measurements. Leaderfollower effects manifest themselves in measured correlation coefficients at nonzero time lags significantly in excess of statistical uncertainty. When looking for leaderfollower 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×(141)/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 t_{d} = t_{1}t_{2} Obviously, when the time series are renumbered such that 1 becomes 2 and vice versa, t_{d} flips sign.
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 t_{d} = 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 t_{d}: 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. 