## 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 reportsRegularly 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 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.- 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 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×(14-1)/2 = 91 unique correlations among the different time series.
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 t Obviously, when the time series are renumbered such that 1 becomes 2 and vice versa, t
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 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 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. |