

Introducing CERPI, the correlationbased forex inefficiency index 
Written by Forex Automaton  
Saturday, 10 March 2012 15:39  
Currency Exchange Rate Predictability Index (CERPI) is a measure of market inefficiency with a specified time frame (time scale) and measurement interval. For quantities we report regularly, measurement interval is the same as period of measurement. The quantities reported in the Forex Correlation Analysis Reports 1H.1M section of the site are measured monthly at the end of a month and include the whole month of data. This article defines the way CERPI is constructed. ForexAutomaton follows the convention whereby time scale and period of measurement enter the name of the quantity being reported in the time scale.time interval format. For example, quantities reported in the Forex Correlation Analysis Reports 1H.1M are 1H.1M quantities, having time scale of one hour (1H) and period of measurement one month (1M). CERPI is constructed from lagged autocorrelation and intermarket correlation coefficients among 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. The lag equals one unit of time, or the chosen time scale (hour in the 1H.1M case). The 14 currency pairs form 14×(141)/2 = 91 unique intermarket combinations. However, due to permutations in the order of the combinations, the total number of intermarket combinations is 14×13 = 182. The permutations reveal new information since the correlation coefficient at positive time lag of one timescale unit among time series A and B does not need to be the same as the negative one timescale unit lag correlation coefficient of the same time series. To these 182 quantities, 14 onehour lag autocorrelation coefficients are added to characterize selfpredictability of the time series. In constructing CERPI, as elsewhere in the ForexAutomaton project, logarithmic returns rather than actual price quotes are used. CERPI is defined as the average of the 196 abovedescribed coefficients, each of which is taken by modulus or absolute value. Here is the general formula: CERPI = Sum_{i,j}C(1x_{i},x_{j}) /Sum_{i,j} 1 = Sum_{i,j} P[x_{i}(t),x_{j}(t+1)]_{over an interval of t}/Sum_{i,j}1, where P[x_{i}(t),x_{j}(t+1)]_{over an interval of t} is the Pearson correlation coefficient of the two time series, taken with a unit lag and averaged over the time interval of measurement. To the extent efficient markets are understood as lacking memory, CERPI is a measure of market inefficiency in the 14 markets on a particular time scale. An important caveat is that as any random quantity, CERPI is subject to fluctuations. Moreover, while deviation of CERPI from zero measures the degree of predictability, a perfectly random market will usually have nonzero CERPI. The exact magnitude of this CERPI on average will depend on how the perfectly random market is modeled. Therefore, while CERPI itself is relatively easy to measure, its interpretation is difficult because there is no modelindependent reference ("benchmark"). 