Measuring the Efficiency of the Intraday Forex Market with a Universal Data Compression Algorithm

The Efficient Market Hypothesis (EMH) states that the current market price fully reflects all available information. The weak form of the EMH considers only past price data and rules out predictions based on the price data only. The prices follow a random walk, where successive changes have zero correlation. Universal coding methods were developed within the context of coding theory to compress a data sequence without any prior assumptions about the statistics of the generating process. The universal coding algorithms - typically used for file compression - constructs a model of the data that will be used for coding it in a less redundant representation. Connection between compressibility and predictability exists in the sense that sequences, which are compressible, are easy to predict and conversely, incompressible sequences are hard to predict. Here we use the context tree algorithm of Rissanen which can be used to compress even relatively short data sets - like the ones available from economic time series. The weak form of the EMH is tested for one year for 12 pairs of international intra-day currency exchange rates. The currencies are described in table 1. The intra-day currency exchange rates were encoded for series of 1,5,10,15,20,25 and 30 minutes to a tri-nary string indicating a {low, stable, high} trend. Statistically significant compression is detected in all the time-series. A simulation of opening and closing positions demonstrated no profit beyond the commission for the intra-day trade. Our conclusion is that though the context tree is a useful tool for forecasting time series, the Forex market is efficient most of the time, and the short periods of inefficiency are not sufficient generating excess profit.