Intraday alternation of trending and mean-reversion in FX

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Written by Forex Automaton   
Wednesday, 23 February 2011 16:13

This post is the first attempt to summarize intra-day seasonality findings from the six major exchange rates involving USD, focused on the hour-scale correlation structures. Taking advantage of the "non-trivial" (non-zero time lag) correlations in forex is complicated since their structure changes during the day, and a residual structure that survives the multi-day averaging is for this reason weaker than what may exist in a stable way at a certain time period during the day. Averaging is necessary to accumulate statistics and let the signals dominate the noise. But in doing that, I contain averaging within temporal classes or "bins", combining bars of the data recorded at the same or close times during different days, months and years of observation. When cyclicity of time is thus taken advantage of, a weak but significant and stable pattern of intra-day alternation between trend-like and mean-reversion behavior emerges.

The report uses hourly data from January 1st, 2003 through January 1st, 2011.

As usual, the quantities I am going to look at are not the actual close prices. Since prices are always positive, they are trivially correlated; this feature is absent in the correlations of the so-called logarithmic returns (or logarithmic increments) which are the ratios of price levels at close to the values they had at the close of the previous hour-long time interval. Here as almost everywhere else on this site, correlations and autocorrelations refer to correlations and autocorrelations in the time series of logarithmic returns.

For intra-day seasonality studies, I choose Central European time because it allows me to split the forex week into five full non-interrupted trading days.

By mean reversion (same as "bipolar disorder") I will mean the tendency of the price time series to form quickly alternating rises and falls, more pronounced than in a fully unpredictable time series of the same volatility. In an intuitive sense, such a time series looks as if a rise during this hour is caused by the previous hour's fall, or this hour's fall is caused by the previous hour's rise, since rises and falls tend to cluster in an alternating fashion. Mathematically, using correlations, a manifestation of this behavior would be the negative autocorrelation of (logarithmic) returns with an hour lag and/or, depending on the character of the phenomenon, other lags.

Mean-reverting markets can be traded algorithmically or intuitively once the characteristic time scale (period of reversion) has been reconstructed or otherwise recognized. On an intuitive level, the trading involves the psychological attitude known as "being a contrarian". Pair trading involves artificial market instruments (pairs) with enhanced mean-reversion properties, compared to those of the ingredients.

Trending markets are the opposite extreme and present a situation psychologically comfortable to many people, where you can bet on the continuation of a trend, once the trend has been recognized. Traders use the mantra "trend is your friend"; moving average techniques are a technical approach which can work in trending markets. Mathematically, trends look like broad positive correlations of (logarithmic) returns.

To summarize, trends manifest themselves in positive autocorrelation magnitudes at non-zero lags, while mean-reversion -- in negative ones. These situations are diametric opposites; you need to know which regime you are in at each hour of the day. In what follows, I take only one such autocorrelation magnitude, namely the one at the one hour lag, and focus on the behavior of that quantity across the forex markets and years of observation.

According to the averaging technique idea already introduced in the introduction, I average the lagged autocorrelation quantity for each hour of the day separately using profile histograms. The resulting histograms are plotted in Fig.1.

Average 1-hour lag autocorrelation as a function of the hour of the day, averaged for 2003-2010, for AUD/USD, EUR/USD, GBP/USD, USD/CAD, USD/CHF, USD/JPY.

Fig.1. Averaged one-hour lag autocorrelations of logarithmic returns vs hour of the day in CE time for the six leading exchange rates of the US dollar.

Fig.1 presents hourly "seasonal" averages of the one-hour lag autocorrelation of logarithmic return in AUD/USD, GBP/USD, EUR/USD, USD/CAD, USD/CHF, USD/JPY. The errorbars assigned to the points represent the estimated precision of the mean for each time bin. One should bear in mind that due to the strongly non-Gaussian nature of the distribution of products of (even logarithmic) returns, the confidence levels associated with these intervals are generally lower than would be expected for a Gaussian distribution.

Despite these caveats, Fig.1 shows a distinctive intra-day pattern, some aspects of which are common to all six currencies. The set of points can be approximated with a single curve, with the exception of AUD/USD during the ealy European afternoon hours. As always in these studies, the hour labeled on the axis is the end hour of the second hourly interval used to construct the return. The trend-like behavior reaches the maximum strength between 15:00 and 17:00 CET (morning in New York). The peak of the mean reversion is European midnight (end of business in New York).

To look at the temporal stability of the effect, I first obtain the net pattern for a year across the six currency pairs. This is done by adding the profile histograms.

Average 1-hour lag autocorrelation of logarithmic returns as a function of the hour of the day, averaged over six leading exchange rates, for 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010

Fig.2. Averaged one-hour lag autocorrelations of logarithmic returns vs hour of the day in CE time. Here the summation is done over the different exchange rates, while different years are preserved as independent measurements.

Fig.2 adds an important temporal dimension to put the Fig.1 data in perspective. 2008, year of the financial panic, and 2009, seem to stand out. However, for much of the hours covered (except the early afternoon CET), the outlier data from 2008 and 2009 do not violate the overall pattern, but on the contrary, amplify it. It looks as if being put under the extreme pressure, the markets chose to stick to the familiar behavior to an extent proportional to that pressure, as far as the correlation regimes are concerned.

It is also interesting that the resulting shape of 2008 is that of AUD/USD -- not too surprising given that the basic theme driving the events was that of de-leveraging, not unlike the (fear of) carry-trade unwinding which drives AUD/USD. No doubt AUD/USD contributed a lot to the overall shape for 2008.

One thing common to all six exchange rates is of course the exposure to the US dollar. It remains to be seen whether similar patterns are found in yen, another popular funding currency, or Swiss franc.

The information presented in this post has immediate and very heavy implications for Heidi, our experimental hour-scale trading system. The problem with Heidi is the systematically negative Pearson correlation coefficient between the predicted and actual logarithmic returns, despite the systematically successful forecasting of the next hour's direction of hourly low and high. The figures illustrate that you simply can not approach the 24 hours of the day with a one-size-fits-all plan of attack (Heidi's current  practice); if you do, you are bound to average the mutually exclusive patterns of mean-reversion and trending. The result to be expected is not unlike that of a stopped watch which shows the right time only twice a day.

The future of Heidi therefore lies with seasonally specialized adaptive learning objects, in addition to scale specialization of such objects which is already part of our algorithms.

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Last Updated ( Sunday, 01 April 2012 14:54 )