AUD/USD intraday seasonality overview, 2003-2010

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Written by Forex Automaton   
Monday, 10 January 2011 17:24
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AUD/USD intraday seasonality overview, 2003-2010
Variances and correlations
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A notable stable effect on the hour scale in AUD/USD is mean-reversion dominance during the morning hours of the Asia-Pacific trading session. Qualitatively this is common to all exchange rates studied in this set of reports so far, but quantitatively, the 1-hour negative autocorrelation is very strong in AUD/USD. The pattern of residual non-zero average hourly returns in AUD/USD in 2003-2010 is similar to AUD/JPY.

The report uses hourly data from January 1st, 2003 through December 7, 2010.

As always, the quantities we are going to look at are not the actual low, high and close. 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 (low, high, close) to the values they had during the previous hour-long time interval.

Central European time is chosen because it allows one to split the forex week into 5 non-interrupted full trading days.

Seasonality effects in first-order statistics (means) are straightforward to utilize in trading, therefore one could argue that such effects are not likely to be found. Nevertheless, sometimes such effects are visible and significant. To look for them, we average logarithmic returns for each hour of the day separately using profile histograms. The resulting histograms are plotted in Fig.1.

AUD/USD averaged log return vs CET hour of the day, in 2003, 2004, 2005, 2006 1.1 AUD/USD averaged log return vs CET hour of the day, in 2007, 2008, 2009, 2010 1.2 AUD/USD averaged log return vs CET hour of the day, sum over 2003-2010 1.3

Fig.1. Averaged logarithmic return vs hour of the day in CE time (see time conversion table for other time zones) for AUD/USD. 1.1: Years 2003, 2004, 2005, 2006. 1.2: Years 2007, 2008, 2009, 2010. 1.3: All years added. Vertical bars indicate RMS precision of the mean.

Fig.1 presents hourly "seasonal" averages of the hourly logarithmic return in AUD/USD. The log return behavior that takes place in a relatively low-liquidity market during the "forex night" between 19:00 and 3:00 very much resembles what has been seen in AUD/JPY. During the "forex day" between 3:00 and 19:00 CET, AUD/USD predominantly moves upward. The hourly averages can be as high as 2 pips in either direction.

AUD/USD also seems to be taking a "lunch break" during the hour finishing at 12:00. During this "lunch break", AUD/USD moves down. This is a multi-year effect. This effect is stronger in AUD/USD than in AUD/JPY.


AUD/USD variance of log returns vs CET hour of the day, in 2003, 2004, 2005, 2006 2.1 AUD/USD variance of log returns vs CET hour of the day, in 2007, 2008, 2009, 2010 2.2

Fig.2. Hour-scale variance of logarithmic returns vs hour of the day in CE time for AUD/USD. 2.1: Years 2003, 2004, 2005, 2006. 2.2: Years 2007, 2008, 2009, 2010. Hatched bands in the plots are twice as wide as the measurement's precision of the mean. The mean is the middle of the band. European trading in AUD/USD has been gaining volume progressively during these eight years, as the comparison of the relative magnitude of the European and US volatility peaks indicates.

Daily variations in volatility can be studied in at least two different, but related ways: first, directly by calculating variance of logarithmic returns (Fig.2) and second, by observing probabilities of establishing daily extremes of price (low and high) during particular hours of the day (Fig.3). If the price evolution is random walk, it's hard to think of a reason why these two approaches would yield different results, provided that the intra-day variations of volatility are taken into account: the larger volatility is during a particular hour, the more likely it is that a daily extreme will be recorded during that hour. And since in hypothetic efficient markets, all information is discounted instantly, there is, hypothetically, nothing more to it than just the volatility.

A note added on January 14, 2011: one should be careful not to over-interpret the fact that the extremes of the daily range seem relatively more likely to be achieved in the first and last hours of trading. The same effect has been seen in random walk data.

AUD/USD distribution of time moments when daily extremes are achieved

Fig.3. Distribution of time moments when AUD/USD daily high and low are achieved, 2003-2009.

A possible mechanism for a daily extreme to be had in low volatility regime is for this volatility to be of a mean-reverting nature, rather than purely random. I hypothesize that the mean reversion dynamics on an hour scale may result in the market making a change in direction for the day during those hours when the mean-reversion dominates.  The transitions between mean-reversion and trend-following regimes could be seen in the magnitude of autocorrelations at non-zero lags, in particular, one-hour lag. This magnitude as a function of hour is presented in Fig.4.

AUD/USD 1-hour lag autocorrelation of log returns vs CET hour of the day, in 2003, 2004, 2005, 2006 4.1 AUD/USD 1-hour lag autocorrelation of log returns vs CET hour of the day, in 2007, 2008, 2009, 2010 4.2 AUD/USD 1-hour lag autocorrelation of log returns vs CET hour of the day, sum of years 2003-2010 4.3

Fig.4. 1-hour lag autocorrelation of logarithmic returns vs hour of the day in CE time for AUD/USD. Every hour's candle is correlated with two adjacent ones. 4.1: Years 2003, 2004, 2005, 2006. 4.2: Years 2007, 2008, 2009, 2010. Hatched bands in the plots are twice as wide as the measurement's precision of the mean. The mean is the middle of the band.

In the autocorrelation of returns, trend manifests itself in positive autocorrelation magnitudes at non-zero lags, while mean-reversion -- in negative ones. The two effects can coexist, if the range of non-zero lags with non-zero correlation signals is broad enough for that. Fig.4 looks only at one-hour lag.

As Fig.4 reveals, AUD/USD was in trend-following regime during American trading activity peak, 15:00-19:00 CET on the plot, in 2003-2006. The effect is no longer there in 2007-2010.

In the time window where, hypothetically, mean-reversion was required to explain the difference between Fig.2 and Fig.3, we indeed see mostly negative autocorrelation values in Fig.4.

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Last Updated ( Thursday, 10 February 2011 09:46 )