AUD/USD intraday seasonality overview, 2003-2010 - Variances and correlations

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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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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 )