GBP/USD intraday seasonality overview, 2003-2010

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Written by Forex Automaton   
Tuesday, 28 December 2010 15:52
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GBP/USD intraday seasonality overview, 2003-2010
Variances and correlations
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This GBP/USD report continues a new series of reports about intra-day "seasonality" effects in FX, gathering facts on the ground for an upgrade of the hour-scale algorithmic forecasting system. From the point of view of this approach and the features it reveals, GBP/USD is somewhat similar to EUR/USD.

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 for the following reason. Forex week begins, roughly speaking (since the volume increase is gradual) on Sunday 5pm and ends Friday 6pm Eastern time. It is convenient to define this week to consist of 5 full days, from 6pm Sunday to 6pm Friday New York time. When it's 6pm in New York, it's midnight in Berlin, Paris, Madrid, Rome, Geneva and Frankfurt. These cities use Central European Time or CET. Therefore, the convenience of using CET is that one gets 5 non-interrupted, full 24-hour long trading days per week. Table 1 is a conversion table for the four time zones including major trading centers of the world.

Tokyo 9 1011 1213 14 15 16 17 18 19 20 21 2223 0 1 2 3 4 5 6 7 8
Central Europe 123456789101112 13141516171819202122230
Greenwich 01234567891011 121314151617181920212223
Eastern US 19202122230123456 789101112131415161718

Table 1. Time zone conversion table. Seasonal time shifts, such as daylight saving time, may complicate the picture if the nations choose to enact them on different days, and are ignored.

To look for seasonality effects in first-order statistics (averages), we average logarithmic returns for each hour of the day separately using profile histograms. The resulting histograms are plotted in Fig.1.

GBP/USD averaged log return vs CET hour of the day, in 2003, 2004, 2005, 2006 1.1 GBP/USD averaged log return vs CET hour of the day, in 2007, 2008, 2009, 2010 1.2 GBP/USD averaged log return vs CET hour of the day, in 2003-2010. All years aggregated. 1.3 GBP/USD averaged log return vs CET hour of the day, in 2003-2010. All years aggregated. Coherent time window. 1.4

Fig.1. Averaged logarithmic return vs hour of the day in CE time for GBP/USD. 1.1: Years 2003, 2004, 2005, 2006. 1.2: Years 2007, 2008, 2009, 2010. 1.3: All years added. Vertical bars show precision of the mean. 1.4: Years 2003-2010, showing the time window of the highly consistent behavior only. 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. Because hourly returns do not have Gaussian distributions, the usual quantitative rules of thumb about confidence intervals and confidence probabilities do not apply here. Nevertheless, stability of the effect in panel 1.4 is hard to deny.

Fig.1 presents hourly "seasonal" averages of the hourly logarithmic return in GBP/USD. There is a considerable variation among the patterns, and like EUR/USD, the 00:00--4:00 slot (ends included, hour quoted indicates the end of the time interval for which the returns are averaged) seems to be the time window where the same pattern of non-zero residual average tends to reproduce itself year after year. Fig.1.3 reveals a non-zero residual pattern surviving after aggregating the yearly data.


GBP/USD variance of log returns vs CET hour of the day, in 2003, 2004, 2005, 2006 2.1 GBP/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 GBP/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 GBP/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 a 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.

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

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

A possible mechanism for a daily extreme to be had in a low volatility regime is for this low 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.

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

Fig.4. 1-hour lag autocorrelation of logarithmic returns vs hour of the day in CE time for GBP/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. 4.3: All years added. Vertical bars show precision of the mean.

In the autocorrelation of returns, trends manifests themselves 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.

In the time window 00:00-03:00 we see two negative autocorrelation values in Fig.4, and one of them is significantly negative. This is very similar to the picture observed in the previous reports for other currency pairs.

These results reveal the nature of non-stationarity in forex time series: the time series are non-stationary not only in the second statistics (volatility variations during the day and auto-correlations with non-zero lags), but also in the first. However, the non-stationarity exhibits a peculiar stationarity within itself: even though there is no invariance of the time series properties with respect to an arbitrary time interval, there seems to be some degree of translation invariance with respect to the 24-hour time interval. This is the main conclusion from Fig.1 and Fig.4, consistent with that drawn from similar studies for EUR/USD, AUD/JPY and USD/JPY.

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