USD/CAD intraday seasonality overview, 2003-2010

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Written by Forex Automaton   
Thursday, 30 December 2010 15:40
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USD/CAD intraday seasonality overview, 2003-2010
Variances and correlations
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The regime change from mean reversion to trend following is seen to occur daily in USD/CAD. Like in other pairs studied so far, the statistically preferred time to bet on a trend reversal in USD/CAD is the morning hours of the Asia-Pacific trading session. Evidence for that comes from time dependence of autocorrelations of logarithmic returns with 1-hour lag. The hour ending at 17:00 CET (11am ET) favors trend following.

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.

For years 2003 through 2009, the entire yearly data sets are used. For 2010, the data from the beginning of the year to November 1 are used.

Central European time is chosen because it allows one to split the forex week into five 24-hour long non-interrupted trading days.

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.

USD/CAD averaged log return vs CET hour of the day, in 2003, 2004, 2005, 2006 1.1 USD/CAD averaged log return vs CET hour of the day, in 2007, 2008, 2009, 2010 1.2 USD/CAD averaged log return vs CET hour of the day, in 2003-2010. All years aggregated. 1.3 USD/CAD 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 (see time conversion table to other time zones) for USD/CAD. 1.1: Years 2003, 2004, 2005, 2006. 1.2: Years 2007, 2008, 2009, 2010. 1.3: All years added. Vertical bars show estimates for the 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 USD/CAD. There is a considerable variation among the patterns, and like EUR/USD and GBP/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.


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

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

Fig.3. Distribution of time moments when USD/CAD 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.

USD/CAD 1-hour lag autocorrelation of log returns vs CET hour of the day, in 2003, 2004, 2005, 2006 4.1 USD/CAD 1-hour lag autocorrelation of log returns vs CET hour of the day, in 2007, 2008, 2009, 2010 4.2 USD/CAD 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 USD/CAD. 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 manifest 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 00:00-02:00  we indeed see negative autocorrelation values in Fig.4, and the first of them is quite significantly negative. This is very similar to the picture observed in the previous reports for other currency pairs.

USD/CAD behaviour between 15:00 and 19:00 is the most volatile during the day. As positive 1-hour lag correlation values in Fig.4 indicate, year after year there is a tendency to form trends during this time slot (this time slot corresponds to the morning hours in New York). The difficulty lies in the fact that the exact position of the time window when the 1-hour lag correlation is positive varies year after year. In 2009 and 2010, there is no significant positive 1-hour lag correlation magnitude in the morning hours in New York. In the long term integral however, the positive signal at 17:00 (again, the number plotted is the end of the hour) survives the averaging.

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 )