USD/JPY intraday seasonality overview, 2003-2010

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Written by Forex Automaton   
Monday, 27 December 2010 17:04
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USD/JPY intraday seasonality overview, 2003-2010
Variances and correlations
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This USD/JPY report continues a new series of reports about intra-day "seasonality" effects in FX, reinforcing the emerging picture of peculiar "stationary" non-stationarity in these time series: 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 in both variance of logarithmic returns (expected), lagged covariance (not-so-well known) and mean logarithmic return (not-so-well known). Like in other time series studied so far, the hourly movements in USD/JPY do not average to zero for every hour of the day.

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.

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

Fig.1. Averaged logarithmic return vs hour of the day in CE time for USD/JPY. 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.

Fig.1 presents hourly "seasonal" averages of the hourly logarithmic return in USD/JPY. There is considerable variation among the patterns, and unlike EUR/USD, one can not pinpoint a time window where the same pattern of non-zero residual average would reproduce itself year after year, being strong and statistically significant each year. Despite this fact, there is a non-zero residual pattern surviving after aggregating the yearly data. The negative log return in the 4:00-6:00 window (ends included, the time quoted labels the end of the hour) survives the summation of the 8 years. The largest contributions, as seen in Fig.1, come from 2008 and 2009. The up-down-up-down pattern of the last four hours of the day resembles very closely that of AUD/JPY.



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