# Data Synchronization

I'm working on market trends. I have daily prices for 33 assets from different markets. I was wondering if there is a way to cancel the effects of different opening/closing times.

I have been told that a moving average over four days would be enough; I think a weekly moving average should improve many thing. As I observe a 50-day moving average to observe market trends, I don't really see the point in doing this first moving average.

Is there any literature about this topic? Are there simple solutions to cancel the effects of markets desynchronization?

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Time scale transformations olsen.ch/fileadmin/Publications/Working_Papers/… If this fits your needs, Olsen has a few more papers on this topic. –  montyhall Apr 2 '13 at 14:52

The conclusion is that a moving average process in the sense of time-series analysis can handle the resulting cross-autocorrelation. This means that in each time-step you have lagged correlations (e.g. Japan today to US yesterday) but only for lag $1$.

In case you want to use e.g. the Hodrick-Prescott-filter in a Kalman filter setting for fitting a trend, this model approach could improve the picture (I can not tell from experience but as an idea ...). For hints on the HP-filter you can start here.

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What is the advantage of Hodrick-Prescott-filter over kalman filter ? Am I supposed to use filter before or after modelising ? –  lmorin Apr 11 '13 at 13:19
The Kalman filter is a general framework and the HP-filter can be described by means of the Kalman filter (pls. look into my link). Concerning before/after modeling: the filter "is" the model. The filter gives you a model for the trend. –  Richard Apr 15 '13 at 8:40
as you decided to take a try with HP filter - it is already implemented in a much better way then usually described in a books, fastest version of HP can be found here quantcode.com/modules/mydownloads/singlefile.php?lid=136 (written in C) and here mql5.com/en/code/143 (written in MQL and also you can see there how this "model" should look like) –  Art Jul 13 at 13:16

Another solution is to convert the daily series to weekly. Alternately, if you have to use the daily data, this paper describes how to construct a synchronized return, which you could presumably adjust it into a synchronized hypothetical price.

In general, the issue is one of missing data, which can quickly get you into some advanced techniques (e.g. generating the missing data in a Gibbs sampling approach). The Kalman Filter approach that Richard mentioned also is popular in the literature. In economics, they use Kalman filters to "Nowcast" in order to handle different publication lags, which is similar to some data not being available from some markets. I would take extra care that the results makes sense.

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The approach in the paper that you reference is indeed very interesting and close to our paper. However, they use a $VAR(1)$ mode, in which auto-correlations do not vanish but just decay. We chose a $VMA(1)$ model as there the autocorrelations vanish after one time step. If autocorrelation comes from non-contemporaneous trading then it should vanish after one day. In practice a $VMA(1)$ and a $VAR(1)$ model will give similar results in most applications. –  Richard Apr 3 '13 at 8:57
I tend to shy away from moving average models and just increase the number of lags in a autoregressive model, but what you're saying makes sense. –  John Apr 3 '13 at 13:38
Just one more and last comment: if you look at the preprint above page 5 formula 1.6 then you see how the regression of returns on lagged returns is represented. This looks at first glance like $VAR(1)$ but when you analyze the residual then this can not be shown to be White Noise, which it should be for $VAR(1)$. –  Richard Apr 4 '13 at 7:20
I don't keep my promise, one more comment: you are right, that the calibration of $VAR(1)$ is more intuitive (it cna be done by a regression) than the calibration of $VMA(1)$. Our experiments in this context gave good results for the calibration of $VMA(1)$ too. –  Richard Apr 4 '13 at 7:41
I've read about the use of a garch process, what do you thik about it ? –  lmorin Apr 11 '13 at 13:43
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If you're asking for the covariance structure, then the simplest asynchronous estimator is that from Hayashi-Yoshida - Corsi-Audrino which avoids any bias from synchronization. There is a wide literature developed on top, from dealing with microstructure noise&autocorrelation to improving efficiency, but the basic form should usually suffice in practice.

VMA&c and filters are surely also feasible, but sometimes overkill, just like classical missing data methods such as expectation maximization.

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