I was reading some slides on high frequency data and i came across these statements:

data discreetness induces high degree of kurtosis


Non synchronous trading and risk premium are sources (spurious) of serial correlation

Does anyone have any comments that can enlighten my understanding ?

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    $\begingroup$ What are the slides you're talking about? Are they available somewhere? What is it in the statements that you don't understand? Is it that you don't understand or don't agree? $\endgroup$ – SRKX Mar 12 '15 at 5:46
  • $\begingroup$ The rest of the slides talks about Market Microstructure and high frequency data. These statements have been made without justification and i can't really think of any reason why they could be true. i can share the slides with you but i am sure it won't be of any help as the rest of the course is not talking about that. $\endgroup$ – Nour Mar 14 '15 at 22:11
  • $\begingroup$ It would always be good to include them in the question as a reference. Context might help us answer your question, for example. $\endgroup$ – SRKX Mar 16 '15 at 1:10

1) Spurious autocorrelation of non-synchronous trading data was analyzed in this article: http://www.amazon.com/An-econometric-analysis-nonsynchronous-trading/dp/1245789457

During some time intervals a lot of trades occur and during some nothing happens(so prices are stale). So serial correlation of traded prices may be present but this may be due to stale prices.

See this paper for an example when prices are generated by a stochastic drift and measured with non-synchronous traded prices: http://eml.berkeley.edu/~anderson/Sources-042212.pdf They also proposed a way to compute autocorrelation without this bias: eliminate NT by computing returns over disjoint return subperiods, separated by a trade.

2) Discreteness introduces large kurtosis since most of the price moves are one tick up/down for liquid securities. If the "fair" price has to move 1.6 ticks away, due to discreteness it has to move 2 ticks.

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    $\begingroup$ Would have been good to have a supporting research paper for your first point. It's not really clear to me that the fact that sometimes there are more trades than other induces serial correlation. Regarding your second statement, isn't the fact that a fair price of 1.4 tick away would have to move only 1 tick offsetting the 1.6 case? $\endgroup$ – SRKX Mar 12 '15 at 5:49
  • $\begingroup$ i don't understand why a "large trade numbers in a short time horizon." will induce a serial correlation?? is your explanation for the kurtosis that discretness (due to the minimum tick move) in space make prices move more than what a normal distribution imply? $\endgroup$ – Nour Mar 14 '15 at 22:14
  • $\begingroup$ @SRKX I think if the fair price has to move 1.4 ticks away, as a result of discreteness, it also has to move 2 ticks. It only rounds up. The trade is likely not to happen if it moves only 1 tick away while the fair price is more than 1 tick. $\endgroup$ – hotsource Mar 16 '15 at 3:57
  • $\begingroup$ @Nour I rephrased the first point and added some references. For the second point please see the comment above. $\endgroup$ – hotsource Mar 16 '15 at 3:57

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