How Price Discreteness and Stale Trades Affect High-Frequency Returns

Summary

The document explains two sources of unusual patterns in high-frequency price data. First, trades do not occur continuously: during quiet intervals, the last traded price may remain stale while the underlying fair value changes. Returns measured from these nonsynchronous trades can therefore appear serially correlated even when that pattern does not reflect genuine predictability in the underlying price process.

One suggested way to reduce this bias is to calculate returns over disjoint subperiods separated by trades. Second, prices move in discrete tick increments. For liquid securities, many observed changes are only one tick, and rounding a changing fair value to the available tick grid can produce a return distribution with high kurtosis. These mechanisms warn against reading autocorrelation or tail behavior in transaction prices at face value. The exchange gives conceptual explanations and points to prior research, but does not provide detailed derivations or establish that these biases dominate in every market or sampling scheme.

Key ideas

• Nonsynchronous trades can leave stale prices that create apparent serial correlation.
• Returns across disjoint periods separated by trades can reduce nonsynchronous-trading bias.
• Tick-size discreteness can concentrate observed moves in one-tick changes.
• Rounding latent price changes to tick increments can increase measured kurtosis.
• High-frequency return patterns may reflect trading and measurement effects rather than predictable price dynamics.

Tags

# Can you explain me these comments on high frequency data?


# Can you explain me these comments on high frequency data?












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

> data discreetness induces high degree of kurtosis

and

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

Does anyone have any comments that can enlighten my understanding ?

## Answer by hotsource (score 3, accepted)

https://quant.stackexchange.com/a/16940

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.