Autocorrelation Tests with Sparse and Irregularly Spaced Returns

Summary

The document asks whether autocorrelation and Ljung–Box or Box–Pierce tests are meaningful for six observed returns recorded at several different time offsets after a trade. The response says that a test can technically be computed with so few observations, but emphasizes that the resulting estimates have very high uncertainty and are unlikely to support reliable inference. A computed statistic should therefore not be mistaken for persuasive evidence of serial dependence.

The answer also flags the irregular spacing of the observations as a separate concern: standard time-series autocorrelation calculations assume observations indexed at regular intervals, so unevenly spaced returns may require an adjustment or a different method. The example and response do not specify such an adjustment, quantify power, or offer a replacement procedure. The central lesson is caution: a short, irregularly sampled sequence is not a sound basis for a strong conclusion about post-trade price behavior.

Key ideas

• Autocorrelation statistics can be computed from a very small sample, but inference will be highly uncertain.
• Irregular observation intervals complicate standard autocorrelation and portmanteau tests.
• Six observations do not provide a dependable basis for concluding that post-trade returns are autocorrelated.
• The document flags the need for an adjustment without specifying a particular method.

Tags

# Does it make sense to interpret autocorrelation and box test on 5 data points?


# Does it make sense to interpret autocorrelation and box test on 5 data points?












I am trying to see if after I trade a stock the price movements at 2, 5, 7, 10, 30 and 60 seconds after exhibit any autocorrelation. Below I have the returns from my trade price to the trade 2,5,7,10 30 and 60 seconds after my trade.

Does it make sense to run and acf test in r to see if there is autocorrelation and the box test OR is 6 data points not enough data to run the test?

Does it also matter that my returns are not evenly spaced apart?

```
r<- c(.2,.3,.3,.5,1,1.1)
acf(r)
Box.test(r, lag = 1, type = c("Box-Pierce", "Ljung-Box"), fitdf = 0)
```

Thank you

## Answer by phdstudent (score 1)

https://quant.stackexchange.com/a/18893

You can do it with 6 data points. However two caveats:

1) With returns no evenly spaced apart you need some adjustments. This topic might help.

2) With only six data points you will get huge standard deviations, so almost sure your statistics will not be significant and you cannot do anything with them.

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