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A highly cited article "Empirical properties of asset returns: stylized facts and statistical issues" by R. Cont use the Figure 8. below to illustrate

the well-known phenomenon of volatility clustering: large price variations are more likely to be followed by large price variations.

enter image description here

Note the burst of autocorrelation of $x^2$ (red dotted line) at lag $\approx 85$.

Later on the author publishes even higher cited book "Financial Modelling with Jump Processes" (together with P. Tankov). On the FIGURE 7.3 in the book (shown below) the same autocorrelation of $x^2$ as above is shown. But this time without the burst!

enter image description here

Also I have to admit that I couldn't understand x axis legend for both pictures above.

So it would be great if someone who has access to S&P 500 Index futures intraday 1-minute data for 1991-1995 could calculate autocorrelation function of squared price increments and publish it here!

UPDATE I've quickly prepared a similar graph using data for 1998-2012 kindly provided by @David Addison. In appears that

  • autocorellations are two times higher than in the article and in the book
  • power law (blue line) does not seem to be a very good fit

enter image description here

P.S. I do not claim that above I and David has provided a reliable evidence of anything. Rather it should be considered as an additional justification for the question and request. Let's reproduce the results of Professor Rama Cont !

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  • $\begingroup$ I have index futures data from 1997-2011... not what you're looking for, but may be useful to your broader analysis. $\endgroup$
    – David Addison
    Jul 12, 2017 at 3:04
  • $\begingroup$ @DavidAddison Thanks! I could calculate acf for 1997-2011 and add it to the question as an additional illustration $\endgroup$
    – zer0hedge
    Jul 12, 2017 at 4:54
  • $\begingroup$ No problem. Here's a link that I will temporarily put up for you: the-world-is.com/blog/wp-content/uploads/2017/07/ES.zip $\endgroup$
    – David Addison
    Jul 12, 2017 at 5:02
  • $\begingroup$ @DavidAddison Are the data in EST timezone? $\endgroup$
    – zer0hedge
    Jul 12, 2017 at 7:51
  • $\begingroup$ I'm actually not certain. My apologies. I downloaded the data a while back from my broker, so it's either Western Or Eastern ST. $\endgroup$
    – David Addison
    Jul 12, 2017 at 7:59

1 Answer 1

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The 'burst' in the first figure is just due to overnight returns, so nothing fancy (the unit if you read the axis is T/5 min so 84 corresponds to 84 x 5 min= 7 hours = 1 trading day). There is always a peak at 1-day lag due to overnight returns.

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  • $\begingroup$ In this case it will be autocorrelation of 5 mins at closing with 5 mins at opening, not overnight? $\endgroup$
    – zer0hedge
    Jan 9, 2020 at 9:06

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