Interpreting a Daily-Lag Spike in Squared-Return Autocorrelation
Summary
The document questions whether a prominent spike in the autocorrelation of squared intraday price changes supports the usual account of volatility clustering. It compares a figure in a highly cited article with a later figure in a book by the same authors, notes that the spike appears in one but not the other, and asks for a reproduction using historical one-minute S&P 500 futures data. An additional plot using a later sample is mentioned, but the author explicitly treats it as inconclusive and questions the fit of a power law.
The response offers a specific interpretation: the spike is associated with overnight returns, and the plotted lag scale means the cited location corresponds to about one trading day. This points to a calendar and sampling effect that can be mistaken for ordinary persistence in squared returns. The exchange does not show the underlying data or a full replication, so the explanation remains a brief interpretation rather than a demonstrated reanalysis. It highlights the need to understand sampling intervals and market closures when interpreting intraday autocorrelation.
Key ideas
- A spike in squared-return autocorrelation near one trading day may reflect overnight returns.
- Autocorrelation plots must be interpreted using the units and sampling interval on their lag axis.
- Differences between published figures motivate checking data handling and reproducing calculations.
- The additional plot described in the discussion is explicitly not treated as reliable evidence.
Tags
Full text
# Are Cont's "stylized facts" based on reliable evidence? # Are Cont's "stylized facts" based on reliable evidence? 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. 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! 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 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 ! ## Answer by XiaoWang (score 1) https://quant.stackexchange.com/a/50621 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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