Bar Size and Long Memory in Realized Volatility

Summary

The document examines how the sampling interval used to construct realized volatility relates to the estimated fractional differencing parameter d in an ARFIMA(0,d,0) model fitted to log realized volatility. The author reports that d appears to fall as bar size increases and interprets smaller d as indicating shorter memory. They propose that finer bars may retain more intraday trading patterns, strengthening the relationship between current volatility and values from earlier days.

This is an exploratory observation and proposed explanation, not a demonstrated causal result. The plots referenced in the original discussion are not included in the supplied text, and no market, sample, estimation details, or statistical uncertainty are given. A change in d could also reflect how realized volatility is measured at different resolutions, including sampling noise or intraday effects. The suggested explanation therefore needs further empirical checks before it can be treated as a general property of realized volatility or used in forecasting.

Key ideas

• The author reports that estimated ARFIMA fractional differencing d declines as the bar size used for realized volatility increases.
• A smaller d is interpreted in the document as shorter memory in the modeled series.
• The proposed explanation is that finer sampling captures intraday patterns that increase persistence.
• The observation is exploratory, and the supplied text lacks the plots and methodological details needed to assess it.
• Sampling effects and other measurement choices could account for the apparent relationship.

Tags

# Examining the dependence of the fractional difference parameter in ARFIMA(0,d,0) vs bar size for Realized Volatility


# Examining the dependence of the fractional difference parameter in ARFIMA(0,d,0) vs bar size for Realized Volatility












Realized volatility is a long-memory process and so I fitted an ARFIMA(0,d,0) to log(RV15) where RV15 is realized volatility calculated from 15-min bars. I proceeded to examine how changing the bar size from which RV is constructed impacts the $d$ parameter in ARFIMA(0,d,0). Below are the plots. It seems that the parameter $d$ decreases with increasing the bar size (see left figure). Lower $d$ parameter means a "shorter" memory time series (see right figure).

I cannot properly explain why this happens. That is, I cannot sit down and verbalise it to explain it to someone else. And even with my explanation, I'm not sure it is correct.

My explanation is the following. Using higher resolution when calculating RV means more information about intraday trading patterns is summarised in the RV. This increase in information contained in the RV allows the value from 20 days ago to better explain the value today. This also captures patterns that repeat themselves and they increase the correlation whereas the lower resolution does not capture these patterns as well.

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.