Testing Differences Between Overlapping Volatility Series

Summary

The document asks how to compare daily five-day volatility estimates for two countries’ benchmark government bonds. Because both series use rolling windows, adjacent observations share most of their underlying price data and are serially dependent. Simply treating each day as an independent observation can therefore overstate the evidence for a difference. Sampling weekly may reduce overlap, but does not by itself establish independence or solve every inference problem.

The discussion raises a paired comparison: both countries are observed on the same dates, so a test should account for that pairing and for dependence over time. It does not provide a worked test or empirical results. The volatility measure is defined from standard deviations of daily log price changes, while the question notes that the countries may have different currencies. It also asks whether close, open, high, or low prices are preferable; the document offers no recommendation. Conclusions depend on the precise volatility construction, the sampling scheme, and suitable treatment of serial dependence.

Key ideas

• Rolling five-day volatility estimates overlap across adjacent dates, creating serial dependence.
• A comparison should use the matched observations for both countries and account for time dependence.
• Weekly sampling can reduce shared observations but does not guarantee independent data.
• The document poses questions about price reference and cross-currency comparability without resolving them.

Tags

# For each day I have volatility for country A and B. How to test if volatilities are different?


# For each day I have volatility for country A and B. How to test if volatilities are different?












I have a dataset with 10Y benchmark government bond volatilities of two countries. So, my data looks like this:

Date, Volatility5day_A, Volatility5day_B

The volatility measure itself is from Bloomberg with the following definition: "Measure of risk of price moves for a security calculated from the standard deviation of day to day logarithmic historical price changes." That is, the way I understand it, two countries can have different currencies.

I want to test if the volatility of country A is different from volatility of country B. What would be the best way to do that?

There might be a problem with overlapping. For example, today, say, on day t, the volatility is calculated from prices on days t-1, t-2, t-3, t-4, t-5. Tomorrow, on day t+1, the volatility will be calculated from prices on days t, t-1, t-2, t-3, t-4. Hence, there is a lot of overlap - does it make sense to have a dataset with daily data, or would it make more sense to have weekly data (e.g. for every Wednesday) - then there will be no overlap?

Finally, this volatility can be measured relative to close price, open price, high price or low price. Is any of these options better than the others or more common to use?

But again, the main question is - with this data, how can I test if volatility of country A is different from volatility of country B?

Thank you in advance! And have a great day!

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