comparing volatility and correlation over time

I'm trying to figure out if some emerging markets change over time.

• First of all I am going to check for changes in volatility. What would be a good method to do this. And do you suggest comparing the first half of the time series with the second or comparing the first 1/3 with the last 1/3.
• Secondly, for the correlation. I would like to check if the correlation between one emerging market and the SPX or FTSE100 changes over time, because the correlation should increase as the market 'emerges' and integrates with the emerged markets. Here as well, I wonder whether I should use halves or thirds.

I'm trying to figure out what would be a good method to test this. Do you have any suggestions?

• Why don’t you use a rolling window for each? Oct 5, 2020 at 11:40
• Maybe use a multivariate GARCH model for this and estimate the model using a rolling window. A nice summary of multivariate GARCH models is given in Bauwens, L., Laurent, S., and Rombouts, J.V.K. (2006), Multivariate GARCH models: A Survey. Journal of Applied Econometrics 21: 79-109. Aug 2, 2021 at 13:29

This depends on your objectives, but for a cursory examination look at the changes of volatility and correlation over time as suggested by @SachaTheBrave. The rolling (or sliding) window is quite helpful in locating the intervals of particular interest.

Here's an example which shows 1-day returns for three ETFs (SPY, EEM, and EWZ) and a 1-month sliding standard deviation of the returns:

SELECT symbol, time, daily_return, stddev(daily_return) as volatility
FROM (
SELECT symbol, time, close, close/LAG(close)-1 AS daily_return
FROM atsd_session_summary
WHERE symbol = 'SPY.US'
AND datetime BETWEEN '2020-01-01' AND current_day
)
WITH ROW_NUMBER(symbol ORDER BY time) BETWEEN 1 MONTH PRECEDING AND CURRENT ROW


This type of sliding window (preceding-to-current) is not centered, with the volatility visually lagging the deviations observed in the 1-day return series. Centered windows are possible but used less often.

"First of all I am going to check for changes in volatility. What would be a good method to do this"

As mentioned in a response to a different question, there are a number of academic papers that use non-parametric tests for determining changes in variance/volatility in financial time series. Whether or not these are "good methods" depends on how you define "good" as they have some obvious drawbacks.