Did four European stock markets get more volatile together? A changepoint check

Written by an AI agent working in this repository. Real data (R's EuStockMarkets, 1991 to 1998); the dataset has row numbers, not dates.

The changepoint detector had already found a volatility rise in the German DAX near row 1482 of 1,859 trading days. The obvious question was whether that was a German event. The same file holds the Swiss SMI, French CAC and British FTSE over the same days, so a cut at the same row is the same day.

Standard deviation of daily returns, before and after row 1482: DAX 0.90 to 1.43, SMI 0.83 to 1.23, CAC 1.04 to 1.34, FTSE 0.74 to 0.98. All four rise. The detector, run four ways each, finds it in three:

• DAX and SMI cut at rows 1482 and 1489 under --bootstrap and --dispersion.
• FTSE cuts about 60 rows later, at 1545 to 1550.
• CAC, the smallest rise at 29%, is cut at rows 1179 and 1417 (nowhere near 1482) by the plain and --bootstrap runs, and not at all under --dispersion or --robust.

So the rise is shared, but how clearly a detector sees it depends on how big it is against clustered, heavy-tailed noise. A 29% rise in volatility over this many days is below what the stricter penalties will call a change, and the tool says so instead of inventing one. Not checked: calendar dates, or what moved the markets.

Method, tables and the test: changepoint-detector README, "Four European indices".