# Inter-temporal structural stability of stock markets

For my bachelor thesis I am trying to determine structural stability of some stock market in the following way:

• Identify an ARMA model for the whole sample
• Split the sample in two parts, and estimate the ARMA model of step one on both sub samples.
• Use the F test to determine whether the coefficients in the first sub sample differ from the second.

If they do then the markets are not stable.

But here is my problem. The best ARMA model is a (0,0) model. So there are no coefficient to compare with the F test. As far as I know, this makes this method unusable. Is this correct, and if so, is there another way to test stability of returns?

Thank you!

• Stock return autocorrelations tend to be small, which likely why your "best" model includes no lags. If you look closely though you can probably find some statistically significant autocorrelations for some horizons. Even when there is no autocorrelation you could for example test for structural breaks for mean stock return. Not sure what you mean by structural stability though.
– fes
Sep 13, 2020 at 13:27
• You can certainly find structural breaks in variance, I think. Sep 13, 2020 at 13:55
• You seem to be conflating stability of returns (rarely true, hence GARCH modeling) with determining the systemic stability of the market. If the latter is really what you want to do, you would do better to try estimating/determining regimes when markets are (and are not) stable -- and then comparing metrics (like volatility, liquidity measures, ARMA model fits) between those regimes. Perhaps look at Brunnermeier and Pedersen (2009), Gromb and Vayanos (2002,2010), and Boudt, Paulus, and Rosenthal (2017)? Sep 13, 2020 at 14:04
• @fesman I'm afraid there really is no statistically significant autocorrelation. The term 'structural' was not really helpful, indeed. What I am trying to figure out is whether the behaviour of the index returns of certain emerging markets has changed over time. I think I'll go with your suggestion about checking the mean stock returns and noob2 his suggestion about variance. One question about this though: my samples contain around 500 (weekly, so 10 years) observations. Do you think this will be enough for checking stability of the mean and variance? Thanks to both of you!
– JMK
Sep 13, 2020 at 19:16
• 500 weekly observations is a bit on the short side (especially for the mean) but you can still try. Daily observations should be quite easy to get which would help you at least for variance.
– fes
Sep 14, 2020 at 5:31